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3 years ago

Which congruence theorem can be used to prove WXS and YZS?

Mathematics

1 answer:

mariarad [96]3 years ago

3 0

I am going to make what is hopefully not an incorrect assumption and say that since the segmentXSZ is black and the other lines are blue, that XS is congruent to ZS. If that be the case we have a side in each triangle that is congruent to each other and an angle that is marked as congruent. Angles XSW and ZSY are vertical angles. By definition, vertical angles are congruent. In each triangle, then, we have an angle, a side and an angle which gives us the congruency postulate ASA.

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nika2105 [10]

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2 years ago

Read 2 more answers

A manager is comparing wait times for customers in a coffee shop based on which employee is

anyanavicka [17]

Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if there is no difference, that is:

$H_0: \mu_A - \mu_B = 0$

At the alternative hypothesis, it is tested if there is difference, that is:

$H_1: \mu_A - \mu_B = 0$

<h3>What are the mean and the standard error of the distribution of differences?</h3>

For each sample, we have that:

$\mu_A = 73, s_A = \frac{2}{\sqrt{100}} = 0.2$

$\mu_B = 74, s_B = \frac{4}{\sqrt{100}} = 0.4$

For the distribution of differences, we have that:

$\overline{x} = \mu_A - \mu_B = 73 - 74 = -1$

$s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.2^2 + 0.4^2} = 0.447$

<h3>What is the test statistic?</h3>

It is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{-1 - 0}{0.447}$

$t = -2.24$

<h3>What is the p-value and the decision?</h3>

Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.

Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.

More can be learned about the t-distribution at brainly.com/question/16313918

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2 years ago

7. algebra sara allen is interested in buying a notebook

seropon [69]

A percentage is a way to describe a part of a whole. The regular selling price of the computer notebook will be $937.5.

<h3>What are Percentages?</h3>

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the selling price of the computer notebook be represented by x.

Now, if Sara buys the computer this week, the selling price of the computer will be (100%-16%)x = 0.84x.

Also, the saving she made by buying this week will be $150, therefore, we can write,

x-0.84x = $150

0.16x = $150

x = 937.5

Hence, the regular selling price of the computer notebook will be $937.5.

Learn more about Percentages:

brainly.com/question/6972121

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2 years ago

Write an equation of the line that passes through the points (2, -3) and (1,4).

Lelu [443]

I thiiink the line equation would be y=7/1+12

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3 years ago

an astronomer wishes to measure on a photograph the distance between the image of a certain star and three star other star image

Greeley [361]

The astronomer has to choose 3 star images out of 8.This is a problem of combinations. This can be expressed as 8C3 i.e. combination of 8 objects taken 3 at a time.

$8C3= \frac{8!}{3!*5!}=56$

This means, if 8 images are nearby the astronomer will have 56 choices <span>of the three stars.</span>

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3 years ago