To determine if the ratios \( 33 \text{ packages} : 41 \text{ hours} \) and \( 46 \text{ packages} : 53 \text{ hours} \) are equivalent, we can express each ratio as a fraction and compare them:
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For the first ratio: \[ \text{Ratio 1} = \frac{33 \text{ packages}}{41 \text{ hours}} \approx 0.8049 \]
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For the second ratio: \[ \text{Ratio 2} = \frac{46 \text{ packages}}{53 \text{ hours}} \approx 0.8679 \]
Now, let's check if the two ratios are equal by cross-multiplying:
\[ 33 \times 53 \quad \text{and} \quad 41 \times 46 \]
Calculating each:
- \( 33 \times 53 = 1749 \)
- \( 41 \times 46 = 1886 \)
Since \( 1749 \neq 1886 \), the two ratios \( 33 : 41 \) and \( 46 : 53 \) are not equivalent.