Rates and Measurement Unit Test%0D%0A1 of 151 of 15 Items%0D%0A%0D%0AQuestion%0D%0AIn 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)%0D%0AResponses%0D%0A%0D%0ANo, because the model is in inches and the actual distances are in millions of miles.%0D%0ANo, because the model is in inches and the actual distances are in millions of miles.%0D%0A%0D%0ANo, because the ratios of model length to actual distance are different for the two planets.%0D%0ANo, because the ratios of model length to actual distance are different for the two planets.%0D%0A%0D%0AYes, because the ratios of model length to actual distance are equal for the two planets.%0D%0AYes, because the ratios of model length to actual distance are equal for the two planets.%0D%0A%0D%0AYes, 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.
To determine if the model's distances are proportional to the actual dimensions of the solar system, we need to compare the ratios of the model's distances to the actual distances for both Earth and Neptune.
Let's first find the ratio of the model distance to the actual distance for Earth:
Model ratio for Earth = Model distance / Actual distance
Model ratio for Earth = 7 inches / 91.549 million miles
Now let's find the ratio of the model distance to the actual distance for Neptune:
Model ratio for Neptune = Model distance / Actual distance
Model ratio for Neptune = 19 inches / 2780.5 million miles
Now we need to compare these ratios to determine if they are equal or not.
Looking at the options provided:
- "No, because the model is in inches and the actual distances are in millions of miles." is incorrect because the units do not determine if the ratios are equal or not.
- "No, because the ratios of model length to actual distance are different for the two planets." is correct because the ratios for Earth and Neptune are different.
- "Yes, because the ratios of model length to actual distance are equal for the two planets." is incorrect because the ratios for Earth and Neptune are different.
- "Yes, because the ratios can be simplified, and those ratios are equal." is incorrect because simplifying the ratios does not determine if they are equal or not.
Therefore, the correct answer is: "No, because the ratios of model length to actual distance are different for the two planets."