To determine the cost of an order with 6 boxes using the given piecewise function [tex]\( C(x) \)[/tex], we need to analyze which part of the piecewise function to use when [tex]\( x = 6 \)[/tex].
The piecewise function is defined as:
[tex]\[
C(x) = \begin{cases}
3.75x & \text{if } x < 6 \\
3.25x + 5 & \text{if } x \geq 6
\end{cases}
\][/tex]
Given that [tex]\( x = 6 \)[/tex], we fall into the second part of the piecewise function because [tex]\( x \geq 6 \)[/tex]. Therefore, we use the equation:
[tex]\[
C(x) = 3.25x + 5
\][/tex]
Now, substituting [tex]\( x = 6 \)[/tex] into this equation, we get:
[tex]\[
C(6) = 3.25 \times 6 + 5
\][/tex]
First, calculate [tex]\( 3.25 \times 6 \)[/tex]:
[tex]\[
3.25 \times 6 = 19.5
\][/tex]
Next, add 5 to the result:
[tex]\[
19.5 + 5 = 24.5
\][/tex]
Therefore, the cost of an order with 6 boxes is:
[tex]\[
\$ 24.50
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{24.50}
\][/tex]
