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MakcuM [25]
3 years ago
10

Find the exact length of the third side.

Mathematics
2 answers:
frez [133]3 years ago
7 0

Step-by-step explanation:

Hello there!

Use the Pythagoream theorem:

a^{2} +b^{2} =c^{2} \\4^2+2^2=c^2\\16+4=20\\x=\sqrt{20} \\x=4.472135

:)

Natali [406]3 years ago
4 0

Answer:

4.47

Step-by-step explanation:

Using Pythagorean's theorem, we know that a^{2} + b^{2} = c^{2}.

c^{2} is the hypotenuse which is what we are trying to figure out.

a^{2} and b^{2} are the measurements of the legs.

4^{2}+ 2^{2} = c^{2}

4^{2}= 16

2^{2}=4

16 + 4 = 20

20 = c^{2}

\sqrt{20} = \sqrt{c^{2} }

2\sqrt{5} = 4.47

Answer: 4.47

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a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 8.7% and standard deviation 20.2%.

This means that \mu = 8.7, \sigma = 20.2

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This means that n = 40, s = \frac{20.2}{\sqrt{40}}

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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

Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}

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0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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