To determine if the model’s distances from the sun to Earth and Neptune are proportional to the actual distances, we need to compare the ratios of model distances to actual distances for both Earth and Neptune.
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The distance from the sun to Earth in the model is 7 inches, and the actual distance is 91.549 million miles.
- Ratio for Earth: \[ \text{Ratio}_{\text{Earth}} = \frac{\text{Model Distance}}{\text{Actual Distance}} = \frac{7 \text{ inches}}{91.549 \text{ million miles}} \]
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The distance from the sun to Neptune in the model is 19 inches, and the actual distance is 2,780.5 million miles.
- Ratio for Neptune: \[ \text{Ratio}_{\text{Neptune}} = \frac{\text{Model Distance}}{\text{Actual Distance}} = \frac{19 \text{ inches}}{2,780.5 \text{ million miles}} \]
Next, calculate the two ratios:
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For Earth: \[ \text{Ratio}_{\text{Earth}} = \frac{7}{91.549} \approx 0.0763 \]
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For Neptune: \[ \text{Ratio}_{\text{Neptune}} = \frac{19}{2,780.5} \approx 0.00684 \]
Now we see that the ratios \(0.0763\) and \(0.00684\) are not equal. Therefore, the model's distances are not proportional to the actual dimensions of the solar system.
The correct response is: No, because the ratios of model length to actual distance are different for the two planets.