Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of free dash throw attempts before the first shot is made. (b) The distance a baseball travels in the air after being hit. (a) Is the number of free dash throw attempts before the first shot is made discrete or continuous?

a) Discrete Variable

b) Continuous Variable

Step-by-step explanation:

We are given the following in the question:

Discrete and Continuous:

(a) The number of free dash throw attempts before the first shot is made.

Since the number of shots made will always be expressed in whole numbers and the number of shots made will counted and not measured. Thus, number of free dash throw attempts before the first shot is made. is a discrete variable.

(b) The distance a baseball travels in the air after being hit.

The distance is a continuous variable as its value can be expressed in decimals. Also distance is always measured and not counted. Thus, distance a baseball travels in the air after being hit is a continuous variable.

yes

yes yes yes

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2