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3 years ago

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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for solving this linear equation

First, subtract 35 from both sides.

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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.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

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:

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