{"id":"cb_question_bank:a104cf30-d05c-4650-b21e-cd3730e6433f","source_id":"cb_question_bank","source_item_id":"a104cf30-d05c-4650-b21e-cd3730e6433f","external_id":null,"ibn":"029000-DC","question_id":"5910bfff","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"D equals, T minus, the fraction 9 over 25, end fraction, times open parenthesis, 100 minus H, close parenthesis The formula above can be used to approximate the dew point D , in degrees Fahrenheit, given the temperature T , in degrees Fahrenheit, and the relative humidity of H percent, where H is greater than 50 . Which of the following expresses the relative humidity in terms of the temperature and the dew point?","stimulus":"","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \"></p>\n      </div>\n","stem_html":"<p class=\"para_center\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e83321caef9adce4cc963c0bf3e2a621206125e0aa4ef847e5939f89f0718563\" alt=\"D equals, T minus, the fraction 9 over 25, end fraction, times open parenthesis, 100 minus H, close parenthesis\"></span></p><p class=\"stem_paragraph \">The formula above can be used to approximate the dew point <span class=\"italic\">D</span>, in degrees Fahrenheit, given the temperature <span class=\"italic\">T</span>, in degrees Fahrenheit, and the relative humidity of <span class=\"italic\">H </span>percent, where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98643d6c7402a5a32ee712b02cdfb024269fa4a29ce5a36fc92cbcadf70777f0\" alt=\"H is greater than 50\"></span>. Which of the following expresses the relative humidity in terms of the temperature and the dew point?</p><p></p>\n","rationale_html":"<p>Choice A is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/74c245c89c8f0a4b819e2f88701ce586646cb2406f1a585aabc426c0cd6268c0\" alt=\"D equals, T minus the fraction 9 over 25, end fraction, times, open parenthesis, 100 minus H, close parenthesis\"></span>. Solving this formula for <span class=\"italic\">H</span> expresses the relative humidity in terms of the temperature and the dew point. Subtracting <span class=\"italic\">T</span> from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/04850e7bdb4d5b69b501717518bd57ddd9a8c6a68208dd065bf4b2dcb15b823a\" alt=\"D minus T equals, the negative of the fraction 9 over 25, end fraction, times, open parenthesis, 100 minus H, close parenthesis\"></span>. Multiplying both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/83ec63dd4d35e6a9af4f678d3c8986fbb62544eb28e22c93dd3c91e2ff0c93d6\" alt=\"the negative of the fraction 25 over 9\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c1a227de2a8704474f70cbe36773dac4e42f74fd2bdaf01791da80b46b57764\" alt=\"the negative of the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, equals, 100 minus H\"></span>. Subtracting 100 from both sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9293e4df5c0a590b7d436eb926e8e18d7375f20096fb7beed1d439c92b0cc2c5\" alt=\"the negative of the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, minus 100, equals negative H\"></span>. Multiplying both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1 \"></span> results in the formula <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c931aa483fee07b30134dfbff403366d3f9f8546779bfdab560313e2b9ebecb0\" alt=\"the fraction 25 over 9, end fraction, times, open parenthesis, D minus T, close parenthesis, plus 100, equals H.\"></span>.</p><p>Choices B, C, and D are incorrect and may result from errors made when rewriting the given formula.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.623000+00:00","source_updated_at":"2023-08-02T20:25:59.623000+00:00","options":[{"label":"A","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b87e185a4354880165e46b6ab6b7d7e8ae104dda4a441dcb0e8aa2ef966bf37a\" alt=\"H equals, the fraction 25 over 9, end fraction, times open parenthesis, D minus T, close parenthesis, plus 100\"></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/52de237cb8267919adb465ba17db210e724a395c5e808fdcf4561ef45d384e71\" alt=\"H equals, the fraction 25 over 9, end fraction, times open parenthesis, D minus T, close parenthesis, minus 100\"></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9ae8c6626687912503c505cc435c331c32879cd99eb7a0bbed1b5c235acd5a86\" alt=\"H equals, the fraction 25 over 9, end fraction, times open parenthesis, D plus T, close parenthesis, plus 100\"></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/29a7ad75e1444f64c4eeecabfd4af4b0252843bbcd739517be75b5abc9c1ed12\" alt=\"H equals, the fraction 25 over 9, end fraction, times open parenthesis, D plus T, close parenthesis, minus 100\"></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}