Question

11.
Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.

Answer 1

In this situation, we can identify the following:

**Independent Quantity:** The number of hours Wendy works, which can vary between 30 and 35 hours per week. This is the quantity that Wendy can choose or control.

**Dependent Quantity:** Wendy's weekly pay, which depends on the number of hours she works. The more hours she works, the more she earns.

### Reasonable Domain and Range Values:

- **Domain (independent quantity):** The number of hours Wendy plans to work ranges from 30 to 35 hours per week. Thus, the reasonable domain is given by:
\[
30 \leq h \leq 35
\]
where \( h \) represents the number of hours worked.

- **Range (dependent quantity):** Wendy's pay can be calculated using the formula:
\[
\text{Pay} = \text{Hourly Rate} \times \text{Hours Worked} = 12h
\]
Substituting the values from the domain:
- If she works 30 hours:
\[
\text{Pay} = 12 \times 30 = 360
\]
- If she works 35 hours:
\[
\text{Pay} = 12 \times 35 = 420
\]

Thus, the reasonable range for Wendy's weekly pay is:
\[
360 \leq P \leq 420
\]
where \( P \) represents Wendy's weekly pay.

In summary:
- **Independent Quantity:** Hours worked (30 to 35 hours)
- **Dependent Quantity:** Weekly pay ($360 to $420)
- **Domain:** \( [30, 35] \)
- **Range:** \( [360, 420] \)