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3 years ago

Given the following triangle, what is the measure of the missing side?

Mathematics

1 answer:

Karolina [17]3 years ago

8 0

It's a half of an equilateral triangle because their angles measure 30° and 60° (an equilateral triangle has 3 angles of 60°)
So x=(2h/√3)/2=h√3=27√3≈15.6

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In the United States, 7% of all registered voters belong to the Green party. A random sample of 50 registered voters is taken. U

Maksim231197 [3]

Answer:

The expected value of the sample proportion is of 0.07.

1. P(p < .02) = 0.0823

2. P(p > .15) = 0.0132

3. P(.05 < p < .09) = 0.4176

Step-by-step explanation:

This question is solved using 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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

7% of all registered voters belong to the Green party. 50 voters:

This means that $p = 0.07, n = 50$

So, for the normal distribution:

$\mu = 0.07, s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{50}} = 0.036$

The expected value of the sample proportion is of 0.07.

1. Determine P(p < .02).

This is the pvalue of Z when X = 0.02. So

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

By the Central Limit Theorem

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

$Z = \frac{0.02 - 0.07}{0.036}$

$Z = -1.39$

$Z = -1.39$ has a pvalue of 0.0823

P(p < .02) = 0.0823

2. Determine P(p > .15).

This is 1 subtracted by the pvalue of Z when X = 0.15. So

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

$Z = \frac{0.15 - 0.07}{0.036}$

$Z = 2.22$

$Z = 2.22$ has a pvalue of 0.9868

1 - 0.9868 = 0.0132

P(p > .15) = 0.0132

3. Determine P(.05 < p < .09).

This is the pvalue of Z when X = 0.09 subtracted by the pvalue of Z when X = 0.05. So

X = 0.09

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

$Z = \frac{0.09 - 0.07}{0.036}$

$Z = 0.55$

$Z = 0.55$ has a pvalue of 0.7088

X = 0.05

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

$Z = \frac{0.05 - 0.07}{0.036}$

$Z = -0.55$

$Z = -0.55$ has a pvalue of 0.2912

0.7088 - 0.2912 = 0.4176. So

P(.05 < p < .09) = 0.4176

3 0

3 years ago

The answers <br> To this I don’t understand

Nataly_w [17]

Answer:nvuycghg

Step-by-step explanation:

ngyufuf

6 0

3 years ago

7.<br> (1-3 and (4, -3)<br> Formula:<br> Slope:

maw [93]

Answer:

Formula: y2-y1/x2-x1

Slope: -3/4

Step-by-step explanation:

-3-(-3/4)/4-1

=(-9/4)/3

= -3/4

8 0

3 years ago

Annette drove through an intersection without looking and hit Vincent's car that he had driven into the intersection without obe

Karolina [17]

Answer:

$80,000

Step-by-step explanation:

Under a Comparative negligence theory, people involved in an accident are entitled to compensation according to their contributions towards the accident. In this case, Annette contributed 20% to the collision and, thus, should receive 100% - 20% of her total loss determined by the jury. Annette should be awarded:

$A= \$ 100,000*(1-0.2)\\A=\$ 80,000$

Therefore, the jury should award Annette $80,000

7 0

3 years ago

1). Ben will toss a penny, a nickel, and a dime. The tree diagram shows the possible

ale4655 [162]

Answer:

3 possible outcomes I think

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3 years ago

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