Answer: -6.26
Step-by-step explanation:
Test statistic for population proportion is given by :-
![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
, where p = population proportion.
= sample proportion.
n= sample size.
As per given , we have
![H_a:p](https://tex.z-dn.net/?f=H_a%3Ap%3C0.93)
n= 1021
Then, the test statistic will be :-
![z=\dfrac{0.88-0.93}{\sqrt{\dfrac{0.93(1-0.93)}{1021}}}\\\\=\dfrac{-0.05}{\sqrt{0.0000637610186092}}\\\\=\dfrac{-0.05}{0.0079850496936}\\\\=-6.26170179506\approx-6.26](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.88-0.93%7D%7B%5Csqrt%7B%5Cdfrac%7B0.93%281-0.93%29%7D%7B1021%7D%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-0.05%7D%7B%5Csqrt%7B0.0000637610186092%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-0.05%7D%7B0.0079850496936%7D%5C%5C%5C%5C%3D-6.26170179506%5Capprox-6.26)
Hence, the value of the test statistic is -6.26 .
C. $111.65 would be the answer
Answer:
b=-3
Step-by-step explanation:
If the expression simplifies to bx that means the
terms and the constant terms must be cancel out.
Simplify it first.
![(4x+4)(ax-1)-x^{2} +4\\=(4ax^{2} -4x+4ax-4)-x^{2} +4\\=4ax^{2} -x^{2} -4x+4ax-4+4\\=4ax^{2} -x^{2} -4x+4ax](https://tex.z-dn.net/?f=%284x%2B4%29%28ax-1%29-x%5E%7B2%7D%20%2B4%5C%5C%3D%284ax%5E%7B2%7D%20-4x%2B4ax-4%29-x%5E%7B2%7D%20%2B4%5C%5C%3D4ax%5E%7B2%7D%20-x%5E%7B2%7D%20-4x%2B4ax-4%2B4%5C%5C%3D4ax%5E%7B2%7D%20-x%5E%7B2%7D%20-4x%2B4ax)
We know –4 + 4 will cancel out. If we simplify this expression to only an x term, then the
terms should be cancelled. Therefore, we say that 4ax^2 – x^2 = 0.
![4ax^{2} -x^{2} =0\\x^{2} (4a-1)=0\\4a-1=0\\4a=1\\a=\frac{1}{4}](https://tex.z-dn.net/?f=4ax%5E%7B2%7D%20-x%5E%7B2%7D%20%3D0%5C%5Cx%5E%7B2%7D%20%284a-1%29%3D0%5C%5C4a-1%3D0%5C%5C4a%3D1%5C%5Ca%3D%5Cfrac%7B1%7D%7B4%7D)
If we put a = ¼, then we can find the value of b:
![=4(\frac{1}{4} )x^{2} -x^{2} -4x+4(\frac{1}{4} )x\\=x^{2} -x^{2} -4x+x\\ (cancel out x^{2} terms)\\](https://tex.z-dn.net/?f=%3D4%28%5Cfrac%7B1%7D%7B4%7D%20%29x%5E%7B2%7D%20-x%5E%7B2%7D%20-4x%2B4%28%5Cfrac%7B1%7D%7B4%7D%20%29x%5C%5C%3Dx%5E%7B2%7D%20-x%5E%7B2%7D%20-4x%2Bx%5C%5C%20%28cancel%20out%20x%5E%7B2%7D%20terms%29%5C%5C)
![=-3x](https://tex.z-dn.net/?f=%3D-3x)
if the expression is equivalent to bx
Therefore, b = –3.
To make 5 dinner rolls, 1/2 cup of flour is used. How much is needed to make one dinner roll?
0.5 ÷ 5 = 0.1 ( for one dinner roll)
How many cups of flour are needed to make 3 dozen rolls?
3 × 12 = 36
0.1 × 36 = 3.6 (for 3 dozen rolls)
Answer:
1227 feet
Step-by-step explanation:
Let x is the the length of the base along Michigan
Given:
- The highest of the building is 28 feet less than 7 times the length of the base along Michigan
<=> The highest of the building = 7x -28
- The length of the roof is 65 feet shorter than the length of the base below it.
<=> The length of the roof = x - 65
- The area of one particular side is 149,327.5 square feet
<=>
*(7x -28 ) = 149327.5
<=> (2x -65) (7x -28) = 298655
<=>
- 511x = 296835
<=> x = 165.
So the building's height is: 7(165) -28 = 1227 feet