{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60956,"title":"P(girl likes you | she smiled at you)","description":"Compute the probability\r\n\r\n\r\n\r\nGiven the input probabilities\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 401.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 200.933px; transform-origin: 408px 200.933px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.4833px 8px; transform-origin: 80.4833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCompute the probability\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjcAAAAoCAYAAAACN9vJAAAV80lEQVR4Xu2dW8i1W1XHt/dKmldKWJQXSlmJlqIYKKUQhVRYaSIfGJZCSKhRIbIRUdEkwgs1IkTsCBViBKkYJEmZkYckL1J2EnqlFnaf88e3/u3/HszTc1rvWu87Hpi837fW88xnjv8cc5znXI96IK9EIBFIBBKBRCARSARuEQKPukW0JCmJQCKQCCQCiUAikAg8kMZNMkEikAhcGwK/VQb8w6X9wrUNPMebCCQC50EgjZvz4JxvSQQSgf0QeEfp6sdKe/Z+XWZPiUAicJsQSOPmOmcTz/V9pX3jOoefo04ENiGQxs0m+PLhRODqEPjVMuI/X6Lz0ri5ujl+4M/KkP+utPde39BzxInALgikcbMLjNlJInA1CPxIGem7S/u10v55ZtRp3MygdDn3YNh8prS3Xc6QuiN5Yfn2e0t7+umuX9lp3N9X+qH9eGk/VNobZxk+vP87y/9/orRvlvaRncaW3RyPwCUbNwjhL5WWUdX1fLDX+l47At7/zNKQt3ldDgKsrQ+V9uIZeT8yblBOryuNv73rn04vzVTJwyjtjd25BDrveUNphADXFmwiHDBkXl7aE06Q/P7ps61LhfDk80v7eevo8eXfUZm06ICmXy/t+0t79KmPV5e/GQnbOjPne/5ca2GGIvgR4x0j+1mnB15U/qax3EYP+fCJ0h5T2gtKc098dn3PzM3sPZLV32Fz+KNhXLN95X3HIsBc/V5pz63I/Ee8eWTc6GaMlled/vO/5e/PnRYvnu9vloYy1JVM8cjJ3QM7JvRvS3tyaXiFR17/Z51vFdIYEn966u8Xy989PaF/L/09pbQvlvbUCiAjOhiLDKRz4HrknN21vi/JuAF7KWsMeeTjd5eWkZs2V8rx4A4c41ph+Gh9H8HzeufXSuc/kHN4BMS79IkufKi0biZg1rgZMaN/z+LGIs/rPgJ7YPePpZ//LG1tJGXJXEjpYzQMreNBx27Y1aIrS8bl92JUf/30QSsiNKIDTPG096BzLR353DoELs24gYqvloZxQ8QGpyCvNgKkFz5eGpHTWtR0Zn0fga9kQs7hEeju1yfOxH+c1lkzQjpr3GjSGd47S/uNME69TB/v7aXvB8v5e9qK3TmjNkIH4TNVtDWA8yjvazYi1KPjWyfhule67PycdXffeGnGjcu/3y7Tci01cTfJQRgwjyutFomeXd97j1/R3ktMUyPLwCvTnfdnHb36PycDp8oHs8bNKMRP535PLvCH4d6KHSG4J5VWS73svbj37M+9r5pBvOVdigitTQEgKD51GkAa4ltm4maevTTjhqMZ3nqCIlOc23li6/peMwI3qC5tDpGl/1baB0uLgYU1tN6GZ6jNek9pzbmaMW4UOQCQnjJxJZ4K4z77bMVOBsI1RhdcWGyt3YmLURGhVr5+tHhdGe2ZLhu9N7/fB4FLM25wQFjrmeLcZ363ru81o5BBdWlziA74h9KoL8x61odnVtHSZiBlxrjxuolWLjKmpXIS7k/CVuxkIJzLWERAP6O0PY62P8r7mokIjehwZXRtEbE1gvumnmGu2FLL9enS9iqyvTTjRinOLTsMb2qOzv1ebbNGzny5tLhLcWZ9HzFm1Uxd0hwi//+gNGqT7lKRs1JwHNHRK49g3X2ytGqN24xxIysahmpZSbFo9id3FGRHMPK5+tyKnXBdGvlAgBC+5Ih6XWxzJKz5sdMH5LqV78YQ4V68A67ovWhrN32w5ZVt1OyQQzCxAH+3NIopPcJ0lPfViwiN6BAWijIqXSb6hBe53D8s7aMNPsZ4emVp7IohZUgBPSHSWsiYhfqW0p5T2hdKA8PPlfaDpT1Y2tYdZIyF3YvMC30zhzVjWPPRiwIy1teX9thTX8wzY35TaZ7rRwGxU4EaADADgw+fPit//v86qqD8aOPGjwvQnP19oeplpcWdUK0UJ9FBDhxjXcxEA5bwlGO85N8zdEEPZ1NhfGhu31z+zVpn3qknAgcUbuQl5oV6Fb6LukLbrVkHvSMYlkR8Jeec9zFOGEPLkNYO358u97DO4V2OhjhqV6fPjzDgnbxbcob3s7lBct5339Xmd2vaLMo73l2TCx7NajmB4Mmu03uG53eVfyMP3x7mAfo5m4w1ROO9MXK+pJicuhuwfGINpJFxMxOR8cVN2iqeW1B77zk+85TQlvetrR/aAztFGEbz5PSRi0Rpc/1yaVKevvWZ7yIzO17Re9GhWn7mEQuMA/BgYl3aln2k9zWKCPXoYJz+fTQa8d4+X9prSqsVOkLX35wWJXzBWLi0cyv2x/3sckOY67ujwszQ9Rend9W2x7uhXRMozCNCSnShHHz8cR3w3Z+c8ASDmgEub3ht+tBY6xH/PNK4EX/gKT/vxAfa3YOnGLcIu2MHrlzwCNdnS9MRGq26s6U81cJk9PksXdCKYcN4ZYSILtIjMszlCPl3KGsZ2IynlvL1DRY1JT1a36JT9yGr4E3Wq3i8hbVk43+Ve19RGlEB11+tMY+wHX3va8XXV9SdPcP5iCJn5Ppfl+Zz6UahOyc1h0mOLfMuPMFCa6IWbXL5W5MLqqWhn5FTL16q6seR0vQXxXobJuYlpemMGwi5V9qlVHPftHGzB3bdyausKKc5LgYXwrV59/G2FpL6QHk+WBoRGxQAxZQoRgmVJd7XSDDE70cRoREdoiHys05/ZkHXvL7W9lU3YuNibNX2aIx71/v4HMfUsJQoyse3+OvUTyIMNUPeBVzkGxnftVo854G9C8qPNG5aKUv4g2hb9GC1RhHURKwxAD5QGrgR2WLLKlcNgzU8tXS96P6ldLlh6nQRuXHlxfpHQYpmnXvWqs9Uv61o1mh9u3MQnTD1XcO6V1OjSO7eRjjY+3hr60vvrpV8nKNQ3XVGb/1HQ9Tx/KlCpzuDPefWDbraPGn+ZzaLiA+rkayRcePePsYLAtAvGBRLnt86gtH2yqmvXcCX9Nwe2C01biTAahbzKEXg420pXT8H4mkF7Hul1YxZvWvvPLEvmlZEbURHTXgy3n8trXVKsUcwYsRLtEq5+Rpw4eQGowTe1nOEIr+7oVUTHAgDvEMMDy7u5+c88NBbtQZuMEXvrReZ8XkYeWBL1+05jBvG5EITzH7WsNOYPcVJeoRojdKTPv8Ru7U8tRQr3S/ZMENXVE6kcDBetMXd5cB/l8+JTopmN/bi4XzOn7U0yMz6jsak1puMaZQiNYOubDUPte/AI6ap12Icn3PDppUO1rtr8swN0r1lhY+1t44xfuKJwB5da2VqRFeMIvciM84fM4Zmt2xjZNyoUA4gjgiL7cVEl9jPHtgtNW7EUDVFJaXeMjjco2rlV51hqUFonRCpvloF6GvnyxdGq2i9R0cU2uSESSHEmpI4Ps1DFI4aj5/a7c/6Yp3xRNbi4s/1PF++e21pMkhbdHl/LeOmd7bL0XQfadw4j40ErEenWHPUKr20NClcNyiiw7CWp9byyFq64JWHwlqXbAMfUhJOc09Z+xhqaY7R+m7xokfAarU+zENLh3nkYu+NMD1nk/H4u2vRB2HZq5Nbyw/+XC86y3fMsYxXH3NvXC3jRk5PTQ+5QzQT7V1t3MRc5NYipj0m4Vr62Au7tcZNZLqRxzQKFYK7C/KWB8R9Rx5o1lsYvHtEh9OAsc4CQlBXC9JOzObPCFdoVCrOc/41/nTBMVKWe/C3KwBfswglCkNJMaB8XZH0hFSrRqKniFxIHUHzkcYNc+D1ST0h63PrNTqaRzcCPIqxlafW8slSuljn1KfENOanTgOIcmBkKPTSmHTZW98eZVSUlGdIg7GWa4XvPpe1yCrf9+pD1uLMc6N0D/f0UmX+/NG7ZVvlDDiDnK+j2jPGLOexpwN6dY8txzfWqM5Ee4VfNdPQi9x4SLX1+z0zk6+dFdo5wDMohL88MXOtD+3aIMdNhIALr2ivHSYz495yz17YabGPImwaq4RHjNx4eDPmR3nWx9tiKhfkPWU48r624DqKCI3ocKXr4+gJD1fu4Epah7oV+JJtmqOTnD00zTuP9sJaQhE6qJECAy5XdD3HxT0wV3ItRRSF1NqC/B6fHG3ceCSAcbT4wzGM9/QM7a08tXYNzdKldcZ7enVkcW5HhkLL2BM9vfXtRrsiRuyUoSyipUvciGzx4UimrMVac9yKlHtashZpF73nivjWokSMAVmnCH2MVCq9HTHyufKMT8/xjWUcM7/t1XX+e0rTF+BMiGjEBK5gW2kP+tCkR48BwAAq5lNb773JguK9sOuG3SqEu/AixEremTz5q0pDIPzS6bP46Mij4v4Zi537RtGVEZ+0vp+JCI3o8JQV6RmFq3vpMy82JH3lW+hnaYlKZe/wdxxHFFQxauPpud42ZTdUo3IQllEwo/AJY7PNk+sIWo82bhi30177vbxYH6CImObCDe2IwR48Nct78b4ldNXWRU9pey1OPHtkFFUdrW9P43H0wegMFOhu1RkJk1bEYi22es5pmallq5V8jAqrt44xPi98fcdrjNq4g9srU5FsiIad816sZ9N2eMY1W87AmDG+qvZEy7hx4cfLZkJEI7BF8MhQklCITAEjvr+0XgrBx3BTxs2e2ImGJfVOWNNEFAjTclHsh2fTOrOFe+RRtZjKF+uI8Y7yhGYiQj06asLTjdCaEp7NL9cUCPzrxcXuzYzWwGgtjb6Pgoo5QXgoatMLG3vfErC1c4+0C8h5ExqJbBFl5R17F5RrbEcYN8gdFczqPc4fUQY6P9bWZ6sYdC1Pjea89f1Sutwoq0WsesW3vd9m6hl7jH20vls1HD1c3JmpFeTORi+XYj/iDU+x0XfvrJejZYWvKe18ZjzvKY1ica+rbKWoHZ+Y+vdNGnJ8XZ4o9UXKnHdyzUZ74YmW8fhAy7iJ9RVx//3Sye5tl419eWjTDRltPb/039bYGzsU9h8HJmvhr0XVnPDKg+5RiamYg7eXJuU8SveoW59nCXzG9PTJ8ff4Ki4M7qUYWNGoER014VmrfaBfFBARGuhRdGeUivNFjBB4f2n+mRu9R6emPKSNwGAXj3vSMwpWc14rlq55YPSpXRU620eGMPdzGq0KmZfKj5qM4IC5uBtnS78Iypiec/6Iil782EobyNCWchIGjHENT62lbSldvciM4xGdAecpcCSygrEo5RiLa9kmz/ERMihH63vGuGF87sT1nnFnQ8oWjKnh2apjvO/aLjmOC1B0U+9G1nB4Ijg4zjKq9flaPhg95/OHHqCMJKaG3Lip1bnIUHlCeRYdhA5wB68W7ZWshB/eehqkZx1am1Yk75uOf8u48fDTyFMfgcb3EoYzntyo+HXmfTd5z97YwdQUdM1ErOIOrRg9qOHihosO5vuZcuNLjTGjYGpt+Y9KD2Z/d2kxZL9mfuLCABeOIJABMaKj5Ul7fYGEsodjhWlNicGrf1Tah0pzrx+hWls3ErZ7REJ7GLqgahX+ia6aIaw0Gu8gBRCNEvG4Qtg6K+fFJ57xqA5GjRcyr5n7+MzekRvh1dppU5v7XoTSDW0ENYLbMVjDU2twW0qXG+A1vqh53hqXFLqUNY6H13g5v6GQUPC+c2+0vj3FFNcP42b9ETF0heqpdHfQkRXwKidw6xiE2pjWYM4zrXSu6u/YVs+hd08pDZx/5yRDGBM1fFpf0pc4KC7r1o5r9JzkE/fVonZRxsaDTsUfNcPGeUt9K5KMMRd5K/JPTQYwZ83AS8248UInOlwSBWiBJ8acNZScOc4VlhtN/Mz3R2AnATWjEL0oS+Nlgej49BoN7mUw1xRtx6Lj3hZz79P7kvWvBTuDX+8er1MgMsDlBW0jOlrK3A0BsMKjIgIho8n7FZYo7FeWhtGJ8RbTGTUjxtOt0aPZik18fua8EBdU7oWBBycdU/Pmysff4R4cPIPxKiPI8aTOi6JP322xB61HGTfRiJHcikZPLUrodDm24IMA9nq3NTy1BjfNxSxdtYiBv7fmeet7YcW7SInXDH7uxfjh8nNz+P9ofccyA+bkX0rjOP+Xl/bh0sC9lQrmvdxDxI86DWScjHCt+zimNZjzTNQDRGq5XlYa0Qnkhejl3Vz3SpMT4fVFnyyfkx5qFe+uHWPtOaXpWnraIzMefeZzDDAd5OpRf72nJhc+Ub6ULHSa4R/Oi2pFbegTXuT5Ji7RuGHRwSiElfyC2HcZ+EsBlWJZUjviivoaDJyjsANrJh6F3mNwpQVQzKSBOHjL57FVOOr5X+b5NaW5Rd7LoUY+oC8YjvfS1xtLG+0mmuUlT1diUODduCDr0eHKqMaDGNP6yQoJHx8X398rTUWyKG2EN4orei+aBwQp6SCUO5d+26u28GcxWHIfwpNx9qJmzO2DpeFBci8Xxt1fnWjrReiEFx4Wnqfm2QUgfY7OEFpCk+7d27ihPx3A5785FA1dvX/kwaruTVEBFHHkkyU8tQYjnllKl2RuLcI+WkMebag5U/59zSEYrW/oYW29rrTnlAa2yLTerkVFdDAq9OOT/L6e1qA73Vv0W21+JAdYWxh8cZ303i2seA55FGXdWn4YPYeeIZrV27QjQwa5gl7/yqlTjJHe7lGe00/XMG/oKc8saE1BM4ZST07KAetuLprdYjwCpfe9L4qlZ+W4gbPEMNoy3kt8Voq7liJgvDA/Czh+DxMgaKSUj671uETs7uKYxC+zOwuvDaO9jZtroz/HmwgcgQDREN94cMQ79uiTCBPOY7c26hzGjedinzqgDKEcPRyFq/AC9ywg3APkc/aBp0eaIFb9K4XXqzD3epPRHJyTpnzX/ggor/9g6Vo57f3fcrM9pnFzs/jn228fAsiKuDvqEqmcXvvnMG6Ux2tFDRDG/Lo01fXUMcTUi9IihEpnimovcUL2GhMTS/7eMZLx1zuITvnO2Zqnvcab/ZwfAYSU/9bP+Udw/BunBdzxQ8k3JAJXjwAOctxEcolEKdU39TtbRxs3XtjYKoglpUJumyJN8viPCajKuEnFfB8YGPH5ZuAoddeL3Ch6dvQx3pe4IG7zmHQ8wscKkawPRWqOLli+aUzTuLnpGcj3XysC6GS2u6Nv2TShjEDt5PpLohFZt2jn7dHGTe08DAdMRURsl3xJaRwiFIuHVeTU+vXRS5qAc40FC/bTpVHw6aff1gxIMMbwqRXKnmu8+Z5jEPBdS0Q2fffBMW+8jF7haeqJzrGD5DIozlEkAvsgEHfqEVi4dMMGyrVdfBqFI40b34nBgBC+VKpzsXNEu3lUS0NdCBXXpF24yP99z+mv78aYJu4O3UitEsVV7Pig2l2nE8O4D5U28xtIdwiuW0Oqdnmxa6G33f/WEJyEJAKJwCYEdCYVGZLRrqRNL7rph480bm6atnx/IpAIJAKJQCKQCNxBBNK4uYOTniQnAolAIpAIJAK3GYE0bm7z7CZtiUAikAgkAonAHUQgjZs7OOlJciKQCCQCiUAicJsRSOPmNs9u0pYIJAKJQCKQCNxBBNK4uYOTniQnAolAIpAIJAK3GYE0bm7z7CZtiUAikAgkAonAHUTg24H/XZLu2Is/AAAAAElFTkSuQmCC\" width=\"283.5\" height=\"20\" style=\"width: 283.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.4667px 8px; transform-origin: 94.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the input probabilities\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"279\" height=\"20\" style=\"width: 279px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"142.5\" height=\"20\" style=\"width: 142.