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
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.
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.
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.
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.
Let's calculate the ratios for each planet:
For Earth:
Model ratio = Model distance / Actual distance = 7 inches / 91.549 million miles
For Neptune:
Model ratio = Model distance / Actual distance = 19 inches / 2,780.5 million miles
Now, let's simplify these ratios:
For Earth:
Model ratio = (7 inches) / (91.549 million miles) = (1 inch) / (13.0784 million miles)
For Neptune:
Model ratio = (19 inches) / (2,780.5 million miles) = (1 inch) / (146.3421 million miles)
Comparing these simplified ratios, we can see that they are different. The ratio for Earth is 1 inch to approximately 13.0784 million miles, while the ratio for Neptune is 1 inch to approximately 146.3421 million miles.
Therefore, the correct answer is: No, because the ratios of model length to actual distance are different for the two planets.