select the correct answer from each drop-down menu.

the revenue that an apparel company earns each month for its different product lines fluctuates throughout the year. over the course of a year, the revenue earned from clothing sales each month is modeled by function $c$, where $x$ is the number of months since the beginning of the year.

the revenue earned from sales of shoes and accessories each month is modeled by function $s$, where $x$ is the number of months since the beginning of the year.

$s(x) = -10.2x^2 + 32.4x + 127.2$

use the drop-down to complete the statement.

between the 4th and 6th months, the revenue earned from sales of shoes and accessories is increasing/decreasing at a faster rate than/the same rate as/a slower rate than the revenue earned from sales of clothing.

Question

select the correct answer from each drop-down menu.

the revenue that an apparel company earns each month for its different product lines fluctuates throughout the year. over the course of a year, the revenue earned from clothing sales each month is modeled by function $c$, where $x$ is the number of months since the beginning of the year.

the revenue earned from sales of shoes and accessories each month is modeled by function $s$, where $x$ is the number of months since the beginning of the year.

$s(x) = -10.2x^2 + 32.4x + 127.2$

use the drop-down to complete the statement.

between the 4th and 6th months, the revenue earned from sales of shoes and accessories is increasing/decreasing at a faster rate than/the same rate as/a slower rate than the revenue earned from sales of clothing.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change", "Increasing and Decreasing Functions" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Increasing and Decreasing Functions", "Function Comparison" ] } ## Calculate the average rate of change for the shoes and accessories function $s(x)$ $$ \begin{aligned} s(x) &= -10.2x^2 + 32.4x + 127.2 \ s(4) &= -10.2(16) + 32.4(4) + 127.2 = -163.2 + 129.6 + 127.2 = 93.6 \ s(6) &= -10.2(36) + 32.4(6) + 127.2 = -367.2 + 194.4 + 127.2 = -45.6 \ \text{Rate of change } (s) &= \frac{s(6) - s(4)}{6 - 4} = \frac{-45.6 - 93.6}{2} = \frac{-139.2}{2} = -69.6 \end{aligned} $$ ## Determine the average rate of change for the clothing function $c(x)$ from the graph $$ \begin{aligned} c(4) &\approx 140 \ c(6) &\approx 110 \ \text{Rate of change } (c) &\approx \frac{110 - 140}{6 - 4} = \frac{-30}{2} = -15 \end{aligned} $$ ## Compare the rates of change and behavior $$ \begin{aligned} &\text{Both rates of change are negative, meaning both revenues are decreasing.} \ &|-69.6| > |-15| \implies \text{Revenue from shoes and accessories is decreasing at a faster rate than clothing.} \end{aligned} $$ Between the 4th and 6th months, the revenue earned from sales of shoes and accessories is decreasing at a faster rate than the revenue earned from sales of clothing. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the average rate of change for the shoes and accessories function \(s(x)\)

Determine the average rate of change for the clothing function \(c(x)\) from the graph

Compare the rates of change and behavior

Answer: