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2 years ago

The diameter of a circle is 22 miles. What is the circle's area? Use 3.14 for pi.. Single choice.

Mathematics

1 answer:

Sonbull [250]2 years ago

6 0

Answer:

379.94 mi²

Step-by-step explanation:

The area of a circle can be figured out with this formula: πr² (3.14 is π here, as it says in the directions).

We know the diameter is 22 miles. Divide that by 2 to get a radius of 11 miles.

The equation now becomes

3.14(11²)

11 squared is 121.

3.14(121)

I recommend splitting the 121 into 100, 20, and 1.

(3.14 * 100) + (3.14 * 20) + (3.14 * 1)

Multiply 3.14 by 100, 20, and 1.

314 + 62.8 + 3.14

Add 314 and 62.8.

376.8 + 3.14

Add 376.8 and 3.14

379.94 mi² is the area of a circle with a 22-mile diameter.

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A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb

Maksim231197 [3]

Answer:

a) $P(X = 1) = 0.38742$

b) $P(X = 3) = 0.05740$

c) $P(X = 9) = 0.00000$

d) $P(X \geq 5) = 0.00163$

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

$P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837$

Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

3 0

3 years ago

Help me find the slope

shusha [124]

Answer:

-3/2

Step-by-step explanation:

Slope is defined as $\frac{rise}{run}$ ,

So the line goes down 6 instead of rising, making the rise negative: -6

The line goes over 4, making the run: 4

So -6/4 or -3/2

7 0

3 years ago

Read 2 more answers

Please help me<br> Sooo confused!!!

SashulF [63]

Well let's say x = -1000
That's what I would do

8 0

3 years ago

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Please help you kind people

mafiozo [28]

Answer:

All I know is that the first picture is 8

Step-by-step explanation:

I know because one times eight is eight so um yeah

5 0

2 years ago

What is value of x? <br> See picture

morpeh [17]

Answer:

x = 71

Step-by-step explanation:

Since 2 sides of the triangle are congruent then the triangle is isosceles.

Thus the 2 base angles are congruent

The sum of the 3 angles in the triangle = 180°, so

x = $\frac{180-38}{2}$ = $\frac{142}{2}$ = 71

6 0

3 years ago

Read 2 more answers