All categories

4 years ago

A circle has an area of 225pift2 find the radius of the circle and find the diameter and circumference of the circle

Mathematics

1 answer:

RideAnS [48]4 years ago

6 0

Answer:

radius: 15 ft
diameter: 30 ft
circumference: 30π ft

Step-by-step explanation:

The area is given in terms of the radius as ...

A = πr^2

so we can find the radius as ...

r = √(A/π)

For your circle, the radius is ...

r = √(225π ft^2/π) = 15 ft

The diameter is twice the radius, so is ...

d = 2r = 2·15 ft = 30 ft

And the circumference is π times the diameter:

C = πd = π·30 ft = 30π ft

You might be interested in

Which of the following are solutions to | x + 4 |= 3x-5

andrey2020 [161]

X= 9/2

X= 4.5

X= 4 1/2

7 0

3 years ago

Read 2 more answers

Kara owns 3 2⁄7 acres of farming land. She grows carrots on 1⁄6 of the land. On how many acres of land does Kara grow carrots?

kotegsom [21]

Answer:

can i have brainliest plssssssssssss im new here

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

A Ferris wheel can accommodate 45 people in 25 minutes. How many people could ride the Ferris wheel in 2 hours? What was that ra

Sliva [168]

Answer:

5400

Step-by-step explanation:

60 min=1 hour

120 min=2 hr

120 x 45=5400

4 0

3 years ago

Read 2 more answers

The decimal -2.97 is the solution to which subtraction problem?

Sladkaya [172]

Answer:

-6.1 - (-3.13) = -2.97

Step-by-step explanation:

two negative symbols = a positive.

7 0

3 years ago

Let X be the number of the cars being repaired at a repair shop. We have the following information:

worty [1.4K]

Answer:

(a) Sample Space

$S = \{0,1,2,3\}$

(b) PMF

$\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {P(x)} & {1/3} & {1/6} & {1/6} & {1/3} \ \end{array}$

(c) CDF

$\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {F(x)} & {1/3} & {1/2} & {2/3} & {1} \ \end{array}$

Step-by-step explanation:

Solving (a): The sample space

From the question, we understand that at most 3 cars will be repaired.

This implies that, the number of cars will be 0, 1, 2 or 3

So, the sample space is:

$S = \{0,1,2,3\}$

Solving (b): The PMF

From the question, we have:

$P(2) = P(1)$

$P(0) = P(3)$

$P(1\ or\ 2) = 0.5 * P(0\ or\ 3)$

$P(1\ or\ 2) = 0.5 * P(0\ or\ 3)$ can be represented as:

$P(1) + P(2) = 0.5[P(0) + P(3)]$

Substitute $P(2) = P(1)$ and $P(0) = P(3)$

$P(1) + P(1) = 0.5[P(0) + P(0)]$

$2P(1) = 0.5[2P(0)]$

$2P(1) = P(0)$

$P(0)= 2P(1)$

Also note that:

$P(0) + P(1) + P(2) + P(3) = 1$

Substitute $P(2) = P(1)$ and $P(0) = P(3)$

$P(0) + P(1) + P(1) + P(0) = 1$

$2P(1) + 2P(0) = 1$

Substitute $P(0)= 2P(1)$

$2P(1) + 2*2P(1) = 1$

$2P(1) + 4P(1) = 1$

$6P(1) = 1$

Solve for P(1)

$P(1) = \frac{1}{6}$

To calculate others, we have:

$P(2) = P(1)$

$P(2) = P(1) = \frac{1}{6}$

$P(0)= 2P(1)$

$P(0) =2 * \frac{1}{6}$ $P(0) =\frac{1}{3}$

$P(3) = P(0) =\frac{1}{3}$

Hence, the PMF is:

$\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {P(x)} & {1/3} & {1/6} & {1/6} & {1/3} \ \end{array}$

<em>See attachment (1) for histogram</em>

Solving (c): The CDF ; F(x)

This is calculated as:

$F(x) = P(X \le x) =\sum\limit^{3}_{x_i \le x} P(x_i)$

For x = 0;

We have:

$P(X \le 0) = P(0)$

$P(X \le 0) = 1/3$

For x = 1

$P(X \le 1) = P(0) + P(1)$

$P(X \le 1) = 1/3 + 1/6$

$P(X \le 1) = 1/2$

For x = 2

$P(X \le 2) = P(0) + P(1) + P(2)$

$P(X \le 2) = 1/3 + 1/6 + 1/6$

$P(X \le 2) = 2/3$

For x = 3

$P(X \le 3) = P(0) + P(1) + P(2) + P(3)$

$P(X \le 3) = 1/3 + 1/6 + 1/6 + 1/3$

$P(X \le 3) = 1$

Hence, the CDF is:

$\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {F(x)} & {1/3} & {1/2} & {2/3} & {1} \ \end{array}$

<em>See attachment (2) for histogram</em>

6 0

3 years ago