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2 years ago

Follow the steps to find the area of the shaded region. 14 46 14

Mathematics

1 answer:

konstantin123 [22]2 years ago

6 0

The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.

<h3>How to calculate the area of the sector?</h3>

The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is

A = (θ/360) πr² sq. units

<h3>How to calculate the area of a triangle with an angle?</h3>

The area of the triangle with measures of two sides and an angle between them is

A = 1/2 × a × b × sinC sq. units

Where a and b are the lengths of sides and ∠C is the angle between those sides.

<h3>Calculation:</h3>

It is given that,

The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².

Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,

Area of the shaded region = Area of the sector - Area of the triangle

⇒ 78.6794 - 70.4956

⇒ 8.1838 cm²

Therefore, the required area of the shaded region is 8.1838 sq. cm.

Learn more about the area of a sector here:

brainly.com/question/22972014

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In Grafton, a rural area in Vermont, the distance (in meters) between telephone poles has a uniform distribution between 40 and

coldgirl [10]

Answer:

a) 60% probability that the distance is environment friendly.

b) The mean of the distances between the telephone poles is 52.5 meters.

c) The standard deviation of the distance between the telephone poles is 7.22 meters.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

Uniform distribution between 40 and 65 meters.

This means that $a = 40, b = 65$

a) Any distance between poles greater than 50 meters is considered to be environment friendly. What is the probability that the distance is environment friendly?

This is $P(X > 50)$

We have that

$P(X \leq 50) + P(X > 50) = 1$

$P(X > 50) = 1 - P(X \leq 50)$

$P(X \leq 50) = \frac{50 - 40}{65 - 40} = 0.4$

$P(X > 50) = 1 - P(X \leq 50) = 1 - 0.4 = 0.6$

60% probability that the distance is environment friendly.

b) Find the mean of the distances between the telephone poles

The mean of the uniform distribution is

$M = \frac{a + b}{2}$

$M = \frac{a + b}{2} = \frac{40 + 65}{2} = 52.5$

c) Find the standard deviation of the distance between the telephone poles.

The standard deviation of the uniform distribution is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

$S = \sqrt{\frac{(65-40)^{2}}{12}} = 7.22$

5 0

4 years ago

In ΔOPQ, the measure of ∠Q=90°, PQ = 3.6 feet, and OP = 9.1 feet. Find the measure of ∠P to the nearest tenth of a degree.

svetlana [45]

Step-by-step explanation:

$\because \cos \: \angle P = \frac{PQ}{OP} \\ \\ \therefore \: \cos \: \angle P = \frac{3.6}{9.1} \\ \\ \therefore \: \cos \: \angle P = 0.3956 \\ \\ \therefore \: \cos \: \angle P = \cos \: 66.6966 \\ \\ \huge \red{ \boxed{\therefore \: \angle P = 66.7 \degree}}$

5 0

3 years ago

50 PINTS！！！！！！！！ PLEASE HELP QUICK!!!!!!!!!!! What is the slope of the line shown in the graph? (4 points) A coordinate plane is

seraphim [82]

Answer:

1 over 2

Step-by-step explanation:

Slope formula:

m = y₂ - y₁ / x₂ - x₁

Two points are given:

(2,2) and (0,1)

m = 1 - 2 / 0 - 2

m = -1 / -2

m = 1/2

7 0

3 years ago

Read 2 more answers

Find the area of the circle <br><br> r = 6 ft

Andru [333]

If the radius of the circle is 6 feet. Then the area of the circle will be 113.097 square feet.

<h3>What is a circle?</h3>

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The radius of the circle is 6 feet.

Then the area of the circle will be

Area = πr²

where r is the radius of the circle. Then we have

Area = π × 6²

Area = 36π

Area = 113.097 square feet

More about the circle link is given below.

brainly.com/question/11833983

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5 0

2 years ago

1. write an absolute value equation that has the solutions x=2 and x=9

Leviafan [203]

Well this might help it might not but |6-4|=x x=2

6 0

3 years ago