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3 years ago

In the diagram, AC - 30 and BC - 30. Find AB. Write your answer in simplest form.

Mathematics

1 answer:

Artist 52 [7]3 years ago

3 0

Answer:

$ab = 30 \sqrt{2}$

Step-by-step explanation:

see the box that means the minimum size must be bigger than 30 or 30° or a and c band c are both 30 each so the total linear distance is smaller than if 30+30 is used for ACB calculation so by default its AB=30square root 2 plus i used a calculator

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A catering company provides packages for weddings and for showers. The cost per person for small groups

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Using the <em>normal distribution and the central limit theorem</em>, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

When two variables are subtracted, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances.

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

For each sample, they are given by:

$\mu_W = 82.3, s_W = \frac{18.2}{\sqrt{9}} = 6.0667$

$\mu_S = 65, s_S = \frac{17.73}{\sqrt{6}} = 7.2382$

For the distribution of differences, we have that:

$\mu = \mu_W - \mu_S = 82.3 - 65 = 17.3$

$s = \sqrt{s_W^2 + s_S^2} = \sqrt{6.0667^2 + 7.2382^2} = 9.4444$

The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, <u>one subtracted by the p-value of Z when X = 0</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

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

$Z = \frac{0 - 17.3}{9.4444}$

$Z = -1.83$

$Z = -1.83$ has a p-value of 0.0335.

1 - 0.0335 = 0.9665.

More can be learned about the <em>normal distribution and the central limit theorem</em> at brainly.com/question/24663213

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