In the term -3k?mn, state the coefficient of a) k²mn b) -mn c) 3k² Help me please

School a has 450 seniors, and 432 of them go to college. School B has 380 seniors, and 361 of them plan to go to college. In whi

Natasha_Volkova [10]

Answer:

School A.

Step-by-step explanation:

School A: % who plan to go to college = (432/450) * 100

= 96%.

School B: % who plan to go to college = (361/380) * 100

= 95%.

5 0

3 years ago

Calculate the angle of depression, x, if the boat is 750 ft. away from the light house and the light house is 300 ft high. Round

I am Lyosha [343]

Firstly , we need to draw diagram

we are given

opposite =300

adjacent =750

now, we can use tan formula

$tan(x)=\frac{300}{750}$

now, we can find x

$x=tan^{-1}(\frac{300}{750})$

we get

$x=21.8 degree$

so,

angle of depression is 21.8 degree.....Answer

8 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

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