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Ymorist [56]
3 years ago
14

Consider function f. f(x) = sqrt 7x- 21

Mathematics
2 answers:
Arada [10]3 years ago
6 0

Answer:

f^-1(x) = (x² + 21)/7

Step-by-step explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7

kipiarov [429]3 years ago
4 0

Answer:look at explanation

Step-by-step explanation:

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A sculpture at a park is in the shape of a rectangular pyramid. What is the volume of the sculpture if the length and width of t
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40

Step-by-step explanation:

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2 years ago
The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men
Komok [63]

Answer:

Critical value: b. 2.33

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0

The significance level is 0.01.

The sample 1 (women), of size n1=150 has a proportion of p1=0.62.

The sample 2 (men), of size n2=200 has a proportion of p2=0.24.

 

The difference between proportions is (p1-p2)=0.38.

p_d=p_1-p_2=0.62-0.24=0.38

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17

The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

6 0
3 years ago
A company wishes to manufacture a box with a volume of 36 cubic feet that is open on top and is twice as long as it is wide. Fin
Nimfa-mama [501]

Answer:

Width is 3 ft

length is 6 ft

Step-by-step explanation:

Let x = the width

Let 2x = the length

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so we have v = volume  = x*2x*h

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h = \frac{18}{x^2}

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S.A. = 2xh + 2x^2 + 4xh

we have calculateh = = \frac{18}{x^2}

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S.A = 2x^2 + \frac{108}{x}

By graphing above equation we can calculate the value of x

Minimum S.A when x is 3  is the width so

2(3) = 6 is the length

h = \frac{18}{3^2} = 2

6 0
3 years ago
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