What is one-fifth of a number, x, increased by 24 is equal to eight tenths of the same number, x.

Answer:

0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17.

This means that [tex]\mu = 118, \sigma = 17[/tex]

A randomly selected group of 40 members

This means that [tex]n = 40, s = \frac{17}{\sqrt{40}} = 2.6879[/tex]

What is the probability of having a sample mean of 115.8 or less for a random sample of this size?

This is the pvalue of Z when X = 115.8.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{115.8 - 118}{2.6879}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a pvalue of 0.2061

0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size

Answer:

Wait what

Step-by-step explanation:

Answer:

not a straight line

Step-by-step explanation:

Linear has the word "line" in it. A linear relation has a graph shaped like a straight line.

Nonlinear means "not like a straight line".

Answer: not a straight line

Answer:

(b-3)(b+3)

Step-by-step explanation:

b^2+3b-3b-9

Answer:

A rational number can expressed as a whole number, integer, square root, fraction, and more as long as it's not imaginary. However, the number has to be clean like 1/2=0.5, 1/3=0.333, -1, 200. If it is a number that goes on forever and is not repeated like 1.22222, then it's an irrational number like pie-3.14159..., 5/0, 2.201845. If you have an imaginary number- 6i, then this would be considered as non real numbers like x+2, red, wind, and y/7.

Step-by-step explanation:

I hope this helped you!

Answer:

59m

Step-by-step explanation:

Length= 3 × ( width)

But perimeter= 2width + 2 Lenght= 472

Let length= X

Width= Y

X= 3Y.........eqn(1)

2X + 2Y= 472........eqn(2)

Substitute X= 3Y in eqn(2)

2(3Y) + 2Y = 472

6Y + 2Y= 472

8Y= 472

Y= 59 m

Hence, the width of the pool is 59 m

Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

What we need to know

1) Rewrite the equation x - y = 5 into slope-intercept form and identify the slope

[tex]x - y = 5[/tex]

Subtract both sides by x

[tex]x - y -x= -x+5\\-y= -x+5[/tex]

Divide both sides by -1

[tex]y= x-5[/tex]

Now, we can tell clearly that the slope (m) of this line is 1. Therefore, a line parallel to this would also have a slope of 1.

Plugging 1 as m into [tex]y=mx+b[/tex], we get:

[tex]y=x+b[/tex]

2) Find the y-intercept (b) of the line parallel to [tex]y= x-5[/tex] and find the final equation

[tex]y=x+b[/tex]

Plug in the given point (-5,-2)

[tex]-2=-5+b[/tex]

Add 5 to both sides

[tex]-2+5=-5+b+5\\3=b[/tex]

Therefore, the y-intercept of this line is 3. Now, plugging this back into our original equation, we get:

[tex]y=x+b\\y=x+3[/tex]

I hope this helps!

Answer:

-4, -3, 0, 2

Step-by-step explanation:

Answer:

-4,-3,0,2 :p ...........