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Ilya [14]
3 years ago
15

A conical (cone shaped) water tower has a height of 12 ft and a radius of 3 ft. Water is pumped into the tank at a rate of 4 ft^

3/min. How fast is the water level rising when the water level is 6 ft?
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

The water rises at a rate of 16/(9π) ft/min or approximately 0.566 ft/min.

Step-by-step explanation:

Volume of a cone is:

V = ⅓ π r² h

Using similar triangles, we can relate the radius and height of the water to the radius and height of the tank.

r / h = R / H

r / h = 3 / 12

r = ¼ h

Substitute:

V = ⅓ π (¼ h)² h

V = ¹/₄₈ π h³

Take derivative with respect to time:

dV/dt = ¹/₁₆ π h² dh/dt

Plug in values:

4 = ¹/₁₆ π (6)² dh/dt

dh/dt = 16 / (9π)

dh/dt ≈ 0.566

The water rises at a rate of 16/(9π) ft/min or approximately 0.566 ft/min.

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Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, 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.

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This means that p = 0.3

A sample of 25 dishwasher detergent customers was taken.

This means that n = 25

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

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P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014

P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074

P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243

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