For a certain data set the regression equation is y = 2 + 3x. the correlation coefficient between y and x in this data set
a. must be 0
b. is negative
c. must be 1
d. must be 3

C. Must be 1

Step-by-step explanation:

The correlation coefficient of an equation represents the relation between the  two variable ( dependent and independent )

It lies between -1 to 1,

If an equation has strongly positive correlation then the value of correlation coefficient is 1,

If there is no relation then the value of correlation is 0,

If there is strongly negative relation then the value of correlation coefficient is -1,

Here, the equation is,

y = 2 + 3x

Since, the value of y is increasing with increasing the value of x,

We can say that there is strong positive relation between the variables x and y,

Hence, by the above statements,

The correlation coefficient between y and x in this data set must be 1.

Option 'C' is correct.

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.

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