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3 years ago

Jamie ran 1/5 of a relay. She ran 3/4 of a mile. How long was the relay?

Mathematics

1 answer:

topjm [15]3 years ago

4 0

(1/5) times (the relay) = 3/4 mile

Multiply each side by 5
The relay = (5) x (3/4) = 15/4 = <span>3.75 miles.</span>

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The circumference of Circle K is pi. The circumference of Circle L is 4xpi.

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Ratio of circumferences: $\displaystyle\frac{1}{4}$

Ratio of radii: $\displaystyle\frac{1}{4}$

Ratio of areas: $\displaystyle\frac{1}{16}$

Step-by-step explanation:

Hi there!

We are given:

- The circumference of Circle K is $\pi$

- The circumference of Circle L is $4\pi$

Therefore, the ratio of their circumferences would be:

$\displaystyle\frac{\pi}{4\pi}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for circumference is $C=2\pi r$ , where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is $\pi$ , or $1\pi$ , then its radius is $\displaystyle\frac{1}{2}$ .

If the circumference of Circle L is $4\pi$ , then its radius is $\displaystyle\frac{4}{2}$ , which is 2.

Therefore the ratio their radii would be:

$\displaystyle\frac{\frac{1}{2}}{{2}}$ ⇒ $\displaystyle\frac{1}{2}*\frac{1}{2}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for area is:

$A=\pi r^2$

First, let's find the area of Circle K:

$A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi$

Now, let's find the area of Circle L:

$A=\pi (2)^2\\A = 4\pi$

Therefore, the ratio of their areas would be:

$\displaystyle\frac{\frac{1}{4}\pi}{4\pi}$ ⇒ $\displaystyle\frac{\frac{1}{4}}{4}$ ⇒ $\displaystyle\frac{1}{4} * \frac{1}{4}$ ⇒ $\displaystyle\frac{1}{16}$ when simplified