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"224\" height=\"20\" style=\"width: 224px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P_LS = verify_bayes_theorem(P_SL, P_L, P_S)\r\n  P_LS = P_SL;\r\nend","test_suite":"%%\r\nP_SL = 0.99;\r\nP_L  = 1/3;\r\nP_S  = 0.5;\r\nP_LS_correct = 0.66;\r\nP_LS = verify_bayes_theorem(P_SL,P_L,P_S);\r\nassert(abs(P_LS_correct-P_LS) \u003c eps)\r\n\r\n%%\r\nP_SL = 0.75;\r\nP_L  = 1/5;\r\nP_S  = 0.25;\r\nP_LS_correct = 0.6;\r\nP_LS = verify_bayes_theorem(P_SL,P_L,P_S);\r\nassert(abs(P_LS_correct-P_LS) \u003c eps)\r\n\r\n%% Test forbidden functions\r\nfiletext = fileread('verify_bayes_theorem.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-10T07:02:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-10T07:02:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-08T12:54:24.000Z","updated_at":"2026-03-27T11:28:52.000Z","published_at":"2025-07-08T13:17:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCompute the probability\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{LS} = P(girl ~likes ~ you ~ | ~ she ~ smiled ~ at ~ you) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the input probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{SL} = P(she ~ smiles ~ at ~ you ~ | ~ she ~ likes ~ you)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_L = P(she ~likes ~ you) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_S = P(she ~ just ~ smiles ~ in ~ general) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":8052,"title":"Stress-Strain Properties - 5","description":"Similar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\r\n\r\nPrevious problem: 4 - \u003chttp://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4 strength-to-weight ratio\u003e. Next problem: 6 - \u003chttp://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6 absorbed strain energy\u003e.","description_html":"\u003cp\u003eSimilar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\u003c/p\u003e\u003cp\u003ePrevious problem: 4 - \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4\"\u003estrength-to-weight ratio\u003c/a\u003e. Next problem: 6 - \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\"\u003eabsorbed strain energy\u003c/a\u003e.\u003c/p\u003e","function_template":"function [EtWR] = stress_strain5(E,density)\r\n\r\nEtWR = 1\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals are generally\r\n% isotropic, whereas others, like composite are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 0.463; %strain-hardening coefficient\r\nEtWR_corr = 2.548e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 0.974; %strain-hardening coefficient\r\nEtWR_corr = 2.528e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1.845; %strain-hardening coefficient\r\nEtWR_corr = 2.540e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)%^\u0026\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 0.325; %strain-hardening coefficient\r\nEtWR_corr = 2.552e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 0.304; %strain-hardening coefficient\r\nEtWR_corr = 1.457e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1.870; %strain-hardening coefficient\r\nEtWR_corr = 2.203e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e9; %Pa\r\ndensity = 1.14; %g/cm^3\r\nEtWR_corr = 0.272e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nEtWR_corr = 0.960e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nEtWR_corr = 34.19e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 114e9; %Pa\r\n\t\tdensity = 4.51; %g/cm^3\r\n\t\tEtWR_corr = 2.528e10;\r\n\tcase 2\r\n\t\tE = 68.9e9; %Pa\r\n\t\tdensity = 2.7; %g/cm^3\r\n\t\tEtWR_corr = 2.552e10;\r\n\tcase 3\r\n\t\tE = 200e9; %Pa\r\n\t\tdensity = 7.85; %g/cm^3\r\n\t\tEtWR_corr = 2.548e10;\r\n\tcase 4\r\n\t\tE = 1200e9; %Pa\r\n\t\tdensity = 3.51; %g/cm^3\r\n\t\tEtWR_corr = 34.19e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 68.9e9; %Pa\r\n\t\tdensity = 2.7; %g/cm^3\r\n\t\tEtWR_corr = 2.552e10;\r\n\tcase 2\r\n\t\tE = 3.1e9; %Pa\r\n\t\tdensity = 1.14; %g/cm^3\r\n\t\tEtWR_corr = 0.272e10;\r\n\tcase 3\r\n\t\tE = 14.5e9; %Pa\r\n\t\tdensity = 1.51; %g/cm^3\r\n\t\tEtWR_corr = 0.960e10;\r\n\tcase 4\r\n\t\tE = 208e9; %Pa\r\n\t\tdensity = 8.19; %g/cm^3\r\n\t\tEtWR_corr = 2.540e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 208e9; %Pa\r\n\t\tdensity = 8.19; %g/cm^3\r\n\t\tEtWR_corr = 2.540e10;\r\n\tcase 2\r\n\t\tE = 463e9; %Pa\r\n\t\tdensity = 21.02; %g/cm^3\r\n\t\tEtWR_corr = 2.203e10;\r\n\tcase 3\r\n\t\tE = 130e9; %Pa\r\n\t\tdensity = 8.92; %g/cm^3\r\n\t\tEtWR_corr = 1.457e10;\r\n\tcase 4\r\n\t\tE = 3.1e9; %Pa\r\n\t\tdensity = 1.14; %g/cm^3\r\n\t\tEtWR_corr = 0.272e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":212,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T19:40:12.000Z","updated_at":"2026-03-10T20:42:38.000Z","published_at":"2015-03-30T19:40:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSimilar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 4 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estrength-to-weight ratio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 6 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eabsorbed strain energy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44861,"title":"Ratio between sums of prime and non-prime numbers","description":"Write a function that calculates the ratio between the sum of the prime numbers lower or equal than x, and the sum of the non-prime numbers lower than x.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 91.5px; vertical-align: baseline; perspective-origin: 332px 91.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if x = 7, then:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_prime = sum([2 3 5 7]) = 17\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_non_prime = sum([1 4 6]) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, the desired ratio is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eprime_ratio = sum_prime / sum_non_prime = 17 / 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 7;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/38;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 20;\r\ny_correct = 77/113;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 31;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 32;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 42;\r\ny_correct = 238/623;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2020-09-29T13:58:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-03-01T22:30:26.000Z","updated_at":"2026-04-01T10:59:16.000Z","published_at":"2019-03-01T22:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if x = 7, then:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[sum_prime = sum([2 3 5 7]) = 17\\nsum_non_prime = sum([1 4 6]) = 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the desired ratio is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[prime_ratio = sum_prime / sum_non_prime = 17 / 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44862,"title":"Ratio between sum of primes and sum of factors","description":"Write a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.","description_html":"\u003cp\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = 17/6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 1060/14;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2019-03-12T22:32:41.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-03-01T22:35:36.000Z","updated_at":"2026-03-16T13:27:48.000Z","published_at":"2019-03-01T22:35:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60956,"title":"P(girl likes you | she smiled at you)","description":"Compute the probability\r\n\r\n\r\n\r\nGiven the input probabilities\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 401.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 200.933px; transform-origin: 408px 200.933px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.4833px 8px; transform-origin: 80.4833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCompute the probability\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"283.5\" height=\"20\" style=\"width: 283.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.4667px 8px; transform-origin: 94.