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stiv31 [10]
3 years ago
6

In Exercise 13, solve y=f(x) for x. Then find the input when the output is 2.

Mathematics
1 answer:
andrezito [222]3 years ago
6 0

Answer:

x = ±(√y)/3

x = ±(√2)/3

Step-by-step explanation:

Put the given information in the given equation and solve for x:

f(x) = 2

2 = 9x^2 . . . . . use 2 in place of f(x)

2/9 = x^2 . . . . divide by 9

±√(2/9) = x . . . take the square root

x = ±(√2)/3 . . . simplify

_____

Using this as an example, we can solve f(x) = y in the same way:

y = 9x^2 . . . . use y for f(x)

y/9 = x^2 . . . divide by the coefficient of x^2

±√(y/9) = x . . . take the square root; next, simplify

x = ±(√y)/3 . . . . the equation solved for x. Note this matches the above when y=2.

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We have given that the karate charges $35 for the first course and $22.50 for each course after that. Our total is $170.

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for solving this linear equation

First, subtract 35 from both sides.

22.50x = 135

isolate x so divide both sides by 22.50.

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2 years ago
Write 7/12 as a percentage correct to two decimal places
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3 years ago
A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proporti
Gre4nikov [31]

Answer:

a. .92

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

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In which

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The margin of error of the interval is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The lower bound is the point estimate \pi subtracted by the margin of error.

The upper bound is the point estimate \pi added to the margin of error.

Point estimate:

The confidence interval is symmetric, so it is the mean between the two bounds.

In this problem:

\pi = \frac{0.372 + 0.458}{2} = 0.415

Sample of 400, which means that n = 400

Margin of error is the estimate subtracted by the lower bound. So M = 0.415 - 0.372 = 0.043

We have to find z.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.043 = z\sqrt{\frac{0.415*0.585}{400}}

z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}

z = 1.745

z = 1.745 has a pvalue of 0.96.

This means that:

1 - \frac{\alpha}{2} = 0.96

\frac{\alpha}{2} = 1 - 0.96

\frac{\alpha}{2} = 0.04

\alpha = 0.08

Confidence level:

1 - \alpha = 1 - 0.08 = 0.92

So the correct answer is:

a. .92

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