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fomenos
3 years ago
9

The director of the library believes that 14% of the library's collection is checked out. If the director is right, what is the

probability that the proportion of books checked out in a sample of 478 books would be less than 13%? Round your answer to four decimal places.
Mathematics
1 answer:
Ksivusya [100]3 years ago
5 0

Answer: 0.2643

Step-by-step explanation:

Let p be the population proportion and \hat{p} be the sample proportion .

As per given question , we have

p=0.14\\\\ \hat{p}=0.13\\\\ n=478

z-score : \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

z=\dfrac{0.13-0.14}{\sqrt{\dfrac{0.14(1-0.14)}{478}}}\\\\=-0.630087269176\approx-0.63

The required probability ( using z-table ):-

P(z

Hence, the probability that the proportion of books checked out in a sample of 478 books would be less than 13% = 0.2643

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Will give brainliest and 5 stars
BaLLatris [955]
First, find what percentage of students had 3 or more by adding up your known percents:

45% + 23 % + 21% + x% = 100%
x = 11%

Since you're given that 96 students had 2 or more, you add up the percentages of 2 and 3 or more:

11 + 21 = 32%

Now set up a proportion that relates it to the whole:

\frac{96 students}{32 percent} = \frac{x students}{100 percent}

This will allow you to find the total number of students at the school.

Cross multiplying and solving for x results in 300 total students.

Question 1:
45% had one or more absences. 45% of 300 students is 135 students.

Question 2:
As we found before, 11% of students had three or more. 11% of 300 is 33 students.
5 0
3 years ago
Select all the factors roots of x^3 +2x^2-16x-32
Ivanshal [37]

Factor by grouping. Group up the terms into pairs, factor each pair, then factor out the overall GCF.

x^3 + 2x^2 - 16x - 32

(x^3 + 2x^2) + (-16x-32) ... pair up terms

x^2(x + 2) + (-16x - 32) ... factor x^2 from the first group

x^2(x + 2) - 16(x + 2) ... factor -16 from the second group

(x^2 - 16)(x + 2) .... factor out (x+2)

(x - 4)(x + 4)(x + 2) .... Use the difference of squares to factor x^2-16

---------------------------

The original expression completely factors to (x - 4)(x + 4)(x + 2)

The three factors are x - 4  and  x + 4   and   x + 2

5 0
3 years ago
Read 2 more answers
Helpppppppppppppppppp​
UNO [17]

Answer:

<em>2 solutions</em>

Step-by-step explanation:

Given the expression

2m/2m+3 - 2m/2m-3 = 1

Find the LCM of the expression at the left hand side:

2m(2m-3)-2m(2m+3)/(2m+3)(2m-3) = 1

open the bracket

4m²-6m-4m²-6m/(4m²-9) = 1

Cross multiply

4m²-6m-4m²-6m = 4m²  - 9

-12m = 4m²  - 9

4m²  - 9+12m = 0

4m² +12m-9 = 0

<em>Since the resulting equation is a quadratic equation, it will have 2 solutions since the degree of the equation is 2</em>

8 0
2 years ago
one high speed internet provider has a $50 setup fee and costs $30 per month. another has no setup fee and costs $40 per month.
vlabodo [156]

Answer:

y=30x+50 and y=40

Step-by-step explanation:


7 0
3 years ago
What is the midpoint of a segment with endpoints at(-4,-8) and (8, 10)?
vekshin1

Answer:

The answer is

<h2>( 2 , 1)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

M = ( \frac{x1 + x2}{2}  , \:  \frac{y1 + y2}{2} )

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4,-8) and (8, 10)

The midpoint is

M = ( \frac{ - 4 + 8}{2}  , \:  \frac{ - 8 + 10}{2} ) \\  = ( \frac{4}{2} ,  \frac{2}{2} )

We have the final answer as

<h3>( 2 , 1)</h3>

Hope this helps you

4 0
3 years ago
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