All categories

3 years ago

Find the area of the shape with a radius of 2

Mathematics

1 answer:

Ahat [919]3 years ago

4 0

Answer:

A = pi units^2

or A = 3.14 units^2

Step-by-step explanation:

This is 1/4th of a circle. Take the area of a circle and multiply by 1/4

A = 1/4 pi r^2

The radius is 2

A = 1/4 pi *2^2

A = 1/4 *pi * 4

A = pi

If we use the approximation that pi = 3.14

A = 3.14

You might be interested in

Crash Hospital Costs. A study was conducts to estimate hospital costs for accident victims who wore seat belts. Twenty randomly

kvv77 [185]

Answer:

a) The 99% confidence interval would be given by (5004.168;12603.832)

b) For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =9004$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=5629 represent the sample standard deviation

n=20 represent the sample size

2) Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=20-1=19$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,19)".And we see that $t_{\alpha/2}=2.86$

Now we have everything in order to replace into formula (1):

$9004-2.86\frac{5629}{\sqrt{20}}=5004.168$

$9004+2.86\frac{5629}{\sqrt{20}}=12603.832$

So on this case the 99% confidence interval would be given by (5004.168;12603.832)

3) Part b

For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I

7 0

3 years ago

In Vancouver, British Columbia, the probability of rain during a winter day is 0.42, for a spring day is 0.23, for a summer day

nadezda [96]

Answer:

31.82% probability that this day would be a winter day

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening

In this question:

Event A: Rain

Event B: Winter day

Probability of rain:

0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).

$P(A) = 0.42*0.25 + 0.23*0.25 + 0.16*0.25 + 0.51*0.25 = 0.33$

Intersection:

Rain on a winter day, which is 0.42 of 0.25. So

$P(A \cap B) = 0.42*0.25 = 0.105$

If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?

$P(B|A) = \frac{0.105}{0.33} = 0.3182$

31.82% probability that this day would be a winter day

6 0

3 years ago

Find the area a of the triangle whose sides have the given lengths. a = 20, b = 15, c = 25 a =?

PIT_PIT [208]

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

<h3>What is Heron's formula?</h3>

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}\\$

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = $\frac{a+b+c}{2}$

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}\\$

Area of the triangle = $\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150$

Thus, the area of a triangle is 150.

Learn more about the Area of triangles here:

brainly.com/question/11952845

#SPJ1

3 0

2 years ago

A school spent $2,587.50 on agendas for its 1,150 students. what is the unit price per agenda

damaskus [11]

For this you can just use a calculator and divide 2587.5 by 1150.

You should get $2.25 for the unit price. Hope this helped ^-^

7 0

3 years ago

A worker is paid $0.05 on the first day, $0.10 on the second day, $0.20 on the third day, $0.40 on the fourth day, and so on. Ho

Novay_Z [31]

This is a geometric sequence with a common ratio of 2

an = a1 * r^(n - 1)
n = term to find = 21
a1 = first term = 0.05
r = common ratio = 2
now we sub
a21 = 0.05 * 2^(21 - 1)
a21 = 0.05 * 2^20
a21 = 0.05 * 1048576
a21 = 52428.80 <==== after working 21 days

7 0

4 years ago