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) = 0.6x^3 - 10.2x^2 + 32.4x + 127.2\

use this information to complete the statement.

between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is choose an answer at choose an answer 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) = 0.6x^3 - 10.2x^2 + 32.4x + 127.2\

use this information to complete the statement.

between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is choose an answer at choose an answer 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": [ "Cubic Functions", "Function Comparison" ], "new_concepts": [], "current_concepts": [ "Cubic Functions", "Function Comparison", "Graphical Analysis" ] } ## Evaluate the shoe and accessory revenue function at the boundaries $$ \begin{aligned} s(3) &= 0.6(3)^3 - 10.2(3)^2 + 32.4(3) + 127.2 \ &= 0.6(27) - 10.2(9) + 97.2 + 127.2 \ &= 16.2 - 91.8 + 224.4 = 148.8 \ s(6) &= 0.6(6)^3 - 10.2(6)^2 + 32.4(6) + 127.2 \ &= 0.6(216) - 10.2(36) + 194.4 + 127.2 \ &= 129.6 - 367.2 + 321.6 = 84 \end{aligned} $$ ## Read the clothing revenue values from the graph $$ \begin{aligned} c(3) &\approx 140 \ c(6) &\approx 100 \end{aligned} $$ ## Compare the two functions on the interval $$ \begin{aligned} &\text{At } x = 3: s(3) = 148.8 > c(3) \approx 140 \ &\text{At } x = 6: s(6) = 84 < c(6) \approx 100 \ &\text{Therefore, the revenue from shoes and accessories starts higher and ends lower than clothing.} \end{aligned} $$ Between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is greater than the revenue earned from sales of clothing at the 3rd month only. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Comparison" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the shoe and accessory revenue function at the boundaries

Read the clothing revenue values from the graph

Compare the two functions on the interval

Answer: