The length of a rectangle is 3 m greater than the width. The area is 108m2. Find the Length and Width

Consider independent simple random samples that are taken to test the difference between the means of two populations. The varia

Arturiano [62]

Answer:

d. t distribution with df = 80

Step-by-step explanation:

Assuming this problem:

Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:

a. t distribution with df = 82.

b. t distribution with df = 81.

c. t distribution with df = 41.

d. t distribution with df = 80

Solution to the problem

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

So on this case the degrees of freedom are given by:

$df= 37+45-2=80$

And the best answer is:

d. t distribution with df = 80

5 0

2 years ago

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

Amiraneli [1.4K]

The correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

<h3>Solving inequality</h3>

From the question, we are to solve the inequality

The given inequality is

–3(2x – 5) < 5(2 – x)

First, clear the brackets

–6x + 15 < 10 – 5x

NOTE: This is one of the correct representations of the inequality

Collect like terms

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1 and flip the sign

x > 5

Representing this on a number line, we get a number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right.

Hence, the correct representations of the given inequality are

–6x + 15 < 10 – 5x

and

A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options

Learn more on Inequalities here: brainly.com/question/246993

#SPJ1

6 0

2 years ago

A musician purchases a pair of cube-shaped speakers that are 9 inches across. If the face of the speaker takes up of the total v

netineya [11]

Answer:

Assuming "the speaker takes up 1/6 of the internal volume"

volume is 9³ in³

you want the remaining volume, which is 5/6 of the total

(5/6)9³ = 607.5 in³

double that if you want the remaining volume for BOTH speakers....

3 0

3 years ago

ASAP What is this ill give brainiest

patriot [66]

Answer:

1. d = 2t

2. d = 2 (13) d = 26 meters

3. I added the graph in a file

8 0

3 years ago

Can anyone please help

shusha [124]

$\text{Hi there! :)}$

$\large\boxed{f'(2) = -\frac{16}{27} }$

$f'(x) = \frac{(5 + x^{2} )(-2x) - (7 - x^{2} )(2x)}{(5+x^{2})^{2} } \\\\f'(x) = \frac{-10x-2x^{3}- 14x + 2x^{3} }{(5+x^{2})^{2} } \\\\f'(x) = \frac{-24x}{(5+x^{2})^{2} }\\\\ \text{Solve for the derivative at f'(2) using substitution:}\\\\f'(2) = \frac{-24(2)}{(5+2^{2})^{2} } \\\\f'(2) = \frac{-48}{81} \\\\\text{Simplify:}\\\\f'(2) = -\frac{16}{27}$

8 0

3 years ago

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