select the correct answer from each drop - down menu. the revenue that an apparel company earns each month…

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 at the revenue earned from sales of clothing.

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 at the revenue earned from sales of clothing.

Answer

Explanation:

Step1: Calculate revenue from shoes - accessories at x = 3

Substitute x = 3 into $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$. [ \begin{align*} s(3)&=0.6\times3^{3}-10.2\times3^{2}+32.4\times3 + 127.2\ &=0.6\times27-10.2\times9 + 97.2+127.2\ &=16.2-91.8+97.2 + 127.2\ &=(16.2+97.2+127.2)-91.8\ &=240.6 - 91.8\ &=148.8 \end{align*} ]

Step2: Calculate revenue from shoes - accessories at x = 6

Substitute x = 6 into $s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2$. [ \begin{align*} s(6)&=0.6\times6^{3}-10.2\times6^{2}+32.4\times6+127.2\ &=0.6\times216-10.2\times36 + 194.4+127.2\ &=129.6-367.2+194.4 + 127.2\ &=(129.6+194.4+127.2)-367.2\ &=451.2-367.2\ &=84 \end{align*} ]

Step3: Estimate clothing - revenue from graph at x = 3 and x = 6

From the graph of $c(x)$, at x = 3, $c(3)\approx130$, at x = 6, $c(6)\approx100$.

Step4: Compare revenues

For x = 3, $s(3)=148.8>c(3)\approx130$. For x = 6, $s(6)=84 < c(6)\approx100$. So between 3rd and 6th months, the revenue from shoes - accessories is sometimes greater than the revenue from clothing.

Answer:

sometimes greater than