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ArbitrLikvidat [17]
1 year ago
10

Find m∠DEA if m∠DEA= x + 30, m∠AEF= x + 132, and m∠DEF= 146 degrees

Mathematics
1 answer:
nevsk [136]1 year ago
6 0

The numerical sum of the degree measures of m ∠DEA and m ∠AEF and  m ∠DEF is 360°; The numerical measures of the angles is,

m ∠DEA = 56°

m ∠AEF = 158°

m ∠DEF = 146°

Based on the given data,

m ∠DEA= x + 30,

m ∠AEF= x + 132, and

m ∠DEF= 146 degrees

If the sum of two linear angles is 360° then, they are known as supplementary angles.

∠A + ∠B + ∠C = 360°, (∠A and ∠B and ∠C are linear angles.)

So,

We can write,

m ∠AEF + m ∠DEA + m ∠DEF = 360°

( x + 132) + (x + 30) + 146  = 360°

x + 30 + x + 132 + 146  = 360°

2x + 308 = 360°

2x = 360° - 308

x = 52/2

x =26

Now, we will substitute the value of x = 26° in the ∠DEA and ∠AEF, hence we get:

m ∠DEA = x + 30

m ∠DEA = 26 + 30

m ∠DEA = 56 degrees

Also,

m ∠AEF = x + 132

m ∠AEF = 26 + 132

m ∠AEF = 158

Hence,

m ∠DEA + m ∠AEF + m ∠DEF = 360°

56 + 158 + 146 = 360°

360° = 360°

Therefore,

Therefore, the numerical sum of the degree measures of m ∠DEA and m ∠AEF and  m ∠DEF is 360°; The numerical measures of the angles is,

m ∠DEA = 56°

m ∠AEF = 158°

m ∠DEF = 146°

To learn more about information visit Supplementary angles :

brainly.com/question/17550923

#SPJ1

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The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

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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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

It is estimated that 25% of these tanks leak.

This means that p = 0.25

15 tanks chosen at random

This means that n = 15

a.What is the expected number of leaking tanks in such samples of 15?

E(X) = np = 15*0.25 = 3.75

b.What is the probability that fewer than 3 tanks will be found to be leaking?

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559

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This probability is 1 subtracted by the pvalue of Z when X = 600. So

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

Z = \frac{600 - 500}{19.36}

Z = 5.16

Z = 5.16 has a pvalue of 0.

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