Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $36,000 on a clear day and $17,000 on a cloudy day.They will make a loss of $5,000 if it rains. The weather channel has predicted a 48% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 13% that it will be sunny and 39% that it will be cloudy. Do not include the $ sign when you type your answer. (Blackboard can't understand it.)

The value of the expected profit from the concert is 8,910

Step-by-step explanation:

Profit on a clear day X₁ = 36,000 with  13% probability.  

i.e  X₁ = 36000

    P(X₁) = 0.13

Profit on a cloudy day = 17,000 with 39% probability.

i.e  X₂ = 17000

    P(X₂) = 0.39

else,

loss of 5,000 if it rains with the probability of 48%.

i.e  X₃ = 5000

    P(X₃) = 0.48

The value of the expected profit from the concert is obtained as follows

Expected Value = (36,000*0.13) + (17,000*0.39) - (5,000*0.48)

                           = 4,680 + 6,630 - 2,400

                           = 8,910

16π m2

Step-by-step explanation:

The area of a sector (A) is given by:

Where

is the angle of the sector

r is the radius of the circle

We can see that the angle of the sector is 90, and the radius of the circle is 8. Plugging these into the formula, we get:

The area is 16π m2