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the input probabilities\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"279\" height=\"20\" style=\"width: 279px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAAAoCAYAAADDqi7RAAAMZElEQVR4Xu2dW8h22xTHv31PTldcUOyLLcfaTiWKHEok5LA36SvlsEsSW0iSC+SQpJxCX3IuJKVQiOycyjkuUCSukLhn/PrWv/4Nc8411/Os9Tzre9+5avS+37vmmnPMMcf4jzHHHGt9N10Z15DAkMCQwAklcNMJxxpDDQkMCQwJXBmgM5RgSGBI4KQSGKBzUnGPwYYEhgQG6OxHB+4drLwi6J37YWlwMiTQlMCD4u6jgr6wRE4DdJZIa7u2AM7Xg14d9JPthhk9DwmsLoF3R48PCHphb88DdHoltV07AOcHQS/dCHDoH4+0VzCDN+gpQY8IesuBvDLPpwb9M+ib2y3X6LkgAUU6XcAzBzpPiwFeF8TP1vWjuPnVoI8G/eOCL8srY36vCbqlMc//xL27gr4S9JEZefww7n8v6A0ryQ0DZpuGAT8s6L5BrM/jVup/zW6Q5ZOCXmCd3qegQ3jTO4O+GOSKze+vDXpI0N2mPl7VIfM15zD6ui4B9Phaj+znQEcCBUxePv0Dg3peEN4E7/LGSSHU9jHxy1696poK8tvoTMDzu/j9mUF/CMLoPxQkoP5b/P7QoBIYY0wvCbrfmoxNfclQ+ed7gtYCtQ1YvSJZIscHFwb4r/3t6ZPueTM8rYDr5mkdtuBz9FmXwKPj1reDHjkn/17QcQUueU2/Dyjd/RKsDsj+2GmeJaP2+wA0xuIXgP2nIDz4XDR0iDiJIj48PbhnR4Ac/j7x+bH4SZSWL4EKoPT4oAzgknXt/iHyG88slwDrRH6nGVX3gs6cgeHdf288vih+X5TRXj6/sz8x533d6GE2bxu2jHIYT4bairTOLsRggC3S5ydGWnqDJ61F0P+Oe2yvaqC1h3leBh6I7r8R1HRyvaAzZ2AI1Nu8Of59kY9+JVzmTWQHumfv621olxcCQ/lsUMmzr6GgMsScB1mj7zX70Na9Jse5sQCjH3eA1lw/4/46EvhrdPP9yZkUe+wBnR4Dy6Bz0SOdue0m8sig45GOvPtWcnJD3HtiVfmcQ5PdbwpZv2PS7lISeh1TGr30SoAI+xlB1RRLD+h4ErmUm4CZvL3acw6hV3itdp5ErkV1vr3KWxzJdCsjcUPcc2LV8zm1ZDfgfWsQCcrSkSzhPG1qSeg11nv0cf3QiEJArp8G1U6ppXtVDOgBnR4Dy54fpLuoR+duKCxATbieB8u5Bt3rkb8UHhk/K+geQf+a6Bfx84lB+cSnZIj5VG0uAlKF9LMnBkiaE42sWcDo+Zx8KgUwMzc/ISwlkbWtF2ipZIBnuZDVJ4O+VdFJAOtlQWyR7x+EhyYBXzrt8yP630xrQbnD7dPzx+q8SgjEC+UO2TExv58HkcOay4G9Ptrcc+KTsgJ4fmuQ1zFpne81yRsZfC0ob/s9+Gg5S0X4Vf2aU/qeCMZDefblTw7a8sjcjXnSq8U/jjlha0UwYsQjjdKJCvkWFKC3dkagjrLcNhmP+ChFnzJEgR1tUTaUyQ25tv60x4j/EqSiRSndodug0iLN5XN8i1rKTfn9DFrkFn4VdEcQpQz5UhU4YEq0Ci9cOknL/WksotYnTH3qmJj1rJVFLFbOeMD1JzssB51SdMe8AE1KCDQvwFCnpYBVjs6597kglXmUyhKQZ0/Nl+RULdOYAx03sJzoQ+DPD+LIl4vFuBq0dTXouUHHa0KyAeZiSu6/eFJQVz5AYYnx1k5nUITslbIhPjDaUMwo8BD/tcRt7Xhaf1/C95zBzeVzXP9KnlNgnOcCr0QDtWJVgQUG6P26k82GV9vGMdbDg0r1RXPzb92XnpccJPxTjJsTtvo74FDa9nu0km1f8yvphUekPTVf6Hf1AGMOdNzAABUm4xdI+8ug70yDHBteHrNIp3pWiM94JZlglGx7KJSqlQ0cCjqM54WEKNHPgrzOxw2RIs5rQfLM8CwAK3lJf9aLvHpD+iVr4NvUWl7M9a8U0pdAqyQT58s9fo4iPJrLKQIZJX15ngyDfG5Q1ysACwTkgFuKPHIFsK9RzeA9DZK3Zq1IxtehxEueVlO/50BHCkqnczmABfK8YZv6VjIr35JJLQUdX/Q5T+OGyP78apCiT+c/G5xHSH5P74aRW0GZ0YM1nEtP8aIMobaN0FYImbwriJdmc84ir4tHEA6s4scr7v1Z53fNaK+mN60ku4DTSzVq8/L+a6DjEV52AH6vt6zhYNBZy8CWGOPe287lanr5Xwo67sUYo+ZtcpI7A5Tzn/sQWKFYMkblghjz7UFrVk7PFS+6/pWA1kN+gJA2OMnWKyX+jIAV2XLkTg4EUMXoSjkgZOCHKnPg36sLrXYCkhzhAh4cKCjZ64DYKpD01IRHay0H0EonlHiXDlb5aEU62cAO3bMqO86ph7ZnLO6Xg2rbjzUWbIs+PMQ+pvoVD/7noN5EMnOZq3CmjRsV3ri2Rcgey6McFJxcAXkKeOSlVdZrjejG10RRTK0MowWQ9OPG4P22TnTc6JgTkQLGywnUx4PmDkA8F8SYW9VZaT4emWh7iT39Osi3zA6GrRIJHTDkw42aA8gHST1Fv0clkn2B1kD1teopzplI7qnM7gG7Q47Ms6GVjNUNsWQQ2i7nZ125iRr+GLTlgUArnJf8WolN2vjWi0Q57blqIMY9rR+AzDaMiKYW1dTWMR+ubPmeoTsDrWeOcjy6bb175nxn8JAscy4IMKPkQO8Y9tTfiecqINcinRym9ySP5oxNEzsWwM4FOh5F9O5tazKRkbe8UumrbJ4Epe+8fm6IuaalVaXsMt2qYNFl0ZPPqQEk/ZRAy+dQMo5azmpOb4m48is9PtYattHiwcsf0BtO5TwXNVdWoL79TX7XDZel520Zi0iQOh/G6H2Hb1a3a6CzpoFlJdl6keaU6ND7ftx4bCJRANAKz1noa0E5R1Er0nLlKQG7tisCTOSAMZEX6AEdeOaa24L0yDcfy/MMSWCVFzhAyiujzCSL2eaVQKuUr6Ff5KhPjigaam2N6dtzVxh9dg69L6n2yGKujdaGCI6tIEflDoI9YOprr8/SaFyXpeZJnx8IApz4EgKlBYogad+KhJEx33Gq5tZqoOOK3QpX5wSWJ9aLlr39nrJdT2X2En6ISlovxsljZK+tv2fgm4setF3ReqLM7w8CADx/UgMsKpNLNUdL5qy2OZyHB8ouZOzOD4bAFwGfE3RbEKDjW3X32l7OwHN8RdDzH4qeSpEqoP2ZIDdqGXTejujvx0a8PbLrqfZvvdyrPBRjZcDhb7J1nRCq1of1Rtb6eoS23RwotN44AKSbu5kS6OQQvlrk0yOxqU1W+AWP7qKpexMYWqN8AGWin9Ib6oxRAhclEckjZAWSjGvALsXkPpW63w2Sxyyt+SfivgoL2devBTjMzXMreFIur3NxQ0P/SGrrI2m0rRlZTojDNx5bYOb9IgcMCK/NaxAkZj9oMmGcGrhI1j2J1Wl6B//wqKqWU3GQ9u0x/H8piMpy8l6lPF1OrgMo0i2XJ06OEgxPYOdJyfE13/fLoMOi8CW7XAQIs++rMN0jTSnJGsbaM95abfB+vINze5A+h6m+CdGR19JEpJ6f+4gXykCRIRevLmBAvD9zV2UtWt6OPvz4tXT8raNjlIr11ynWFqeMMn7GwNDxtn465iUC6N4dJue5N+hRfDwtF0fhOR/D/atBSo5iTEQ3gFteS/jks6+sA++9sQYYXgazabhNfsjw505LAae3Bd0SxJy44HPu9NHlxRb3vUHaQsvJoQ9KvrcOGKSzOsovCmSuOHANKbqS7PmN5zXmurQPFIWj2lq0s7S/0f7iSUAg2drS7GHW3bp8CtCRVxufHiirhmqV1i6j34MiDh6Ok4DyK60tzXEjrPO0ovZSzuj/RjgF6CgBWwsPYZhE4Y1WKLjOcl3vhbD0WtCaFb9r8jf6Or0E9PpJLRdzeo7qIy7S361Bx+t9akfl7OfZe+75fys4xQLnE5xTjDnG2I8EiHRvDcIeOHXj/0L7VFDOSe2H4+ucLNbbrUGnVAPgQlPWvafScW/C3oIfFO8yR3xbyPRG6dOr3ZVg3zvgkPAnsFhUu7Ul6Hg2nYVHkJ+eNIAiJ04DlBVf8g7SjaJEg88hgSUSUL1MzynRkn5313ZL0NndZAdDQwJDAueXwACd86/B4GBI4FJJYIDOpVruMdkhgfNLYIDO+ddgcDAkcKkkMEDnUi33mOyQwPklMEDn/GswOBgSuFQSGKBzqZZ7THZI4PwS+B/IiJ1Wu1JXsQAAAABJRU5ErkJggg==\" width=\"142.5\" height=\"20\" style=\"width: 142.