Answer:
We need at least 243 stores.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
The margin of error of the interval is:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
For this problem, we have that:
![n = 70, p = \frac{62}{70} = 0.886](https://tex.z-dn.net/?f=n%20%3D%2070%2C%20p%20%3D%20%5Cfrac%7B62%7D%7B70%7D%20%3D%200.886)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.04 with 95% confidence using the large-sample method.
We need at least n stores.
n is found when M = 0.04. So
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.04 = 1.96\sqrt{\frac{0.886*0.114}}{n}}](https://tex.z-dn.net/?f=0.04%20%3D%201.96%5Csqrt%7B%5Cfrac%7B0.886%2A0.114%7D%7D%7Bn%7D%7D)
![0.04\sqrt{n} = 1.96\sqrt{0.886*0.114}](https://tex.z-dn.net/?f=0.04%5Csqrt%7Bn%7D%20%3D%201.96%5Csqrt%7B0.886%2A0.114%7D)
![\sqrt{n} = \frac{1.96\sqrt{0.886*0.114}}{0.04}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.96%5Csqrt%7B0.886%2A0.114%7D%7D%7B0.04%7D)
![(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.886*0.114}}{0.04})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%28%5Cfrac%7B1.96%5Csqrt%7B0.886%2A0.114%7D%7D%7B0.04%7D%29%5E%7B2%7D)
![n = 242.5](https://tex.z-dn.net/?f=n%20%3D%20242.5)
Rounding up
We need at least 243 stores.
Factor out -4
-4(x^3+3x^2-2x-6
Factor out x^2
-4(x^2(x+3)-2x-6)
Factor out -2
-4(x^2(x+3)-2(x+3))
Factor out x+3
-4(x+3)(x^2-2)
Y=mx +b plug that in , so the 23.95 would be the flat fee then you add 0.32
250 =23.95+0.32 subtract from both sides then divide the answer is 10 miles
Answer:
y = 5
Step-by-step explanation:
Expand the logarithm:
![\log_y{(5)}+\log_y{(y)}=2\\\\\dfrac{\log{(5)}}{\log{(y)}}+1=2 \quad\text{change of base formula}\\\\\dfrac{\log{(5)}}{\log{(y)}}=1 \quad\text{subtract 1}\\\\\log{(5)}=\log{(y)} \quad\text{multiply by log(y)}\\\\5=y \quad\text{take the anti-log}](https://tex.z-dn.net/?f=%5Clog_y%7B%285%29%7D%2B%5Clog_y%7B%28y%29%7D%3D2%5C%5C%5C%5C%5Cdfrac%7B%5Clog%7B%285%29%7D%7D%7B%5Clog%7B%28y%29%7D%7D%2B1%3D2%20%5Cquad%5Ctext%7Bchange%20of%20base%20formula%7D%5C%5C%5C%5C%5Cdfrac%7B%5Clog%7B%285%29%7D%7D%7B%5Clog%7B%28y%29%7D%7D%3D1%20%5Cquad%5Ctext%7Bsubtract%201%7D%5C%5C%5C%5C%5Clog%7B%285%29%7D%3D%5Clog%7B%28y%29%7D%20%5Cquad%5Ctext%7Bmultiply%20by%20log%28y%29%7D%5C%5C%5C%5C5%3Dy%20%5Cquad%5Ctext%7Btake%20the%20anti-log%7D)
_____
You can also take the antilog first:
5y = y²
y(y -5) = 0 . . . . . subtract 5y, factor
y = 0 or 5 . . . . . y=0 is not a viable solution, so y=5.