Suppose F⃗ (x, y)=ey/5i⃗ −sin(x)j⃗ and C is the counter-clockwise oriented rectangle with vertices (0,0), (2,0), (2,4), and (0,4). Use Green's theorem to calculate the circulation of F⃗ around C.

Determine which expressions represent real numbers and which expressions represent complex number. asaaap! plis!

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

Organic apples are on special for $1.50 per pound. does total cost vary inversely or directly with the number of pounds purchased? find the cost of 3.4 pounds of apples. a. inversely: $5.10 b. directly; $5.10 c. inversely: $2.27 d. directly; $2.27