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pav-90 [236]
3 years ago
6

A teacher wants to build a scale model of the Earth and Pluto to compare their sizes. The Earth has a diameter of approximately

8000 miles and Pluto has a diameter of approximately 1500 miles. If the teacher builds a model of Earth with a diameter of 32 inches, what should be the diameter of her model of Pluto? Please explain the answer.
a) 5 1/3 inches
b) 6 inches
c) 6 3/2 inches
d) 8 inches
Mathematics
1 answer:
koban [17]3 years ago
3 0

Answer:

B

Step-by-step explanation:

A scale model means that the ratios stay the same.

Therefore, Earth's diameter divided by Pluto's diameter is equal to the ratio of Earth's model's diameter divided by Pluto's model's diameter.

We can write this as

8000 / 1500 = 32/ Pluto's model's diameter. Representing Pluto's model's diameter as P, we can say

8000 / 1500 = 32 / P

multiply both sides by 1500 to remove a denominator

8000 = 32 * 1500 / P

multiply both sides by P to remove the other denominator

8000 * P = 32 * 1500

divide both sides by 8000 to isolate the P

P = 32 * 1500/8000

= 6 inches

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Now, how to go about doing this: 

In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared. 

For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:
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8 0
3 years ago
Jen picked 3/4 of a gallon of strawberries in half an hour.If she keeps picking strawberries at the same time, how many gallons
MrRa [10]

Answer:

Number of gallons of strawberries will she have picked in 2 hours is, 3

Step-by-step explanation:

Unit rate defined as the rate are expressed as a quantity of 1, such as 4 feet per second or 6 miles per hour, they are called unit rates.

Given the statement: Jen picked 3/4 of a gallon of strawberries in half an hour.

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Unit rate per hour = \frac{\frac{3}{4} }{\frac{1}{2}} =\frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}

To find the number of gallons will she have picked in 2 hours.

Number of gallons = unit rate per hours \times 2

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Therefore, the number of gallons will she have picked in 2 hours is, 3

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Answer:

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Step-by-step explanation:

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2 years ago
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Answer:

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Step-by-step explanation:

80 is twice as much as 40. 5 minutes is twice as long as 2 1/2 minutes. Her unit rate never changed.

8 0
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