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4 years ago

Consider the standard matrix of a counterclockwise rotation of a vector in R 2:_________

Mathematics

1 answer:

lyudmila [28]4 years ago

4 0

Answer:

The rotation matric that rotate the plane counter clockwise around the origin is given in the attached file

Step-by-step explanation:

The composition of transformation is given by

$(T_{B}*T_{A})(x)$

$=(T_{B}(T_{A}(X})))$

$=T_{B}(A_{X} )$

$=BA{X}$

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There are five marbles in a bag. Three are green and two are yellow. You draw a

algol13

Answer: 2/5 chance

Step-by-step explanation: Since there are 5 marbles and 3 aren't yellow, you have a 2/5 chance to choose the other two yellow marbles

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3 years ago

The US Census reported that it takes workers an average of 28 minutes to get home from work with standard deviation 5 minutes. A

xz_007 [3.2K]

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

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

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

$H_0: \mu = 28$

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

$H_1: \mu > 28$ .

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

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

In this problem, the values of the parameters are given by:

$\overline{x} = 32, \mu = 28, \sigma = 5, n = 10$

Hence:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}$

$z = 2.53$

<h3>What is the decision?</h3>

Considering that we have a <em>right-tailed test</em>, as we are testing if the mean is greater than a value, with a standard <em>significance level of 0.05</em>, the critical value is of $z^\ast = 1.645$ .

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

To learn more about the z-distribution, you can check brainly.com/question/26454209

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2 years ago

Which of the following statements is true about the triangles below

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Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Among the choices above the statements is true about the triangles below triangle JKN is congruent to triangle LKM by SAS. The answer is D.

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3 years ago

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Rayla and her friends were carving their pumpkins for Halloween. They noticed that there was a proportional relationship between

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answer

12.5

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3 years ago

What are the coordinates of the vertex of the graph of

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3 years ago