The ages (in years) of a random sample of shoppers at a gaming store are given below: 12 19 23 14 20 16 21 18 14 19 What is the variance

the required variance is 11.6555

Step-by-step explanation:

Given data;

xi = 2 19 23 14 20 16 21 18 14 19

mean x" = 2+19+23+14+20+16+21+18+14+19 / 10

mean x" = 166 / 10 = 16.6

so;

X      xi - x"   (xi - x")²

12     -4.9     24.01

16     -0.9     0.81

23     6.1      37.21

13     -3.9     15.21

18      1.1       1.21

18      1.1       1.21

19      2.1      4.41

18      1.1       1.21

13     -3.9     15.21

19      2.1      4.41

Total           104.9

Variance =  n_i=1∑(xi - x")² / n-1

Variance = 104.9 / 9

Variance = 11.6555

Therefore, the required variance is 11.6555

linear

step-by-step explanation:

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.