a game has 3 possible outcomes, with probabilities p 1, p 2, and p 3. the amount of money that you will win or lose for each outcome is v 1, v 2, and v 3, respectively. what is the expression p 1 v 1 + p 2 v 2 + p 3 v 3 equal to?
the total amount you will win (or lose) in the long run.
the average amount you will win (or lose) per game in the long run.
the exact amount you will win (or lose) per game.
the amount that you will win (or lose) for 3 games.

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.