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 10.8583px; transform-origin: 392px 10.8583px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.8583px; text-align: left; transform-origin: 364px 10.8583px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"224\" height=\"20\" style=\"width: 224px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P_LS = verify_bayes_theorem(P_SL, P_L, P_S)\r\n  P_LS = P_SL;\r\nend","test_suite":"%%\r\nP_SL = 0.99;\r\nP_L  = 1/3;\r\nP_S  = 0.5;\r\nP_LS_correct = 0.66;\r\nP_LS = verify_bayes_theorem(P_SL,P_L,P_S);\r\nassert(abs(P_LS_correct-P_LS) \u003c eps)\r\n\r\n%%\r\nP_SL = 0.75;\r\nP_L  = 1/5;\r\nP_S  = 0.25;\r\nP_LS_correct = 0.6;\r\nP_LS = verify_bayes_theorem(P_SL,P_L,P_S);\r\nassert(abs(P_LS_correct-P_LS) \u003c eps)\r\n\r\n%% Test forbidden functions\r\nfiletext = fileread('verify_bayes_theorem.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-10T07:02:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2025-07-10T07:02:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-08T12:54:24.000Z","updated_at":"2026-03-27T11:28:52.000Z","published_at":"2025-07-08T13:17:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCompute the probability\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{LS} = P(girl ~likes ~ you ~ | ~ she ~ smiled ~ at ~ you) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the input probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_{SL} = P(she ~ smiles ~ at ~ you ~ | ~ she ~ likes ~ you)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_L = P(she ~likes ~ you) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP_S = P(she ~ just ~ smiles ~ in ~ general) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":8052,"title":"Stress-Strain Properties - 5","description":"Similar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\r\n\r\nPrevious problem: 4 - \u003chttp://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4 strength-to-weight ratio\u003e. Next problem: 6 - \u003chttp://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6 absorbed strain energy\u003e.","description_html":"\u003cp\u003eSimilar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\u003c/p\u003e\u003cp\u003ePrevious problem: 4 - \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4\"\u003estrength-to-weight ratio\u003c/a\u003e. Next problem: 6 - \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\"\u003eabsorbed strain energy\u003c/a\u003e.\u003c/p\u003e","function_template":"function [EtWR] = stress_strain5(E,density)\r\n\r\nEtWR = 1\r\n\r\nend\r\n","test_suite":"%% Note\r\n% The following properties are measured at room temperature and are tensile\r\n% in a single direction. Some materials, such as metals are generally\r\n% isotropic, whereas others, like composite are highly anisotropic\r\n% (different properties in different directions). Also, property values can\r\n% range depending on the material grade. Finally, thermal or environmental\r\n% changes can alter these properties, sometimes drastically.\r\n\r\n%% steel alloy (ASTM A36)\r\nS_y = 250e6; %Pa\r\nS_u = 400e6; %Pa\r\ne_y = 0.00125;\r\ne_u = 0.35;\r\nnu = 0.26;\r\nG = 79.3e9; %Pa\r\nE = 200e9; %Pa\r\ndensity = 7.85; %g/cm^3\r\nsh_exp = 0.14; %strain-hardening exponent\r\nsh_coeff = 0.463; %strain-hardening coefficient\r\nEtWR_corr = 2.548e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% titanium (Ti-6Al-4V)\r\nS_y = 830e6; %Pa\r\nS_u = 900e6; %Pa\r\ne_y = 0.00728;\r\ne_u = 0.14;\r\nnu = 0.342;\r\nG = 44e9; %Pa\r\nE = 114e9; %Pa\r\ndensity = 4.51; %g/cm^3\r\nsh_exp = 0.04; %strain-hardening exponent\r\nsh_coeff = 0.974; %strain-hardening coefficient\r\nEtWR_corr = 2.528e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% Inconel 718\r\nS_y = 1172e6; %Pa\r\nS_u = 1407e6; %Pa\r\ne_y = 0.00563;\r\ne_u = 0.027;\r\nnu = 0.29;\r\nG = 11.6e9; %Pa\r\nE = 208e9; %Pa\r\ndensity = 8.19; %g/cm^3\r\nsh_exp = 0.075; %strain-hardening exponent\r\nsh_coeff = 1.845; %strain-hardening coefficient\r\nEtWR_corr = 2.540e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% aluminum alloy (6061-T6)%^\u0026\r\nS_y = 241e6; %Pa\r\nS_u = 