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2 years ago

A.) y= 5x + 4 B.) y= -x + 8 C.) y= x - 10 D.) y= -4x + 3

Mathematics

2 answers:

creativ13 [48]2 years ago

3 0

Option B is your answer.

If you plug it in, you get:

1 = -(7) + 8
1 = - 7 + 8
1 = 1, a true statement.

Soloha48 [4]2 years ago

3 0

Try the x and y values in the equations and see which works.
A.) 1 = 5*7 +4 . . . . nope
B.) 1 = -7 +8 . . . . . true
C.) 1 = 7 -10 . . . . . nope
D.) 1 = -4*7 +3 . . . nope

The appropriate choice is ...
B.) y = -x +8

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2 years ago

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Given:

The faces on a number cube are labeled 1,2,2,3,4, and 5.

The number cube is rolled 114 times.

To find:

How many times would you expect the number 2 to appear?

Solution:

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Answer:

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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.

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This means that $\mu = 8.7, \sigma = 20.2$

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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%?

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

By the Central Limit Theorem

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