To determine Jordaris' overtime hourly pay from the given piecewise equation, we need to look at the hourly rates described in each segment of the equation. The equation is as follows:
[tex]\[ y = \begin{cases}
25x & \text{if } 0 \leq x \leq 38 \\
30(x-38) + 950 & \text{if } x > 38
\end{cases} \][/tex]
Let's break this down:
1. For [tex]\(0 \leq x \leq 38\)[/tex]:
- The equation is [tex]\( y = 25x \)[/tex].
- This suggests that Jordaris earns [tex]$25 for each overtime hour worked in this range.
2. For \(x > 38\):
- The equation changes to \( y = 30(x-38) + 950 \).
- Here, \( x \) represents the total number of overtime hours worked.
- The term \( 30(x-38) \) indicates that for every hour beyond 38 hours, Jordaris earns $[/tex]30 per hour.
- The additional [tex]$950 in this part of the equation accounts for the cumulative pay for the first 38 hours (since \( 25 \times 38 = 950 \)).
Summarizing the overtime pay per hour:
- For the first 38 hours of overtime, Jordaris earns at a rate of $[/tex]25 per hour.
- For any hour beyond the initial 38 hours, Jordaris earns at a rate of [tex]$30 per hour.
Therefore, the correct answers are:
For hours \(0 \leq x \leq 38\): $[/tex]25
For hours [tex]\( x > 38\)[/tex]: [tex]$30
These correspond to the answers \( A: \$[/tex] 25 \) and [tex]\( C: \$ 30 \)[/tex]. Since the question is asking for Jordaris' overtime hourly pay in general, it can be interpreted as including both rates, depending on the number of hours worked.