300e6; %Pa\r\ne_y = 0.0035;\r\ne_u = 0.15;\r\nnu = 0.33;\r\nG = 26e9; %Pa\r\nE = 68.9e9; %Pa\r\ndensity = 2.7; %g/cm^3\r\nsh_exp = 0.042; %strain-hardening exponent\r\nsh_coeff = 0.325; %strain-hardening coefficient\r\nEtWR_corr = 2.552e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% copper\r\nS_y = 70e6; %Pa\r\nS_u = 220e6; %Pa\r\ne_y = 0.00054;\r\ne_u = 0.48;\r\nnu = 0.34;\r\nG = 48e9; %Pa\r\nE = 130e9; %Pa\r\ndensity = 8.92; %g/cm^3\r\nsh_exp = 0.44; %strain-hardening exponent\r\nsh_coeff = 0.304; %strain-hardening coefficient\r\nEtWR_corr = 1.457e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% rhenium\r\nS_y = 317e6; %Pa\r\nS_u = 1130e6; %Pa\r\ne_y = 0.000685;\r\ne_u = 0.24;\r\nnu = 0.3;\r\nG = 178e9; %Pa\r\nE = 463e9; %Pa\r\ndensity = 21.02; %g/cm^3\r\nsh_exp = 0.353; %strain-hardening exponent\r\nsh_coeff = 1.870; %strain-hardening coefficient\r\nEtWR_corr = 2.203e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6)\r\nS_y = 82e6; %Pa\r\nS_u = 82e6; %Pa\r\ne_y = 0.0265;\r\ne_u = 0.45;\r\nnu = 0.41;\r\nG = 2.8e9; %Pa\r\nE = 3.1e9; %Pa\r\ndensity = 1.14; %g/cm^3\r\nEtWR_corr = 0.272e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% polymer (nylon, 6/6) reinforced with 45wt.% glass fiber\r\nS_y = 230e6; %Pa\r\nS_u = 230e6; %Pa\r\ne_y = 0.016;\r\ne_u = 0.016;\r\nnu = 0.35;\r\nG = 13.0e9; %Pa\r\nE = 14.5e9; %Pa\r\ndensity = 1.51; %g/cm^3\r\nEtWR_corr = 0.960e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%% diamond\r\nS_y = 1200e6; %Pa\r\nS_u = 1200e6; %Pa\r\ne_y = 0.001;\r\ne_u = 0.001;\r\nnu = 0.20;\r\nG = 478e9; %Pa\r\nE = 1200e9; %Pa\r\ndensity = 3.51; %g/cm^3\r\nEtWR_corr = 34.19e10;\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 114e9; %Pa\r\n\t\tdensity = 4.51; %g/cm^3\r\n\t\tEtWR_corr = 2.528e10;\r\n\tcase 2\r\n\t\tE = 68.9e9; %Pa\r\n\t\tdensity = 2.7; %g/cm^3\r\n\t\tEtWR_corr = 2.552e10;\r\n\tcase 3\r\n\t\tE = 200e9; %Pa\r\n\t\tdensity = 7.85; %g/cm^3\r\n\t\tEtWR_corr = 2.548e10;\r\n\tcase 4\r\n\t\tE = 1200e9; %Pa\r\n\t\tdensity = 3.51; %g/cm^3\r\n\t\tEtWR_corr = 34.19e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 68.9e9; %Pa\r\n\t\tdensity = 2.7; %g/cm^3\r\n\t\tEtWR_corr = 2.552e10;\r\n\tcase 2\r\n\t\tE = 3.1e9; %Pa\r\n\t\tdensity = 1.14; %g/cm^3\r\n\t\tEtWR_corr = 0.272e10;\r\n\tcase 3\r\n\t\tE = 14.5e9; %Pa\r\n\t\tdensity = 1.51; %g/cm^3\r\n\t\tEtWR_corr = 0.960e10;\r\n\tcase 4\r\n\t\tE = 208e9; %Pa\r\n\t\tdensity = 8.19; %g/cm^3\r\n\t\tEtWR_corr = 2.540e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n\r\n%%\r\nind = randi(4);\r\nswitch ind\r\n\tcase 1\r\n\t\tE = 208e9; %Pa\r\n\t\tdensity = 8.19; %g/cm^3\r\n\t\tEtWR_corr = 2.540e10;\r\n\tcase 2\r\n\t\tE = 463e9; %Pa\r\n\t\tdensity = 21.02; %g/cm^3\r\n\t\tEtWR_corr = 2.203e10;\r\n\tcase 3\r\n\t\tE = 130e9; %Pa\r\n\t\tdensity = 8.92; %g/cm^3\r\n\t\tEtWR_corr = 1.457e10;\r\n\tcase 4\r\n\t\tE = 3.1e9; %Pa\r\n\t\tdensity = 1.14; %g/cm^3\r\n\t\tEtWR_corr = 0.272e10;\r\nend\r\nassert(abs(stress_strain5(E,density)-EtWR_corr)/EtWR_corr\u003c1e-2)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":212,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-03-30T19:40:12.000Z","updated_at":"2026-03-10T20:42:38.000Z","published_at":"2015-03-30T19:40:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSimilar to the previous problem, materials may be characterized by their stiffness-to-weight ratio, which is the elastic modulus divided by density. Write a function to calculate this ratio for a material provided its elastic modulus and density.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 4 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/8051-stress-strain-properties-4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003estrength-to-weight ratio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Next problem: 6 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/8053-stress-strain-properties-6\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eabsorbed strain energy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44861,"title":"Ratio between sums of prime and non-prime numbers","description":"Write a function that calculates the ratio between the sum of the prime numbers lower or equal than x, and the sum of the non-prime numbers lower than x.