To determine if the sets of ratios are proportions, we can equate the ratios and check if they are equal.
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For the ratio \( \frac{2.25}{10} = \frac{9}{40} \):
First, calculate \( \frac{2.25}{10} \): \[ \frac{2.25}{10} = 0.225 \] Now calculate \( \frac{9}{40} \): \[ \frac{9}{40} = 0.225 \] Since \( 0.225 = 0.225 \), this set of ratios is a proportion.
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For the ratio \( \frac{2.5}{10} = \frac{90}{40} \):
First, calculate \( \frac{2.5}{10} \): \[ \frac{2.5}{10} = 0.25 \] Now calculate \( \frac{90}{40} \): \[ \frac{90}{40} = 2.25 \] Since \( 0.25 \neq 2.25 \), this set of ratios is not a proportion.
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For the ratio \( \frac{2.25}{12} = \frac{90}{40} \):
First, calculate \( \frac{2.25}{12} \): \[ \frac{2.25}{12} = 0.1875 \] Now calculate \( \frac{90}{40} \) again: \[ \frac{90}{40} = 2.25 \] Since \( 0.1875 \neq 2.25 \), this set of ratios is not a proportion.
Conclusion: Only the first set of ratios \( \frac{2.25}{10} = \frac{9}{40} \) is a proportion. Therefore, the correct answer is:
None of these sets of ratios is a proportion. (is incorrect in terms of the first ratio; it is indeed a proportion)
The correct response would summarize: The first set of ratios \( \frac{2.25}{10} = \frac{9}{40} \) is a proportion. The other two sets are not.