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3 years ago

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Alan measures the circular floor of a tepee, then calculates that it has an area of 12.56 square yards. What is the floor's diam

eter?
Use 3.14 for pi.

[ ] yards

1 answer:

-BARSIC- [3]3 years ago

5 0

The area of a circle is found by pi*r^2

We can plug in the values we know to solve for the radius.

12.56 = 3.14*r^2

Divide both sides by pi.

12.56/3.14 = r^2

Square root both sides.

r = 2 yards

The diameter of a circle is twice as long as the radius, so the answer is 4 yards.

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What is the equation of the parabola with vertex (6,7) and focus (7,7)?

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Answer:

Step-by-step explanation:

If you plot these points on a coordinate plane, you see that they are on the same horizontal line, y = 7, with the focus 1 unit to the right of the vertex. This means that the parabola is a sideways opening parabola, to the right, to be more specific. That means that it has the basic vertex form

$4p(x-h)=(y-k)^2$

where p is the distance in units from the vertex to the focus, h is the first coordinate in the vertex, and k is the second coordinate in the vertex. For us, p = 1, h = 6, and k = 7. Now we will just fill the vertex form of the equation in with our values:

$4(x-6)=(y-7)^2$

We will solve this for x now by dividing each side by 4 and adding over the 6:

$x=\frac{1}{4}(y-7)^2+6$

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Eddie has a globe that he is going to unfold and lay flat to hang on the wall as a map. If the radius of the globe is 22.5 cm, w

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B. 6358.5 square centimeters. This is right.

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If I make $14.00 an hour how much will I make monthly?

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3 years ago

Read 2 more answers

The volume of a cone is 200.96 cubic yards. What is the radius of the cone if the height is 12 yd? Use pi =3.14 and round your a

Naddika [18.5K]

Answer:

If I'm doing the problem correctly, the radius should be 4 yards.

Step-by-step explanation:

You work the problem backwards. Multiply 200.96 by 3, since it's a cone, so you're working with the volume of what a cylinder would be with the same dimensions. Then divide by the height (12 yd), then divide by pi. You should end up with 16, and 4 squared equals 16. Work the problem forwards from there to check.

4 squared is 16. 16 times 3.14 is 50.24. 50.24 times 12 is 602.88. 602.88 divided by 3 is 200.96.

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3 years ago

Read 2 more answers

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls invol

bagirrra123 [75]

Answer:

a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message

c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.

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 combinations 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.

25% of the incoming calls involve fax messages

This means that $p = 0.25$

25 incoming calls.

This means that $n = 25$

a. What is the probability that at most 4 of the calls involve a fax message?

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$ .

In which

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

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214$

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . Then

$P(X \geq 4) = 1 - P(X < 4)$

In which

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

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

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904$

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

$P(X \leq 4) + P(X > 4) = 1$

From a), $P(X \leq 4) = 0.214)$

Then

$P(X > 4) = 1 - 0.214 = 0.786$

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

8 0

3 years ago