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 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.
Yes, because the ratios can be simplified, and those ratios are equal.
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 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.
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 length to the actual distance for both Earth and Neptune.
First, let's calculate the ratio of the model length to the actual distance for Earth:
Model ratio for Earth = Model distance from the sun to Earth / Actual distance from the sun to Earth = 7 inches / 91.549 million miles
Next, let's calculate the ratio of the model length to the actual distance for Neptune:
Model ratio for Neptune = Model distance from the sun to Neptune / Actual distance from the sun to Neptune = 19 inches / 2,780.5 million miles
Now, let's simplify both ratios:
Model ratio for Earth = 7 inches / 91.549 million miles
Model ratio for Neptune = 19 inches / 2,780.5 million miles
To check if the ratios can be simplified and if those ratios are equal, we can simplify both ratios:
Model ratio for Earth = 1 inch / 13.078 million miles
Model ratio for Neptune = 1 inch / 146.337 million miles
Since the simplified ratios are not equal, the model's distances are not proportional to the actual dimensions of the solar system. Therefore, the correct response is:
No, because the ratios of model length to actual distance are different for the two planets.