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

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)

Answer 1

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

For Earth:
Model's distance = 7 inches
Actual distance = 91.549 million miles

Ratio = Model's distance / Actual distance = 7 inches / 91.549 million miles

For Neptune:
Model's distance = 19 inches
Actual distance = 2,780.5 million miles

Ratio = Model's distance / Actual distance = 19 inches / 2,780.5 million miles

To determine if the ratios are proportional, we need to compare the ratio for Earth to the ratio for Neptune:

Ratio for Earth / Ratio for Neptune = (7 inches / 91.549 million miles) / (19 inches / 2,780.5 million miles)

Simplifying, we get:

Ratio for Earth / Ratio for Neptune = (7 inches * 2,780.5 million miles) / (19 inches * 91.549 million miles)
= 194.5335 million inches miles / 1731.931 million inches miles
= 0.11222

Since the ratio of the model's distance to the actual distance is not equal for Earth and Neptune, the model's distances are not proportional to the actual dimensions of the solar system.

Answer 2

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

For the model's distance from the sun to Earth:
Model's distance from the sun to Earth = 7 inches

Actual distance from the sun to Earth = 91.549 million miles

We need to convert the actual distance from miles to inches for comparison.
1 mile = 63,360 inches

Actual distance from the sun to Earth (in inches) = 91.549 million miles * 63,360 inches/mile

Now, let's calculate the ratio:
Ratio = Model's distance from the sun to Earth / Actual distance from the sun to Earth (in inches)

For the model's distance from the sun to Neptune:
Model's distance from the sun to Neptune = 19 inches

Actual distance from the sun to Neptune = 2,780.5 million miles

We need to convert the actual distance from miles to inches for comparison.
Actual distance from the sun to Neptune (in inches) = 2,780.5 million miles * 63,360 inches/mile

Now, let's calculate the ratio:
Ratio = Model's distance from the sun to Neptune / Actual distance from the sun to Neptune (in inches)

Once we calculate the ratios for both Earth and Neptune, if they are the same or very close, then the model's distances are proportional to the actual dimensions of the solar system. If the ratios differ significantly, then the model's distances are not proportional to the actual dimensions.

Answer 3

To determine if the model's distances are proportional to the actual dimensions of the solar system, we can set up a proportion using the given information.

Let's represent the model's distances from the sun to Earth and Neptune as "E" and "N" respectively, and the actual distances as "E'" and "N'".

We can set up the proportion as follows:

E/E' = N/N'

Now, let's substitute the given values:

E/91.549 million miles = N/2,780.5 million miles

Since both E and N are given in inches in the model, we need to convert the actual distances to inches for comparison.

1 million miles = 63,360,000 inches (approximately)

So, we can rewrite the proportion as:

E/91.549 million miles = N/2,780.5 million miles
E/91.549 million miles = N/2,780.5 million miles
E/91.549 * 63,360,000 inches = N/2,780.5 * 63,360,000 inches
E/5,798,293,440,000 inches = N/176,038,680,000 inches

Now we can compare the model's proportions to the actual proportions:

7 inches/5,798,293,440,000 inches = 19 inches/176,038,680,000 inches

To simplify the comparison, we can divide both sides of the equation by 1,000,000:

7/5,798,293.44 = 19/176,038.68

This simplifies to:

0.0000012068 ≈ 0.0001079553

The two values are not equal, so the model's distances are not proportional to the actual dimensions of the solar system.