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Travka [436]
3 years ago
8

Circle V is shown. Line segment T V is a radius with length 14 feet.

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

We have been given graph of circle V with radius 14 feet. We are asked to find the area of the circle V.

We will use area of circle formula to solve our given problem.

A=\pi r^2, where r represents radius of circle.

Upon substituting r=\text{14 ft} in above formula, we will get:

A=\pi(14\text{ ft})^2

A=\pi(14)^2\text{ ft}^2

A=\pi\cdot 196\text{ ft}^2

A=196\pi\text{ ft}^2

Therefore, the area of the circle V is 196\pi square feet and option 'c' is the correct choice.

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A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili
Fofino [41]

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

18x = 3*31

x = \frac{31*3}{18}

x = 5.17

So \mu = 5.17

Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

So

P(X \leq 3) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X \leq 3)

In which

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057

P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294

P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760

P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309

So

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242

Finally

P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

8 0
4 years ago
Find the area of the shape
Free_Kalibri [48]

Answer:

14 units²

Step-by-step explanation:

The area of the shape = area of a triangle

Area of triangle = ½ × base × height

base = 7

height = 4

Plug in the value into the formula:

Area = ½ × 7 × 4

Area = ½ × 28

Area = 14 units²

7 0
3 years ago
The length of a rectangular computer chip is 22 x 10 cm and the width is 7 x 104 cm. Explain how to
mash [69]

Answer:

area = 160160 inches²

area = 1.6016 × 10⁵ inches²

Step-by-step explanation:

The length of the rectangular computer chip is 22 × 10 cm and the width is 7 × 104 cm .  

The area of the rectangular computer chip is the product of the length and the width.

area = length × width

area = (22 × 10) × (7 × 104)  

area = 220 × 728

area = 160160  inches²

In scientific notation

area = 1.6016 × 10⁵ inches²

160160 is written as 1.6016 × 10⁵ because 1.60160 × 100000 = 1.6016 × 10⁵

7 0
3 years ago
In the diagram below of circle O, the area of the shaded sector AOC is 12pi in^2 and the length of OA I'd 6 inches. Determine an
blagie [28]
Area of a circle for (360degrees) = pi*(r^2) 
Area of part of a circle with angle θ=(θ/360)*(pi*)*(r^2)
<span>(θ/360)*pi*(6^2)=12*pi
</span>solving, <span>θ=(12/36)*360
</span><span>θ=120 degress
</span>
5 0
4 years ago
What is 87.319 to the nearest tenth?
EleoNora [17]

Answer:

87.3

The answer to get 87.3 is to see if the number in the hundredths  place (this case 1) is bigger or the same as the value of 5. If it is round the tenth up but if not then cut the rest of the numbers off.      

4 0
3 years ago
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