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antoniya [11.8K]
3 years ago
8

A 33​-inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.

Mathematics
1 answer:
GaryK [48]3 years ago
8 0

Answer:

the shorter piece is 11 inches long

Step-by-step explanation:

x+2x=33in

3x=33in

33/3 = 11 =x

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The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 manag
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Answer:

a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

Step-by-step explanation:

Question a:

We have to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a p-value of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{2050}{\sqrt{49}} = 574

The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.

The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.

The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

Question b:

The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

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Therefore,

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z = 87

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Write a response to the following using Claim, Evidence, Reasoning.
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Answer:

The answer is A 21

Step-by-step explanation:

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