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Aleksandr-060686 [28]

2 years ago

5

The formula for the volume V of a cylinder is V = πr2h, where r is the radius of the base and h is the height of the cylinder. S

olve the formula for h.
Choose the correct formula.

A. h=Vπr2

B. h=Vπr2

C. h=Vr2π

D. h=Vπr2

Part B

Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm.

h = __ cm

1 answer:

lana [24]2 years ago

8 0

Answer:

Part A) $h=V/(\pi r^{2})$

Part B) $h=4\ cm$

Step-by-step explanation:

Part A)

we have the formula of the volume of a cylinder

$V=\pi r^{2}h$

Solve for h

That means ----> isolate the variable h

Divide both side by πr²

$V/(\pi r^{2})=\pi r^{2}h/(\pi r^{2})$

Simplify

$V/(\pi r^{2})=h$

Rewrite

$h=V/(\pi r^{2})$

Part B) Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm

we have

$V=36\pi\ cm^3$

$r=3\ cm$

substitute in the formula and solve for h

$h=36\pi/(\pi 3^{2})$

$h=4\ cm$

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Answer:

Volume=355 cm³

Step-by-step explanation:

I assume it should be 10 cm, not 10 m. If it is 10 m, everything will have to be adjusted.

Circumference = 2 $\pi$ r

10=2 $\pi$ r

10÷2 $\pi$ =r

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V= $\pi$ r²h

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A library buys 36 English books, 48 Science books and 72 Mathematics books. The thickness of each book is the same. Now, the lib

fomenos

Answer:

13

Step-by-step explanation:

The GCF of 36, 48, and 72 is 12 so there will be 36 / 12 = 3 stacks of English books, 48 / 12 = 4 stacks of science books and 72 / 12 = 6 stacks of math books for a total of 3 + 4 + 6 = 13 stacks.

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1 year ago

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Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the

Tcecarenko [31]

Answer:

The value of x is 10

Step-by-step explanation:

We can use a system of equations to solve this.

Cups of 25% bleach solution used = x

Cups of 1-% bleach solution used = 5

Cups of solution we get = y

The first equation becomes:

x + 5 = y

Using the decimal forms of each percentage solution

25% solution for x cups = 0.25x

10% solution for 5 cups = 0.1(5)

20% solution for y cups = 0.2 y

The second equation becomes:

0.25x + 0.1(5) = 0.2y

So the system of equations is:

x + 5 = y

0.25x + 0.1(5) = 0.2y

Solve both equations simultaneously to find the values of x and y:

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2 years ago

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n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This 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.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

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

In which

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

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

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

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