Answer:
(a) Margin of error ( E) = $2,000 , n = 54
(b) Margin of error ( E) = $1,000 , n = 216
(c) Margin of error ( E) = $500 , n= 864
Step-by-step explanation:
Given -
Standard deviation
= $7,500
= 1 - confidence interval = 1 - .95 = .05
=
= 1.96
let sample size is n
(a) Margin of error ( E) = $2,000
Margin of error ( E) = ![Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
E = ![Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B.05%7D%7B2%7D%7D%5Cfrac%7B7500%7D%7B%5Csqrt%7Bn%7D%7D)
Squaring both side
![E^{2} = 1.96^{2}\times\frac{7500^{2}}{n}](https://tex.z-dn.net/?f=E%5E%7B2%7D%20%3D%201.96%5E%7B2%7D%5Ctimes%5Cfrac%7B7500%5E%7B2%7D%7D%7Bn%7D)
![n =\frac{1.96^{2}}{2000^{2}} \times 7500^{2}](https://tex.z-dn.net/?f=n%20%3D%5Cfrac%7B1.96%5E%7B2%7D%7D%7B2000%5E%7B2%7D%7D%20%5Ctimes%207500%5E%7B2%7D)
n = 54.0225
n = 54 ( approximately)
(b) Margin of error ( E) = $1,000
E = ![Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
1000 = ![Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B.05%7D%7B2%7D%7D%5Cfrac%7B7500%7D%7B%5Csqrt%7Bn%7D%7D)
Squaring both side
![1000^{2} = 1.96^{2}\times\frac{7500^{2}}{n}](https://tex.z-dn.net/?f=1000%5E%7B2%7D%20%3D%201.96%5E%7B2%7D%5Ctimes%5Cfrac%7B7500%5E%7B2%7D%7D%7Bn%7D)
![n =\frac{1.96^{2}}{1000^{2}} \times 7500^{2}](https://tex.z-dn.net/?f=n%20%3D%5Cfrac%7B1.96%5E%7B2%7D%7D%7B1000%5E%7B2%7D%7D%20%5Ctimes%207500%5E%7B2%7D)
n = 216
(c) Margin of error ( E) = $500
E = ![Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
500 = ![Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B.05%7D%7B2%7D%7D%5Cfrac%7B7500%7D%7B%5Csqrt%7Bn%7D%7D)
Squaring both side
![500^{2} = 1.96^{2}\times\frac{7500^{2}}{n}](https://tex.z-dn.net/?f=500%5E%7B2%7D%20%3D%201.96%5E%7B2%7D%5Ctimes%5Cfrac%7B7500%5E%7B2%7D%7D%7Bn%7D)
![n =\frac{1.96^{2}}{500^{2}} \times 7500^{2}](https://tex.z-dn.net/?f=n%20%3D%5Cfrac%7B1.96%5E%7B2%7D%7D%7B500%5E%7B2%7D%7D%20%5Ctimes%207500%5E%7B2%7D)
n = 864
Answer:
yes
Step-by-step explanation:
1 + 2 = 3
You don't add equal denominators. so 3/4
Answer:
16
Step-by-step explanation:
To start off this problem, we are given that the line AB is equal to the line CD. In addition to that, we are given that the line EF equally intersects line AB and line CD. This provides us proof that angle AGH is equivalent to angle DHG. From this information, we can solve this problem relatively easily.
Lets work with this equation:
![80 = 5x](https://tex.z-dn.net/?f=80%20%3D%205x)
Next, divide 80 by 5.
![\frac{80}{5} =x](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B5%7D%20%3Dx)
![16 = x](https://tex.z-dn.net/?f=16%20%3D%20x)
This means that x is equal to 16.
Answer:
The answer is the last one.
Step-by-step explanation:
When you do the others , they are step by step but when you do the last one, its just one step, which is -100.
Hope this helps :)