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

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 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.

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.

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 Earth and Neptune.

1. For Earth:

   • Model distance: 7 inches
   • Actual distance: 91.549 million miles

   Ratio for Earth = Model distance / Actual distance = 7 inches / 91.549 million miles

2. For Neptune:

   • Model distance: 19 inches
   • Actual distance: 2,780.5 million miles

   Ratio for Neptune = Model distance / Actual distance = 19 inches / 2,780.5 million miles

Now we compare the two ratios:

• Earth ratio = 7 / 91.549
• Neptune ratio = 19 / 2780.5

To check if they are proportional:

• Calculate both ratios and see if they are equal.

1. Earth ratio: \( \frac{7}{91.549} \approx 0.0763 \)

2. Neptune ratio: \( \frac{19}{2780.5} \approx 0.00683 \)

Since the two ratios are not equal, the model distances are not proportional to the actual dimensions of the solar system.

Therefore, the correct answer is:

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