https://file.aiquickdraw.com/mathbot/file/172615607854250tfpbyv.jpg

To solve this problem, we need to find how much Nate is paid for each hour he works over 40 hours.

### Step-by-Step Solution

The piecewise function given is:

\[
\text{Nate's weekly pay} = 
\begin{cases} 
16.50x & \text{if } 0 \leq x \leq 40 \\
24.75(x - 40) + 660 & \text{if } x > 40 
\end{cases}
\]

- **First part**: $16.50x$ is the pay when Nate works between 0 to 40 hours.
- **Second part**: $24.75(x - 40) + 660$ is the pay when Nate works more than 40 hours.

The term $24.75(x - 40)$ represents the additional amount Nate earns for hours over 40.

1. **Interpretation of the expression:**
   - $x - 40$ is the number of hours worked over 40.
   - $24.75$ is the rate Nate is paid for each hour over 40.

### Conclusion

Nate is paid **$24.75** for each hour he works over 40.

### Correct Answer

The correct answer is **B. $24.75**.

Would you like further details or have any questions about this solution?

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Here are 5 related questions to explore further:
1. How would Nate's pay change if the rate for hours over 40 increased to $30 per hour?
2. What would be Nate's total weekly pay if he worked 45 hours in a week?
3. How does the piecewise function ensure a smooth transition in payment at 40 hours?
4. Can we find a general formula for calculating Nate's pay if the rates change?
5. What are other real-world examples where piecewise functions might be useful?

**Tip:** When solving piecewise functions, always carefully check the conditions under which each part of the function applies.

Nate's weekly pay, in dollars, when he works x hours is represented by a piecewise function. How much is Nate paid for each hour he works over 40?

Learn how to calculate Nate's weekly pay using a piecewise function. This problem helps understand how pay changes for hours worked over 40, using rates of $16.50 for up to 40 hours and $24.75 for each additional hour. Suitable for students in Grades 9-10.

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