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3 years ago

A cylindrical tank has a radius of 15 ft. and a height of 45 ft. How many cubic feet of water can the tank hold?

1 answer:

vladimir1956 [14]3 years ago

4 0

The formula to solve for this would be pi(r^2)xheight. Essentially what this formula does is it takes the are of the base (pi x r^2) and multiplies it by the height of the cylinder to find how many times the base can stack on itself until it reaches the top. This formula of base are times height works for all prisms with two bases. Here are the steps to solve:

1) plug in the values
- pi(15^2) x 45

2) solve for the base area of one of the circles
- pi(15^2)=225pi

3) multiply the base area by the height
- 225pi x 45 = 10,125pi

4) final answer: the tank can hold 10,125pi cubic feet of water

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3 years ago

Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 0.5 minute?

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60 seconds in a minute

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3 years ago

Peter wallpapered a wall that was 9 feet wide and 8 feet high. He had 27 square feet of wallpaper left over. How many square fee

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Camilla baked 15 cookies with 3 scoops of flour. How many scoops of flour does Camilla need in order to bake 20 cookies? Solve u

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3 years ago

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters

natita [175]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used 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.

70% of all eligible voters will vote in the next presidential election.

This means that $p = 0.7$

20 eligible voters were randomly selected from the population of all eligible voters.

This means that $n = 20$

What is the probability that fewer than 11 of them will vote?

This is:

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)$

In which

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

$P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308$

$P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120$

$P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039$

$P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010$

$P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002$

$P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0$

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479$

0.0479 = 4.79% probability that fewer than 11 of them will vote

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3 years ago