{"id":"cb_question_bank:9466d27e-3ba9-4d85-9207-33d4cdc277a1","source_id":"cb_question_bank","source_item_id":"9466d27e-3ba9-4d85-9207-33d4cdc277a1","external_id":"06a91641-79ae-4887-9807-53c2c9859f93","ibn":null,"question_id":"56dc8045","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"w left parenthesis t right parenthesis equals 300 minus 4 t The function w models the volume of liquid, in milliliters, in a container t seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"w left parenthesis t right parenthesis equals 300 minus 4 t\"><mi>w</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>300</mn><mo>-</mo><mn>4</mn><mi>t</mi></math></p>\n<p style=\"text-align: left;\">The function <math alttext=\"w\"><mi>w</mi>\n</math> models the volume of liquid, in milliliters, in a container <math alttext=\"t\"><mi>t</mi>\n</math> seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?</p>","rationale_html":"<p>Choice D is correct. It’s given that the function <math alttext=\"w\"><mi>w</mi>\n</math> models the volume of liquid, in milliliters, in a container <math alttext=\"t\"><mi>t</mi>\n</math> seconds after it begins draining from a hole at the bottom. The given function <math alttext=\"w left parenthesis t right parenthesis equals 300 minus 4 t\"><mi>w</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>300</mn><mo>-</mo><mn>4</mn><mi>t</mi></math> can be rewritten as <math alttext=\"w left parenthesis t right parenthesis equals minus 4 t plus 300\"><mi>w</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mo>-</mo><mn>4</mn><mi>t</mi><mo>+</mo><mn>300</mn></math>. Thus, for each increase of <math alttext=\"t\"><mi>t</mi>\n</math> by <math alttext=\"1\"><mn>1</mn>\n</math>, the value of <math alttext=\"w left parenthesis t right parenthesis\"><mi>w</mi><mfenced><mi>t</mi></mfenced></math> decreases by <math alttext=\"4 left parenthesis 1 right parenthesis\"><mn>4</mn><mo>(</mo><mn>1</mn><mo>)</mo></math>, or <math alttext=\"4\"><mn>4</mn>\n</math>. Therefore, the predicted volume, in milliliters, draining from the container each second is <math alttext=\"4\"><mn>4</mn>\n</math> milliliters.</p>\n<p>Choice A is incorrect. This is the amount of liquid, in milliliters, in the container before the liquid begins draining.</p>\n<p>Choice B is incorrect and may result from conceptual errors.</p>\n<p>Choice C is incorrect and may result from conceptual errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"300\"><mn>300</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"296\"><mn>296</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"75\"><mn>75</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"4\"><mn>4</mn>\n</math></p>","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}}