A game is played using ne die. If the die is rolled and shows 3, the player wins $45. If the die shows any number other than 3, the player wins nothing. If there is a charge of $9 to play the game, what is the game's expected value?

-$13.5

Step-by-step explanation:

Let x be a random variable of a count of player gain.

- We are told that if the die shows 3, the player wins $45.

- there is a charge of $9 to play the game

If he wins, he gains; 45 - 9 = $36

If he looses, he has a net gain which is a loss = -$9

Thus, the x-values are; (36, -9)

Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6

Thus;

E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)

E(X) = (1/6)(36 - (5 × 9))

E(X) = (1/6)(36 - 45)

E(X) = -9/6 = -3/2

E(X) = -3/2

This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.