In this situation involving Juan's earnings, we can identify the independent and dependent quantities as follows:
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Independent Quantity: The number of hours Juan works per week (let’s denote this as \( h \)), since he can choose how many hours to work up to a maximum of 30 hours.
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Dependent Quantity: Juan's earnings per week (let’s denote this as \( E \)), which depend on the number of hours worked. His earnings can be calculated using the formula: \[ E = 11h \] where \( 11 \) is the hourly wage.
Reasonable Domain and Range Values
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Domain (the possible values for the independent variable, \( h \)):
- Since Juan works at most 30 hours per week, the number of hours he can work ranges from 0 to 30. Thus, \[ \text{Domain: } h \in [0, 30] \]
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Range (the possible values for the dependent variable, \( E \)):
- Juan's earnings can be calculated from his hours worked. The minimum he can earn is when he works 0 hours: \[ E = 11 \times 0 = 0 \]
- The maximum he can earn is when he works 30 hours: \[ E = 11 \times 30 = 330 \]
- Therefore, the range of his earnings is: \[ \text{Range: } E \in [0, 330] \]
Summary
- Independent Quantity: Number of hours worked per week (\( h \))
- Dependent Quantity: Earnings per week (\( E \))
- Domain: \( h \in [0, 30] \)
- Range: \( E \in [0, 330] \)