Basically u put a one under the two then multiply the numerator by the numerator the multiply the denominator by the denominator
Y - 1 = 2(x - 2)
y - 1 = 2x - 4
y = 2x - 4 + 1
y = 2x - 3
So first thing you look for is whichever graph has a y-intercept at y = - 3. Any of the graphs that DON'T have a y-intercept at (0, - 3) can be eliminated. The only one that does is the first graph so...
Your answer is the first graph.
X-number of weeks
50-2X ≥ 20
-2X ≥ 20-50 multiply both sides by -1
2X ≥ 30
X ≥ 30/2
X ≥15
Katie can withdraw money for at least 15 weeks.
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
![M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\](https://tex.z-dn.net/?f=M_s%3D%5Cdfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5En%5C%2Cx_i%5C%5C%5C%5C%5C%5CM_s%3D%5Cdfrac%7B1%7D%7B12%7D%2869.3%2B56%2B22.1%2B47.6%2B53.2%2B.%20.%20.%2B13.8%29%5C%5C%5C%5C%5C%5CM_s%3D%5Cdfrac%7B524.4%7D%7B12%7D%5C%5C%5C%5C%5C%5CM_s%3D43.7%5C%5C%5C%5C%5C%5Cs_s%3D%5Cdfrac%7B1%7D%7Bn-1%7D%5Csum_%7Bi%3D1%7D%5En%5C%2C%28x_i-M_s%29%5E2%5C%5C%5C%5C%5C%5Cs_s%3D%5Cdfrac%7B1%7D%7B11%7D%28%2869.3-43.7%29%5E2%2B.%20.%20.%20%2B%2813.8-43.7%29%5E2%29%5C%5C%5C%5C%5C%5Cs_s%3D%5Cdfrac%7B3152%7D%7B11%7D%5C%5C%5C%5C%5C%5Cs_s%3D286.5%5C%5C%5C%5C%5C%5C)
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
![M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\](https://tex.z-dn.net/?f=M_n%3D%5Cdfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5En%5C%2Cx_i%5C%5C%5C%5C%5C%5CM_n%3D%5Cdfrac%7B1%7D%7B15%7D%2828.6%2B25.1%2B26.4%2B34.9%2B28.8%2B.%20.%20.%2B13.9%29%5C%5C%5C%5C%5C%5CM_n%3D%5Cdfrac%7B453.8%7D%7B15%7D%5C%5C%5C%5C%5C%5CM_n%3D30.3%5C%5C%5C%5C%5C%5Cs_n%3D%5Cdfrac%7B1%7D%7Bn-1%7D%5Csum_%7Bi%3D1%7D%5En%5C%2C%28x_i-M_n%29%5E2%5C%5C%5C%5C%5C%5Cs_n%3D%5Cdfrac%7B1%7D%7B14%7D%28%2828.6-30.3%29%5E2%2B.%20.%20.%20%2B%2813.9-30.3%29%5E2%29%5C%5C%5C%5C%5C%5Cs_n%3D%5Cdfrac%7B713.3%7D%7B14%7D%5C%5C%5C%5C%5C%5Cs_n%3D50.9%5C%5C%5C%5C%5C%5C)
Now, we can calculate the coefficient of variation:
CV smokers:
![CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387](https://tex.z-dn.net/?f=CV_s%3D%5Cdfrac%7Bs_s%7D%7BM_s%7D%3D%5Cdfrac%7B16.9%7D%7B43.7%7D%3D0.387)
CV non-smokers:
![CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234](https://tex.z-dn.net/?f=CV_n%3D%5Cdfrac%7Bs_n%7D%7BM_n%7D%3D%5Cdfrac%7B7.1%7D%7B30.3%7D%3D0.234)
A replacement value for an open sentence is a solution