Agame involves rolling a fair six-sided die. if the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. if the number is not a multiple of three, the player gets nothing. what is the expected value of a player's winnings on each roll?

$30

Step-by-step explanation:

To find the expected value, first we find the outcomes for the sample space.

Rolling a 6-sided die, we have

1, 2, 3, 4, 5, 6

There are 2 values that are whole number multiples of 3:  3 and 6.

There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.

There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.

Next we multiply the value won or lost by each probability.

If the player rolls a 3, they win 3(20) = 60.  Multiplying it by its probability, we have

1/6(60) = 60/6 = 10

If the player rolls a 6, they win 6(20) = 120.  Multiplying it by its probability, we have

1/6(120) = 120/6 = 20.

If the player rolls a 1, 2, 4 or 5, they win nothing.  0 times all of these will be 0.

Lastly, we add together these products:

10+20+0+0+0+0 = 30

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

the answer is b. 60. each interior angle in 120, so the exterior angle must be 60 in order to add up to 180

step-by-step explanation: