To determine if the table shows a proportional relationship, we need to check whether the ratio of $ earned to hours is constant for each pair.
Let's calculate the ratios for each pair:
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For \(2\) hours: \[ \text{Ratio} = \frac{15}{2} = 7.5 \]
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For \(3\) hours: \[ \text{Ratio} = \frac{22.50}{3} = 7.5 \]
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For \(4\) hours: \[ \text{Ratio} = \frac{30}{4} = 7.5 \]
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For \(5\) hours: \[ \text{Ratio} = \frac{45}{5} = 9 \]
Now, we can see that the ratios are:
- For \(2\) hours: \(7.5\)
- For \(3\) hours: \(7.5\)
- For \(4\) hours: \(7.5\)
- For \(5\) hours: \(9\)
The ratio becomes \(9\) for \(5\) hours, which does not match the other ratios. Therefore, the tables do not show a consistent proportional relationship.
As a result, there is no constant of proportionality for the given table.