To determine if the given ratios form a proportion, we need to check if the cross products are equal. Two ratios a/b and c/d form a proportion if \( a \cdot d = b \cdot c \).
Let's evaluate the two options given:
Option A: \( \frac{2.25}{12} \) and \( \frac{90}{40} \)
Cross multiplication:
\[ 2.25 \cdot 40 = 90 \cdot 12 \]
Calculating both sides:
Left side: \[ 2.25 \cdot 40 = 90 \]
Right side: \[ 90 \cdot 12 = 1080 \]
Since \( 90 \neq 1080 \), this is not a proportion.
Option B: \( \frac{2.25}{10} \) and \( \frac{9}{40} \)
Cross multiplication:
\[ 2.25 \cdot 40 = 9 \cdot 10 \]
Calculating both sides:
Left side: \[ 2.25 \cdot 40 = 90 \]
Right side: \[ 9 \cdot 10 = 90 \]
Since \( 90 = 90 \), this is a proportion.
Option D: \( \frac{2.5}{10} \) and \( \frac{90}{40} \)
Cross multiplication:
\[ 2.5 \cdot 40 = 90 \cdot 10 \]
Calculating both sides:
Left side: \[ 2.5 \cdot 40 = 100 \]
Right side: \[ 90 \cdot 10 = 900 \]
Since \( 100 \neq 900 \), this is not a proportion.
Conclusion:
The only set that forms a proportion is option B: \( \frac{2.25}{10} = \frac{9}{40} \).
So the correct answer is: B. \( \frac{2.25}{10} = \frac{9}{40} \).
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