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 91.5px; vertical-align: baseline; perspective-origin: 332px 91.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if x = 7, then:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_prime = sum([2 3 5 7]) = 17\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003esum_non_prime = sum([1 4 6]) = 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, the desired ratio is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eprime_ratio = sum_prime / sum_non_prime = 17 / 11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 7;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 17/11;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/38;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 20;\r\ny_correct = 77/113;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 31;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 32;\r\ny_correct = 160/336;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 42;\r\ny_correct = 238/623;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2020-09-29T13:58:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-03-01T22:30:26.000Z","updated_at":"2026-04-01T10:59:16.000Z","published_at":"2019-03-01T22:30:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of the prime numbers less than or equal to x, and the sum of the non-prime numbers up to the greatest prime less than or equal to x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if x = 7, then:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[sum_prime = sum([2 3 5 7]) = 17\\nsum_non_prime = sum([1 4 6]) = 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the desired ratio is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[prime_ratio = sum_prime / sum_non_prime = 17 / 11]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44862,"title":"Ratio between sum of primes and sum of factors","description":"Write a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.","description_html":"\u003cp\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = 17/6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = 28/7;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 1060/14;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2019-03-12T22:32:41.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2019-03-01T22:35:36.000Z","updated_at":"2026-03-16T13:27:48.000Z","published_at":"2019-03-01T22:35:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that calculates the ratio between the sum of primes numbers lower or equal to x, and the sum of the factors of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"ratio\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"ratio\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"ratio\"","","\"","ratio","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fa2b6604e28\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fa2b6604d88\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fa2b66044c8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fa2b66050a8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fa2b6605008\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fa2b6604f68\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fa2b6604ec8\u003e":"tag:\"ratio\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fa2b6604ec8\u003e":"tag:\"ratio\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"ratio\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"ratio\"","","\"","ratio","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fa2b6604e28\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fa2b6604d88\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fa2b66044c8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fa2b66050a8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fa2b6605008\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fa2b6604f68\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fa2b6604ec8\u003e":"tag:\"ratio\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fa2b6604ec8\u003e":"tag:\"ratio\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":60956,"difficulty_rating":"easy"},{"id":8052,"difficulty_rating":"easy"},{"id":44861,"difficulty_rating":"easy"},{"id":44862,"difficulty_rating":"easy-medium"}]}}