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4 years ago

Can someone please help meee and show the work i’m stuck

Mathematics

1 answer:

german4 years ago

5 0

Answer:

A. 12

Step-by-step explanation:

Since both lines are the same length you can take 29 and subtract it from 41 to get the length of the line segment AB and it would come out to 12.

41 - 29 = 12

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The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba

blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

$\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537$

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

$\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712$

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

$H_0: \mu_1 - \mu_2 = 0$

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

$H_1: \mu_1 - \mu_2 \neq 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that $\mu = 0$

From the two samples:

$X = \mu_1 - \mu_2 = 1276 - 1439 = -163$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144$

Test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{-163 - 0}{77.3144}$

$z = -2.11$

The test statistic is z = -2.11.

7 0

3 years ago

You have two parents, four grandparents, eight greatgrandparents, and so forth.

Leviafan [203]

A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or $2^{2}$ ancestors.
In the third generation we have 8 ancestors ot $2^{3}$ ancestors.

We can see that each succesive generation has two times more members. The sum is:
$2+4+8+16+...+ 2^{40}$

To calculate number of ancestors we can use formula for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
 $S= a_{1} * \frac{1- r^{n} }{1-r}$
Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements

For this question:
a1 = 2
r = 2
n = 40
 $S= 2* \frac{1- 2^{40} }{1-2} =2 199 023 255 550$

b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years

c.
Total number of people who have ever lived = $10^{10}$
Number of ancestors in 40 generations = $2.2*10^{12}$

The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.

8 0

3 years ago

Can I have some help

Brums [2.3K]