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Nady [450]
3 years ago
8

1) IF DE = 9, find BC

Mathematics
1 answer:
swat323 years ago
5 0

Answer:

1. BC = 18

2. m<ABC = 80°

3. x = 5

Step-by-step explanation:

1. If DE = 9, therefore:

BC = 2 \times 9 = 18 (based on the midsegment theorem, DE is half the length of the third side, BC)

2. m<ADE = 80°, then,

m<ABC = 80°

This is because m<ADC and m<ABC are corresponding angles. Corresponding angles are congruent.

3. DE = 2x + 7 , and BC = 7x - 1, find BC

Thus:

BC = 2 \times DE (midsegment theorem)

7x - 1 = 2 \times (2x + 7) (substitution)

Solve for x

7x - 1 = 4x + 14

Collect like terms

7x - 4x = 1 + 14

3x = 15

Divide both sides by 3

x = 5

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Step-by-step explanation:

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3 years ago
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Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58​, what is the
aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news​ videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

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Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

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Normal probability distribution

Problems of normally distributed samples can be solved using 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.

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

In this problem, we have that:

n = 250, p = 0.58

So

\mu = E(X) = 250*0.58 = 145

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80

If the population proportion of adults who watch news videos is 0.58​, what is the probability that fewer than half in your sample will watch news​ videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

Z = \frac{124 - 145}{7.8}

Z = -2.69

Z = -2.69 has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news​ videos

8 0
3 years ago
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zhannawk [14.2K]

Answer:

144

Step-by-step explanation:

angle A + angle B = 180 (supplementary angle)

A = 4B

4b+b=180

5b=180

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180-36=144

4 0
3 years ago
An employee at a gym wants to select a random sample of gym members for a survey about their exercise habits.
34kurt

Answer:

No, no, yes, no

Step-by-step explanation:

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The fourth one is not random.  He is sampling only volunteers.

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