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Llana [10]
3 years ago
15

I need help with this question

Mathematics
1 answer:
Setler [38]3 years ago
6 0

Answer:

Step-by-step explanation:

radius r = 4

height h = 8

volume = πr²h = π·4²·8 = 128π units³

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Answer:

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Step-by-step explanation:

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Express cos^2 x in terms of cos2x. Hence, express f(x) = 6cos^2 x - 4sin 2x in the form R cos (2x + Y degrees) + p where R, y an
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Which of the following is a unit for area?<br> ◦ m 3<br> ◦ inches<br> ◦ feet<br> ◦ cm 2
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Answer:

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6 0
2 years ago
Read 2 more answers
Task: Nonpermissible Values for Rational Expressions [30 points] Write a rational expression that has the nonpermissible values
igor_vitrenko [27]

Answer:

A rational expression that has the nonpermissible values x = 0 and x = 17 is f(x) = \frac{4}{x\cdot (x-17)}.

Step-by-step explanation:

A rational expression has a nonpermissible value when for a given value of x, the denominator is equal to zero. In addition, we assume that both numerator and denominator are represented by polynomials, such that:

f(x) = \frac{p(x)}{q(x)} (1)

Then, the factorized form of q(x) must be:

q(x) = x\cdot (x-17) (2)

If we know that p(x) = 4, then the rational expression is:

f(x) = \frac{4}{x\cdot (x-17)} (3)

A rational expression that has the nonpermissible values x = 0 and x = 17 is f(x) = \frac{4}{x\cdot (x-17)}.

8 0
3 years ago
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains
AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

f(x) = (1-p)^{x}p

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

\mu = \frac{1-p}{p}

The standard deviation of the geometric distribution is given by the following formula:

\sigma = \sqrt{\frac{1-p}{p^{2}}

In this problem, we have that:

p = 0.383

So

\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61

\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05

(a) What is the probability that a drought lasts exactly 3 intervals?

This is f(3)

f(x) = (1-p)^{x}p

f(3) = (1-0.383)^{3}*(0.383)

f(3) = 0.09

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is P = f(0) + f(1) + f(2) + f(3)

f(x) = (1-p)^{x}p

f(0) = (1-0.383)^{0}*(0.383) = 0.383

f(1) = (1-0.383)^{1}*(0.383) = 0.236

f(2) = (1-0.383)^{2}*(0.383) = 0.146

Previously in this exercise, we found that f(3) = 0.09

So

P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4).

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

P(X \leq 3) + P(X \geq 4) = 1

0.855 + P(X \geq 4) = 1

P(X \geq 4) = 0.145

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0
3 years ago
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