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3 years ago

Remove all perfect squares from inside the inside the square root 63

Mathematics

1 answer:

Dmitrij [34]3 years ago

5 0

Answer:

3 sqrt 7

Step-by-step explanation:

First, let's find the factors of 63. 1x63, 3x21, 7x9. We can see that the only factors that is a square is 9.

sqrt 63=

sqrt 7 x9=

sqrt7 x sqrt 9=

sqrt7 x3

3 sqrt7

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A car park has 20 vehicles 12 of them are cars.what fraction of the vehicles are cars?

svetlana [45]

3/5 of the vehicles are cars.
hope this helped.

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3 years ago

Renee scores an average of 153 points in a game of bowling, and her points in a game of bowling are normally distributed. Suppos

drek231 [11]

Answer:

The standard deviation is 11 points

Step-by-step explanation:

To calculated the z-score of a value x, we use the following equation:

$z=\frac{x-m}{s}$

Where m is the mean, s is the standard deviation and z is the z-score.

If we solve this equation for s, we get:

$s=\frac{x-m}{z}$

So, replacing z by 2, m by 153 and x by 175, we get:

$s=\frac{175-153}{2}=11$

Therefore, the standard deviation is 11 points

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3 years ago

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3 years ago

S=2(lw+lh+wh) solve for w

wolverine [178]

we have

$s=2(lw+lh+wh)$

Solve for w means that clear variable w

$s=2(lw+lh+wh)\\s=2lw+2lh+2wh$

Group terms that contain the variable w, and move the other terms to the opposite side of the equation

$(s-2lh)=(2lw+2wh)$

Factor the variable w

$(s-2lh)=w(2l+2h)$

Divide both sides by $(2l+2h)$

$(s-2lh)/(2l+2h)=w(2l+2h)/(2l+2h)$

$w=(s-2lh)/(2l+2h)$

therefore

<u>the answer is</u>

$w=(s-2lh)/(2l+2h)$

7 0

3 years ago

Read 2 more answers

A survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey samp

Oksanka [162]

Answer:

The null hypothesis is: $H_0: p_M - p_W = 0$

The alternative hypothesis is: $H_1: p_M - p_W > 0$

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

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.

Men:

98 out of 200, so:

$p_M = \frac{98}{200} = 0.49$

$s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353$

Women:

72 out of 200, so:

$p_W = \frac{72}{200} = 0.36$

$s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339$

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

$H_0: p_M - p_W = 0$

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

$H_1: p_M - p_W > 0$

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

$X = p_M - p_W = 0.49 - 0.36 = 0.13$

$s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489$

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, so:

$z = \frac{0.13 - 0}{0.0489}$

$z = 2.66$

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

4 0

3 years ago