2. In a random sample of 100 people, the correlation between amount of daily exercise and weight was found to be –.21. What would be the likely effect on the absolute value of the correlation coefficient under the following circumstances? (Hint: would r be greater or smaller? Why?) a. The sample is restricted to people who weighed less than 180 pounds

Correlation coefficient 'r' would be lower.

Step-by-step explanation:

Correlation is co movement relationship between two variables.

Correlation coefficient 'r' is positive, when variables move in same direction. 'r' is negative when variables move in opposite direction. So, 'r' lies between -1 (perfect negative correlation) & +1 (perfect positive correlation). High 'r' magnitude reflects strong correlation between the variables, Low 'r' reflects  weak weak correlation between the variables.

Correlation studied between amount of daily exercise and weight  : It is negative as exercise & weight are negatively correlated - more exercise, less weight & less exercise, more weight. 'r' is given = -0.21

If sample is restricted to people weighing less than 180 pounds : It would lead to fall in 'r'. Such because these low weight people are likely to have good natural metabolic rate, naturally slim body physique / figure. So, in their case, exercise & body weight are likely to be less (weakly) correlated than normal case.

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.