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3 years ago

What is the exact area of a circle with a diameter of 18 feet?

1 answer:

7 0

The formula for the area of a circle is

$\pi r^{2}$

We know the diameter, and the radius is half of the diameter. So the radius is 9. Now we plug that into the formula.

$\pi 9^{2} =81 \pi$

So the answer is B, 81 pi square feet

You might be interested in

Rina is 6x+3/8 feet tall and Ryan is 5x+1/8 feet tall. How much taller is Rina than Ryan

worty [1.4K]

Answer:

Rina is 1/4 feet taller than Ryan

Step-by-step explanation:

(height of Rina)-(height of Ryan)

6x+3/8-(5x+1/8)

6x+3/8-5x-1/8

x+3-1/8

x+2/8

x+1/4

8 0

4 years ago

Solve Ixl<13{(-13, 13}<br> {xl-13 [XIX<-13 or x 13)

zmey [24]

Answer:

-13 < X < 13

Step-by-step explanation:

It is given |X| < 13.

Note that we have: |x| < a, for any real number 'a', then it equals:

-a < X < a.

So, in this case, |X| < 13 should be equal to -13 < X < 13.

Hence, the answer.

7 0

3 years ago

The number of errors in a textbook follow a Poisson distribution with a mean of 0.03 errors per page. What is the probability th

maksim [4K]

Answer:

The probability that there are 3 or less errors in 100 pages is 0.648.

Step-by-step explanation:

In the information supplied in the question it is mentioned that the errors in a textbook follow a Poisson distribution.

For the given Poisson distribution the mean is p = 0.03 errors per page.

We have to find the probability that there are three or less errors in n = 100 pages.

Let us denote the number of errors in the book by the variable x.

Since there are on an average 0.03 errors per page we can say that

the expected value is, $\lambda$ = E(x)

= n × p

= 100 × 0.03

= 3

Therefore the we find the probability that there are 3 or less errors on the page as

P( X ≤ 3) = P(X = 0) + P(X = 1) + P(X=2) + P(X=3)

Using the formula for Poisson distribution for P(x = X ) = $\frac{e^{-\lambda}\lambda^X}{X!}$

Therefore P( X ≤ 3) = $\frac{e^{-3} 3^0}{0!} + \frac{e^{-3} 3^1}{1!} + \frac{e^{-3} 3^2}{2!} + \frac{e^{-3} 3^3}{3!}$

= 0.05 + 0.15 + 0.224 + 0.224

= 0.648

The probability that there are 3 or less errors in 100 pages is 0.648.

7 0

3 years ago

Read 2 more answers

Simplify this equation please.

Sauron [17]

$\dfrac{\csc^2\theta-3\csc\theta+2}{\csc^2\theta-1}$

Identity:

$\sin^2\theta+\cos^2\theta=1\implies1+\cot^2\theta=\csc^2\theta$

So we can rewrite the denominator to get

$\dfrac{\csc^2\theta-3\csc\theta+2}{\cot^2\theta}$

Multiply numerator and denominator by $\sin^2\theta$ . Several terms will cancel since $\sin\theta\csc\theta=1$ . Also, $\cot\theta=\dfrac{\cos\theta}{\sin\theta}$ . We get

$\dfrac{1-3\sin\theta+2\sin^2\theta}{\cos^2\theta}$

Factorize the numerator, and write $\cos$ in terms of $\sin$ in the denominator to factorize it further to get

$\dfrac{(1-\sin\theta)(1-2\sin\theta)}{\cos^2\theta}=\dfrac{(1-\sin\theta)(1-2\sin\theta)}{1-\sin^2\theta}=\dfrac{(1-\sin\theta)(1-2\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}$

The $1-\sin\theta$ factors cancel, leaving you with

$\dfrac{1-2\sin\theta}{1+\sin\theta}$

which you could simplify a bit further by writing

$\dfrac{1+\sin\theta-3\sin\theta}{1+\sin\theta}=1-\dfrac{3\sin\theta}{1+\sin\theta}$

3 0

4 years ago

Write the slope intercept form Through:(-1,0) and (-5,-5)

jarptica [38.1K]

Answer:

$y=\frac{5}{4} x + \frac{5}{4}$

7 0

3 years ago