In a model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, are the model’s distances proportional to the actual dimensions of the solar system?(1 point)

Question

Responses

No, because the model is in inches and the actual distances are in millions of miles.
No, because the model is in inches and the actual distances are in millions of miles.

Yes, because the ratios can be simplified, and those ratios are equal.
Yes, because the ratios can be simplified, and those ratios are equal.

No, because the ratios of model length to actual distance are different for the two planets.
No, because the ratios of model length to actual distance are different for the two planets.

Yes, because the ratios of model length to actual distance are equal for the two planets.
Yes, because the ratios of model length to actual distance are equal for the two planets.
Skip to navigation

Answer 1

To determine if the model's distances are proportional to the actual distances, we need to compare the ratios of the model distances to the actual distances for both the Earth and Neptune.

1. Model Distance from Sun to Earth: 7 inches

   • Actual Distance from Sun to Earth: 91.549 million miles

2. Model Distance from Sun to Neptune: 19 inches

   • Actual Distance from Sun to Neptune: 2,780.5 million miles

Now, we can calculate the ratios for both:

• Earth Ratio: \[ \text{Ratio for Earth} = \frac{\text{Model Distance}}{\text{Actual Distance}} = \frac{7 \text{ inches}}{91.549 \text{ million miles}} \]

• Neptune Ratio: \[ \text{Ratio for Neptune} = \frac{19 \text{ inches}}{2,780.5 \text{ million miles}} \]

Let's compute those ratios:

1. Earth Ratio Calculation: \[ \text{Ratio for Earth} = \frac{7}{91.549} \approx 0.0764 \]

2. Neptune Ratio Calculation: \[ \text{Ratio for Neptune} = \frac{19}{2,780.5} \approx 0.00683 \]

Since the ratios \(0.0764\) and \(0.00683\) are not equal, the model's distances are not proportional to the actual distances.

Thus, the correct response is:

No, because the ratios of model length to actual distance are different for the two planets.