Question

Stacy works at a factory in her hometown for her job. She makes $18/hour for a 40 hour work week. If she works any overtime, she gets paid time and a half for any additional hours worked.

Question 1: What is Stacy’s gross income for a 40-hour work week?

Question 2: What is Stacy’s gross income for a year?

can you work this out step by step and use desmos

Answer 1

Let's break down the calculations step by step.

**Question 1: What is Stacy’s gross income for a 40-hour work week?**

1. **Hourly Wage**: Stacy earns $18 per hour.
2. **Hours Worked in a Week**: Stacy works 40 hours per week.
3. **Gross Income Calculation**:
\[
\text{Gross Income} = \text{Hourly Wage} \times \text{Hours Worked}
\]
Substituting the values gives:
\[
\text{Gross Income} = 18 \, \text{dollars/hour} \times 40 \, \text{hours}
\]

So, we calculate:
\[
\text{Gross Income} = 720 \, \text{dollars}
\]

**Answer to Question 1**: Stacy's gross income for a 40-hour work week is **$720**.

---

**Question 2: What is Stacy’s gross income for a year?**

1. **Weeks in a Year**: There are approximately 52 weeks in a year.
2. **Annual Income Calculation**:
\[
\text{Annual Income} = \text{Gross Weekly Income} \times \text{Weeks in a Year}
\]
Substituting the values gives:
\[
\text{Annual Income} = 720 \, \text{dollars/week} \times 52 \, \text{weeks}
\]

So, we calculate:
\[
\text{Annual Income} = 37440 \, \text{dollars}
\]

**Answer to Question 2**: Stacy's gross income for a year is **$37,440**.

---

### Summary:
- **Weekly Income**: $720
- **Annual Income**: $37,440

Unfortunately, I cannot use Desmos directly, but you can visualize these calculations using Desmos. You could create a graph where the x-axis represents the number of hours worked and the y-axis represents gross income, which would be a linear relationship defined by the slope of $18. Then, you could calculate and plot the points corresponding to a 40-hour work week and the total for the year.