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3 years ago

Find the radius of a circle with an area of 380 in².

Mathematics

1 answer:

Likurg_2 [28]3 years ago

5 0

Answer:

11 inches

Step-by-step explanation:

The area of a circle can be found using:

$a=\pi r^{2}$

We already know that the area is 380, so we can substitute 380 in for a.

380= $\pi r^2$

Now, we need to find the radius. To do this, we need to get r by itself

First, divide both sides by pi

$380/\pi =\pi r^2/\pi$

120.95775675=r^2

Since r is being squared, we need to take the square root of both sides

$\sqrt{120.95775675}=\sqrt{r^2}$

10.9980796846=r

If we round to nearest whole number, our radius is 11 inches

You might be interested in

“3 less than the quotient of y and 4”

Bingel [31]

Answer:

Expression:

$\dfrac{y}{4}-3$

Value where y = 20

Step-by-step explanation:

Let's take a look at the sentence:

3 less than the quotient of y and 4

3 less indicates that you will subtract

- 3

Quotient means the result of division.

$\dfrac{y}{4}$

So if we combine the two, it says 3 less than the quotient so we subtract 3 from the quotient:

$\dfrac{y}{4}-3$

So if y = 20, we just substitute the y with 20

$\dfrac{y}{4}-3$

$\dfrac{20}{4}-3$

$5-3=2$

8 0

3 years ago

Greg's football team played 16 games this season and won 12 of them.

ruslelena [56]

You need to divide 12 by 16 to get a decimal that you can turn into a percent. 12 ÷ 16 = .75. You turn that .75 into 75%. Greg's football team won 75% of their games.

4 0

3 years ago

Read 2 more answers

solve the formula for h, and find the height of a trapezoid with an area of 60 m2 and bases of 8m and 12m

Allushta [10]

6, the formula is (b1+b2/2)*h
8+12/2=10
10*h=60 so h=6

3 0

3 years ago

A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago

Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with

Stels [109]

Answer:

P(X > 25) = 0.69

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively.

This means that $\mu = 26, \sigma = 2$

Find P(X>25)

This is 1 subtracted by the pvalue of Z when X = 25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{25 - 26}{2}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.31

1 - 0.31 = 0.69.

P(X > 25) = 0.69

4 0

2 years ago