To determine if the values of \( x \) (the amount of money a family donates) and \( y \) (the matching contribution from local businesses) have a proportional relationship, we can check if the ratio \( \frac{y}{x} \) is constant for all the given pairs of \( (x, y) \).
Let's calculate the ratios:
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For \( x = 20 \), \( y = 11 \): \[ \frac{y}{x} = \frac{11}{20} = 0.55 \]
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For \( x = 40 \), \( y = 22 \): \[ \frac{y}{x} = \frac{22}{40} = 0.55 \]
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For \( x = 60 \), \( y = 33 \): \[ \frac{y}{x} = \frac{33}{60} = 0.55 \]
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For \( x = 100 \), \( y = 55 \): \[ \frac{y}{x} = \frac{55}{100} = 0.55 \]
Since the ratio \( \frac{y}{x} \) is constant at \( 0.55 \) for all pairs, we conclude that there is a proportional relationship between \( x \) and \( y \).
Therefore, the answer is: Yes.