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Anna71 [15]
3 years ago
10

Find the lengths of the missing side . Simplify all radicals !!! help mee!!!!!!

Mathematics
1 answer:
larisa86 [58]3 years ago
3 0

Answer:

e = 13\sqrt{2}

f = 13\sqrt{2}

Step-by-step explanation:

The ∆ given is an isosceles ∆ with a right angle measuring 90°, and two congruent angles measuring 45° each.

Using trigonometric ratio formula, we can find the lengths of the missing side as shown below:

Finding e:

sin(\theta) = \frac{opp}{hyp}

sin(\theta) = sin(45) = \frac{\sqrt{2}}{2}

hyp = 26

opp = e = ?

Plug in the values into the formula

\frac{\sqrt{2}}{2} = \frac{e}{26}

Multiply both sides by 26

\frac{\sqrt{2}}{2}*26 = \frac{e}{26}*26

\frac{\sqrt{2}}{2}*26 = e

\frac{\sqrt{2}}{1}*13 = e

13\sqrt{2} = e

e = 13\sqrt{2}

Since side e is of the same length with side f, therefore, the length of side f = 13\sqrt{2}

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A triangle has an area of 56 square units. It's night is 14 units. What is the length of its base?
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Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5
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11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

For the sum of n variables, the mean is \mu*n and the standard deviation is s = \sigma\sqrt{n}

In this question:

n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40

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This is the pvalue of Z when X = 450.

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

By the Central Limit Theorem

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

Z = \frac{450 - 500}{40}

Z = -1.2

Z = -1.2 has a pvalue of 0.1151

11.51% probability that it will take less than 450 days to train all the contestants.

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