At this years state fair, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $20. If you rolled a 7, you won $5. Any other roll was a loss. If the cost is $3 to play one game with one roll of the dice. What is the expectation of the game?

Expectation of the gain;

E = (2×$17 + 6×$2 - 28×3)/36

E = -$1.06

Step-by-step explanation:

For 2 and 12

Number of possible outcomes = 2

Gain = 20 - 3 = $17

For 7

Number of possible outcomes = 6

Gain = 5-3 = $2

For others

Number of possible outcomes = 36-(2+6) = 28

Gain = -$3

Expectation of the gain;

E = (2×$17 + 6×$2 - 28×3)/36 = -$38/36

E = -$1.06

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,