Help me and I'll label the first person the brainest

Solve -r/4 < 8 A.r<-32 B. r. >-32 C.r < -2 D.r>-2

Gnom [1K]

$\frac{-r}{4}$

$Ans.\ B$

4 0

4 years ago

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:

i)

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)

71

Step-by-step explanation:

i)

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

so

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

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

so

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

(*)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)

5 0

4 years ago

How do you solve problem like... x+5=5

lana66690 [7]

<h2>Answer:</h2>

x = 0

<h2>Step-by-step explanation:</h2>

x + 5 = 5

- 5 - 5

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

x = 0

5 0

3 years ago

The fifth term of an arithmetic sequence is 100, and the common difference is 4. Find the first three terms of the sequence.

Ronch [10]

$\bf a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term}\\
d=\textit{common difference}\\
--------------\\
a_5=100\\
n=5\\
d=4
\end{cases}
\\\\\\
a_5=a_1+(5-1)4\implies 100=a_1+(5-1)4
\\\\\\
\textit{solve for }a_1\textit{ to find the first term}$

then use the common difference "d", to get the 2nd and 3rd terms

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

$\bf a_5=a_1+(5-1)4\implies 100=a_1+(5-1)4\implies 100=a_1+(4)4
\\\\\\
100=a_1+16\implies 100-16=a_1\\\\ 84=a_1\quad 
\begin{cases}
a_1=&84\\
a_2=84+4\to &88\\
a_3=88+4\to &92
\end{cases}$

6 0

4 years ago

Marcus needs 108 inches of wood to make a frame. How many feet of wood does Marcus need for the frame?

8_murik_8 [283]

Basically, you are just simply converting inches to feet.
So we need to convert 108 inches to x feet.
12 inches = 1 foot
So, if 12 inches equals 1 foot, just divide 108 by 12 to get the number of feet.
108÷12≈9
So, 108 inches equals your answer of 9 feet.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Hope this helped :)

3 0

3 years ago