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3 years ago

A rectangular prism has dimensions 3.2 in. by 5 in. by 1.5in. what is the volume area of the prism?

Mathematics

2 answers:

morpeh [17]3 years ago

8 0

Answer:

Step-by-step explanation:

3.2x5 x1.5=24

Hope this helps :)

Stells [14]3 years ago

3 0

It’s 24 because 3.2 x 5 x 1.5 = 24

It’s easy

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7236 by 25 7236 divided by 25

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In 2010, the Census Bureau estimated the proportion of all Americans who own their homes to be 0.669. An urban economist wants t

Alexxandr [17]

Answer:

Sample size making use of the Census Bureau: 1,499 American adults.

Sample size without making use of the Census Bureau: 1,692 American adults

ii)

Step-by-step explanation:

The sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

z = 1.645 is the critical value for a 90% confidence level (*) 

p= 0.669 is the population proportion given by the Census

e = 0.02 is the margin of error

$\bf n=\frac{(1.645)^2*0.669*0.331}{0.02^2}=1,498.05\approx 1,499$

rounded up to the nearest integer.

(*)This is a point z such that the area under the Normal curve N(0,1) 1nside the interval [-z, z] equals 90% = 0.9

It can be obtained with tables or in Excel or OpenOffice Calc with

NORMSINV(0.95)

If she ignores the Census estimate, the she has to take the largest sample possible that meets the requirements.

Let's show it is obtained when p = 0.5

As we said, the sample size n is

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

e = 0.02 is the error proportion

z = 1.645

hence

$\bf n=\frac{(1.645)^2p(1-p)}{(0.02)^2}=6765.0625p(1-p)=6765.0625p-6765.0625p^2$

taking the derivative with respect to p, we get

n'(p)=6765.0625-2*6765.0625p

and

n'(p) = 0 when p=0.5

By taking the second derivative we see n''(p)<0, so p=0.5 is a maximum of n

This means that if we set p=0.5, we get the maximum sample size for the confidence level required for the proportion error 0.02

Replacing p with 0.5 in the formula for the sample size we get

$\bf n=6765.0625*0.5-6765.0625(0.5)^2=1691.27\approx 1,692$

rounded to the nearest integer.

ii)

When we do not have a proportion but a variable whose approximate standard deviation s is known, then the sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2s^2}{e^2}$

where

z = 2.241 is the critical value for a 95% confidence level (*) 

s = 7.5 is the estimated population standard deviation

e = 2 hours is the margin of error

$\bf n=\frac{z^2s^2}{e^2}=\frac{(2.241)^2(7.5)^2}{(2)^2}=70.62\approx 71$

(*)This is a point z such that the area under the Normal curve N(0,1) inside the interval [-z, z] equals 95% = 0.95

It can be obtained in Excel or OpenOffice Calc with

NORMSINV(0.9875)

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4 years ago