What is the area of a picture with side<br> lengths that are 12 inches?

CONSTRUCTION Carlos is building a screen door. The height of the door is I foot more than twice its width. What is the width of

-BARSIC- [3]

Answer:

<h2>width = 3 feet</h2>

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this : h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

$\Leftrightarrow w=\frac{h-1}{2}$

now , if the door is 7 feet high then it’s width is equal to :

$\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft$

6 0

2 years ago

Read 2 more answers

How u do dis ............

Norma-Jean [14]

i’ll try to help.

angle 3 and angle 1 are congruent angles, so they both equal 75°.

angle 1 and angle 5 are corresponding angles, so they both equal 75°. (it’s bc they’re positioned the same.

soooo the answer to that is 75° for angle 5. (not really great at explaining) also hope that the answer is right it should be.

5 0

3 years ago

Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa

Debora [2.8K]

Answer:

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:

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

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

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 $\mu = 8.7, \sigma = 20.2$

40 years:

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

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