Question

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) 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 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. 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 can be simplified, and those ratios are equal.

Answer 1

Answer: To determine whether the model's distances are proportional to the actual dimensions of the solar system, we need to compare the ratios of model length to actual distance for both Earth and Neptune.

For Earth:

Model distance: 7 inches

Actual distance: 91.549 million miles

For Neptune:

Model distance: 19 inches

Actual distance: 2,780.5 million miles

Now, calculate the ratios for both planets:

For Earth: 7 inches / 91.549 million miles

For Neptune: 19 inches / 2,780.5 million miles

Now, let's simplify these ratios:

For Earth: 7 / 91.549 = 0.076

For Neptune: 19 / 2,780.5 ≈ 0.00683

The ratios are not equal. Therefore, the model's distances are not proportional to the actual dimensions of the solar system. So, the correct response is:

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

Answer 2

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

Explanation:

To determine if the model's distances are proportional to the actual dimensions of the solar system, we need to compare the ratios of model length to actual distance for the two planets, Earth and Neptune.

Earth

• Model distance from the sun to Earth = 7 inches
• Actual distance from the sun to Earth = 91.549 million miles

Therefore, the ratio of model length to actual distance for Earth is:

`\sf (Model\;length)/(Actual\;distance)=(7\;in)/(91.549\;million\;miles)=7.65 * 10^(-8)\;in/mile`

Neptune

• Model distance from the sun to Neptune = 19 inches
• Actual distance from the sun to Neptune = 2,780.5 million miles

Therefore, the ratio of model length to actual distance for Neptune is:

`\sf (Model\;length)/(Actual\;distance)=\sf (19\;in)/(2780.5\;million\;miles)=6.83 * 10^(-9)\;in/mile`

As the two ratios are not equal, the model's distances are not proportional to the actual dimensions of the solar system. Therefore, the correct answer is:

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