Answer:
![CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}](https://tex.z-dn.net/?f=CI%20%3D%20%280.17%20-%200.27%29%5C%C2%B1%201.65%5Csqrt%7B%5Cfrac%7B%280.17%29%2A%280.83%29%20%2B%20%280.27%29%2A%280.73%29%7D%7B200%7D%7D)
Step-by-step explanation:
Given
![n = 200](https://tex.z-dn.net/?f=n%20%3D%20200)
-- City C
--- City K
Required
Determine the 90% confidence interval
This is calculated using:
![CI = \bar x \± z\frac{\sigma}{\sqrt n}](https://tex.z-dn.net/?f=CI%20%3D%20%5Cbar%20x%20%5C%C2%B1%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%20n%7D)
Calculating ![\bar x](https://tex.z-dn.net/?f=%5Cbar%20x)
![\bar x = \bar x_1 - \bar x_2](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cbar%20x_1%20-%20%5Cbar%20x_2)
![\bar x = \frac{x_1}{n} - \frac{x_2}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7Bx_1%7D%7Bn%7D%20-%20%5Cfrac%7Bx_2%7D%7Bn%7D)
![\bar x = \frac{34}{200} - \frac{54}{200}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B34%7D%7B200%7D%20-%20%5Cfrac%7B54%7D%7B200%7D)
![\bar x = 0.17 - 0.27](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%200.17%20-%200.27)
For a 90% confidence level, the z-score is 1.65. So:
![z = 1.65](https://tex.z-dn.net/?f=z%20%3D%201.65)
Calculating the standard deviation ![\sigma](https://tex.z-dn.net/?f=%5Csigma)
![\sigma = \sqrt{(\bar x_1)*(1 - \bar x_1) + (\bar x_2)*(1 - \bar x_2) }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%28%5Cbar%20x_1%29%2A%281%20-%20%5Cbar%20x_1%29%20%2B%20%28%5Cbar%20x_2%29%2A%281%20-%20%5Cbar%20x_2%29%20%7D)
So:
![\sigma = \sqrt{(0.17)*(1 - 0.17) + (0.27)*(1 - 0.27) }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%280.17%29%2A%281%20-%200.17%29%20%2B%20%280.27%29%2A%281%20-%200.27%29%20%7D)
![\sigma = \sqrt{(0.17)*(0.83) + (0.27)*(0.73)}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%280.17%29%2A%280.83%29%20%2B%20%280.27%29%2A%280.73%29%7D)
So:
![CI = (0.17 - 0.27)\± 1.65\frac{\sqrt{(0.17)*(0.83) + (0.27)*(0.73)}}{\sqrt {200}}](https://tex.z-dn.net/?f=CI%20%3D%20%280.17%20-%200.27%29%5C%C2%B1%201.65%5Cfrac%7B%5Csqrt%7B%280.17%29%2A%280.83%29%20%2B%20%280.27%29%2A%280.73%29%7D%7D%7B%5Csqrt%20%7B200%7D%7D)
![CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}](https://tex.z-dn.net/?f=CI%20%3D%20%280.17%20-%200.27%29%5C%C2%B1%201.65%5Csqrt%7B%5Cfrac%7B%280.17%29%2A%280.83%29%20%2B%20%280.27%29%2A%280.73%29%7D%7B200%7D%7D)
Answer:
f(t) = 1.22·(173/122)^(t/5)
Step-by-step explanation:
(a) An exponential growth (or decay) function can be written using the form ...
f(t) = (initial value)·(ratio in period)^(t/period)
Here, we're given an initial value of 1.22, a growth ratio of 1.73/1.22 in a period of 5 years, so we can write the function as ...
f(t) = 1.22·(173/122)^(t/5)
__
(b) In 2038-2012 = 26 years, the value of the function is ...
f(26) = 1.22·(173/122)^(26/5) ≈ 7.50 . . . . million
Answer:
36
Step-by-step explanation:
EF = is 1/3 of 15
Since the triangles are similar, then the perimeters are similar.
The perimeter of EDF is 12
The perimeter of ABC should be 3 times as large.
3*12 = 36
The perimeter of ABC = 36