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Select the correct function and value.

Suppose your soccer coach is ordering duffel bags online for your team. The online store charges [tex]$\$[/tex]16.49[tex]$ per bag, plus $[/tex]\[tex]$10.50$[/tex] for shipping and handling of the order. Suppose [tex]$x$[/tex] is the number of bags ordered and [tex]$g(x)$[/tex] is the total cost of [tex]$x$[/tex] bags. Select the function that models the relationship. Then, select the cost of buying 12 bags.

[tex]\[
\begin{array}{ll}
A. \ g(x)=16.49x+10.50 & B. \ g(x)=10.50x+16.49 \\
C. \ g(x)=16.49x+10.50x & D. \ g(x)=16.49x \cdot 10.50
\end{array}
\][/tex]

Select the total cost of 12 bags.

Sagot :

GinnyAnsweridn
To find the correct function that models the relationship between the number of bags ordered and the total cost, we need to consider the cost per bag and the shipping and handling fee.

Given:
- The cost per bag is [tex]$\$[/tex]16.49[tex]$. - The shipping and handling fee for the entire order is $[/tex]\[tex]$10.50$[/tex].

So, if [tex]\( x \)[/tex] is the number of bags ordered, the total cost [tex]\( g(x) \)[/tex] will be comprised of two parts:
1. The variable cost due to the number of bags, which is [tex]\( 16.49x \)[/tex].
2. The fixed shipping and handling fee, which is [tex]\( 10.50 \)[/tex].

Thus, the function that models the total cost [tex]\( g(x) \)[/tex] is:
[tex]\[ g(x) = 16.49x + 10.50 \][/tex]

Now, to find the cost of buying 12 bags, we substitute [tex]\( x = 12 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(12) = 16.49 \cdot 12 + 10.50 \][/tex]

From this, the calculated total cost is:
[tex]\[ g(12) = 208.38 \][/tex]

Therefore, the correct function is [tex]\( g(x) = 16.49x + 10.50 \)[/tex], and the total cost of buying 12 bags is $208.38.
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