What is the probability of rolling an even number on a six sided die and then rolling 4?
a.1/36
b.1/12
c.1/5
d.5/6

B. 1/12.

Step-by-step explanation:

There are 3 even numbers on the die so Probability(an even) = 3/6 = 1/2.

Probability (rolling a 4) = 1/6.

Probability ( rolling an even then a 4) = 1/2 * 1/6 = 1/12.

Question:

Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

f(x) = 2x2 + 16

g of x equals the square root of the quantity 5 x cubed

f(g(x))=  

Step-by-step explanation:

Given:

f(x) =

g(x) =

f(x) represents the amount of money Raul earns per ticket

x is the number of tickets he sells

g(x) represents the number of tickets Raul sells per hour

To find:

f(g(x)) = ?

Solution:

f(g(x)) represent the amount Raul earns by selling tickets for x hours

We know,

f(x)  =

f(g(x)) =

The square root and power 2 cancel each other

f(g(x))  =

f(g(x)) =

So at x hours

Raul earns

For example lets assume Raul works for 5 hours, then the amount he earns will be

f(g(x)) =

f(g(x))  = 10(125) +16

f(g(x)) = 1250 +16

f(g(x)) =  1266

You  can also find the amount Raul earns by

g(x) =

g(x) =

g(x) = 25

Substituting in f(x)

f(g(x)) = f(25)

f(25)  =

f(25) = 2(625) +16

f(25) = 1250 + 16

f(25) = 1266

so Raul will be earning 1266 if he sells tickets for 5 hours