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3 years ago

5

A libary has 2000 books. there are 3 times as many non fiction books as fiction books. write and solve a system of equations to

determine the number of nonfiction and fiction books.

1 answer:

Andru [333]3 years ago

4 0

A: number of nonfiction books
b: number of fiction books
a+b=2000
a=3b
b=500
a=1500

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19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years

Juliette [100K]

Answer:

a) Approximately normal.

b) The mean is 75 years and the standard deviation is 0.8485 years.

c) 0.9909 = 99.09% probability that the mean age exceeds 73 years

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.

Sample of 50 retirees

This means that $n = 50$

Mean age and standard deviation are 75 and 6 years

This means that $\mu = 75, \sigma = 6$

a. Describe the shape of the sampling distribution of the sample mean in this case

By the Central Limit Theorem, approximately normal.

b. Find the mean and standard error of the sampling distribution of the sample mean.

By the Central Limit Theorem, the mean is 75 and the standard error is $s = \frac{6}{\sqrt{50}} = 0.8485$

c. What is the probability that the mean age exceeds 73 years?

This is 1 subtracted by the pvalue of Z when X = 73.

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

By the Central Limit Theorem

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

$Z = \frac{73 - 75}{0.8485}$

$Z = -2.36$

$Z = -2.36$ has a pvalue of 0.0091

1 - 0.0091 = 0.9909

0.9909 = 99.09% probability that the mean age exceeds 73 years

5 0

2 years ago

5(2x - 5) + 10x = 75

serg [7]

Answer:

x = 5

Step-by-step explanation:

5(2x-5) +10x = 75

10x -25 +10x = 75

20x - 25 = 75

20x = 100

x = 5

7 0

3 years ago

Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box

hjlf

V = s²h

<span>150 = s²h </span>
<span>150 = s²(3/2)s </span>
<span>(2/3)150 = s³ </span>
<span>100 = s³ </span>
<span>s = ∛100 (approx 4.642 in) </span>

6 0

3 years ago

You decide to enroll in a plan that gives you a 10% discount if you make telephone calls 7pm – 6am. The per minute charge is $0.

yanalaym [24]

<span>If you used the phone 130 minutes from 6 am to 7 pm, that would cost $13.00. 400 minutes from 7 pm to 6 am at a 10% discount would cost you $36.00. Add totals to get $49.00. Tax at 6% is 2.94. Your total bill would be $51.94.

Total bill = (0.10+0.06) x 130 + (0.10+0.06) x 400 x 0.90
= $ 51.94</span>

8 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%28-81%29x%5E%7B2%7D%20%7D" id="TexFormula1" title="\sqrt{(-81)x^{2} }" alt="\sqrt{(

SSSSS [86.1K]

Answer:

We conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$

Step-by-step explanation:

Given the radical expression

$\sqrt{\left(-81\right)x^2}$

simplifying the expression

$\sqrt{\left(-81\right)x^2}$

Remove parentheses: (-a) = -a

$\sqrt{\left(-81\right)x^2}=\sqrt{-81x^2}$

Apply radical rule: $\sqrt{-a}=\sqrt{-1}\sqrt{a},\:\quad \mathrm{\:assuming\:}a\ge 0$

$=\sqrt{-1}\sqrt{81x^2}$

Apply imaginary number rule: $\sqrt{-1}=i$

$=i\sqrt{81x^2}$

Apply radical rule: $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

$=\sqrt{81}i\sqrt{x^2}$

$=9i\sqrt{x^2}$

Apply radical rule: $\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$=9ix$

Therefore, we conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$

7 0

2 years ago