Answer: (16%, 24%)
Step-by-step explanation:
The confidence interval for proportion is given by :-
![p\pm E](https://tex.z-dn.net/?f=p%5Cpm%20E)
Given : Significance level : ![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
The proportion of the respondents answered "crime and violence." : p=0.20
Margin of sampling error : ![E=\pm0.04](https://tex.z-dn.net/?f=E%3D%5Cpm0.04)
Now, the 95% confidence interval for the proportion of the population that would respond "crime and violence" to the question asked by the pollsters is given by :-
![0.20\pm 0.04\\\\=0.20-0.04,\ 0.20+0.04\approx(0.16,0.24)](https://tex.z-dn.net/?f=0.20%5Cpm%200.04%5C%5C%5C%5C%3D0.20-0.04%2C%5C%200.20%2B0.04%5Capprox%280.16%2C0.24%29)
In percentage, ![(16\%,24\%)](https://tex.z-dn.net/?f=%2816%5C%25%2C24%5C%25%29)
Hence, the 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters =(16%, 24%)
Answer:
-9.1r + 3.9
Step-by-step explanation:
-6.2r - 4.6 -2.9r + 8.5
-6.2r and -2.9r are alike, so we combine.
-6.2r + -2.9r = -9.1r
-4.6 and 8.5 are alike, so we combine.
-4.6 + 8.5 = 3.9
Specify how many additional hours did she work
Answer:
13/9
y =-22x+32
Step-by-step explanation:
Given that the functions f and g are differentiable for all real numbers x. The table below gives values for the functions and their first derivatives at selected values of x.
x f(x) f'(x) g(x) g'(x)
1 4 -3 5 2
2 -3 -1 4 6
3 π 8 -1 4
4 -5 unknown 0 3
a) ![h(x) = \frac{f(x)}{g(x)} \\h'(x) = \frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}](https://tex.z-dn.net/?f=h%28x%29%20%3D%20%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5C%5Ch%27%28x%29%20%3D%20%5Cfrac%7Bg%28x%29f%27%28x%29-f%28x%29g%27%28x%29%7D%7B%28g%28x%29%29%5E2%7D)
(using quotient rule)
Substitute 1 for x
![h'(1) = \frac{g(1)f'(1)-f(1)g'(1)}{(g(1))^2}\\=\frac{9-(-4)}{9} \\=\frac{13}{9}](https://tex.z-dn.net/?f=h%27%281%29%20%3D%20%5Cfrac%7Bg%281%29f%27%281%29-f%281%29g%27%281%29%7D%7B%28g%281%29%29%5E2%7D%5C%5C%3D%5Cfrac%7B9-%28-4%29%7D%7B9%7D%20%5C%5C%3D%5Cfrac%7B13%7D%7B9%7D)
b) ![r(x) = f(x) g(x)\\r'(x) = f(x) g'(x)+g(x)f'(x)](https://tex.z-dn.net/?f=r%28x%29%20%3D%20f%28x%29%20g%28x%29%5C%5Cr%27%28x%29%20%3D%20f%28x%29%20g%27%28x%29%2Bg%28x%29f%27%28x%29)
when ![x =2, r(x) = r(2) = f(2) g(2) = -12](https://tex.z-dn.net/?f=x%20%3D2%2C%20r%28x%29%20%3D%20r%282%29%20%3D%20f%282%29%20g%282%29%20%3D%20-12)
point of contact is (2,-12)
Slope of tangent =![r'(2) = f(2) g'(2)+g(2)f'(2)\\=-18+(-4) \\=-22](https://tex.z-dn.net/?f=r%27%282%29%20%3D%20f%282%29%20g%27%282%29%2Bg%282%29f%27%282%29%5C%5C%3D-18%2B%28-4%29%20%5C%5C%3D-22)
Using point slope form, tangent is
![y+12 = -22(x-2)\\y = -22x +32](https://tex.z-dn.net/?f=y%2B12%20%3D%20-22%28x-2%29%5C%5Cy%20%3D%20-22x%20%2B32)