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3 years ago

Which inequality represents this sentence?

2 answers:

6 0

Yes it is correct because c and d are wrong, so if you look at a it is greater than the other problem which is wrong so the answer is b. 6+2<9+3 hope this helped.

olga_2 [115]3 years ago

5 0

6 + 2 < 9 + 3...u r correct

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During a thunderstorm, 600 millimeters of rain fell in 30 minutes. How fast did the rain fall, in millimeters per minute?

madreJ [45]

20 milliliters per minute

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3 years ago

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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

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

$Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = 1.35$

$Z = 1.35$ has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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

$Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = -0.22$

$Z = -0.22$ has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0

3 years ago

Un número real no puede pertenecer a los racionales y a los irracionales a la vez?

Galina-37 [17]

Step-by-step explanation:

eso es cierto y correcto por supuesto, es tan obvio

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3 years ago

8. What angle do the hour and minute hands of a clock form when it is exactly 9.00p.m.?

Elenna [48]

At 9 o clock, the hour hand is at 9 and the minute hand is at 12. The angle between the two hands is 90 degrees.

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3 years ago

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Are x+4=5 and 2x+8=10 equivalent equations?

MatroZZZ [7]

Answer:

Yes

Step-by-step explanation:

You can find the answer to this question by finding the value of x in both equations.

Let's start off with the first equation: $x+4=5$

To find the value of x, you're going to have to subtract 4 from both sides. This is because you're looking for the value of only x, not x + 4. To leave x alone, you'd have to subtract 4, leaving that side with just x.

$x+4-4=5-4$

$x=1$

The answer to the first equation is x = 1.

Now let's start on the second equation: $2x+8=10$

Like before, you're looking for x alone and in this equation, 8 is being added to 2x. Although x itself isn't alone, you'll first start off with 2x since you can simplify it thrughout the process. In this equation, you're going to subtract 8 from both sides to leave the variable x alone.

$2x+8-8=10-8$

$2x=2$

Now you're left with 2x = 2. Since you're looking for the value of x alone, you're going to divide both sides by 2. Because x is being multiplied by 2(2 times x = 2x) you're going to divide(opposite of multiply), which will cancel out the 2(in 2x).

$\frac{2x}{2} = \frac{2}{2}$

$x = 1$

The answer to the second equation is x = 1.

Since both equations have the same solution, the answer to your question would be yes.

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3 years ago

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