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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent and Dependent Variables", "Rate of Change Interpretation", "Rate of Change Rule" ], "new_concepts": [], "current_concepts": [ "Independent and Dependent Variables", "Rate of Change Interpretation", "Rate of Change Rule" ] } ## Identify variables and rate of change Using the *Independent and Dependent Variables* and *Rate of Change Interpretation* knowledge points $$ \begin{aligned} &\text{Dependent variable (y): Water depth (inches)}\ &\text{Independent variable (x): Time (weeks)}\ &\text{Rate of change} = -6\text{ in./week} \end{aligned} $$ ## Select the describing statement Using the *Rate of Change Interpretation* knowledge point $$ \text{The water depth varies with respect to time with a rate of change of } -6\text{ in./week.} $$ ## Calculate change after 5 weeks Using the *Rate of Change Rule* knowledge point $$ \begin{aligned} &\text{Change} = \text{Rate} \times \text{Time}\ &\text{Change} = -6\text{ in./week} \times 5\text{ weeks} = -30\text{ inches} \end{aligned} $$ This represents a decrease of $30$ inches. ## Calculate change after 13 weeks Using the *Rate of Change Rule* knowledge point $$ \begin{aligned} &\text{Change} = -6\text{ in./week} \times 13\text{ weeks} = -78\text{ inches} \end{aligned} $$ This represents a decrease of $78$ inches. ## Question 1 (A) Time varies with respect to the water depth with a rate of change of $-6$ in./week.

(B) The water depth varies with respect to time with a rate of change of $-6$ in./week.

(C) Time varies with respect to the water depth with a rate of change of $-6$ week/in.

(D) The water depth varies with respect to time with a rate of change of $-6$ week/in. ## Question 2 The water depth has decreased by 30 inch(es). ## Question 3 The water depth has decreased by 78 inch(es). { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Rate of Change Rule" ] }

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QUESTION IMAGE

Question

Explanation:

Identify variables and rate of change

Select the describing statement

Calculate change after 5 weeks

Calculate change after 13 weeks

Answer:

Question 1

Question 2

Question 3