Agame has 3 possible outcomes, with probabilities p1, p2, and p3. the amount of money that you will win or lose for each outcome is v1, v2, and v3, respectively. what is the expression p1v1 + p2v2 + p3v3 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.

Matteo makes raspberry punch. the table shows how many parts ginger ale and raspberry juice to use for a batch. raspberry punch parts ginger ale 2 parts raspberry juice 3 matteo decides to add one part of raspberry juice. what is the new ratio of ginger ale to raspberry juice?

1. a driveway has a 15° grade. if the driveway is 40 meters long, how much does the driveway rise? (nearest tenth of a meter) 2. a person located 4 miles from a rocket launch site sees a rocket at an angle of elevation of 32°. at that moment, how high is the rocket above the ground? (nearest tenth of a mile) 3.an airplane approaches an airport landing strip with an angle of depression of 12°. if the airplane is flying at an altitude of 20,000 feet, find the distance on the ground that the plane will need to land. (nearest 1,000 feet) 4.two buildings are located on opposite sides of the street, 40 meters apart. the angle of elevation from the top of the shorter building to the top of the taller building is 53°. if the taller building is 300 meters tall, what is the height of the shorter building? (nearest meter) 5.george is 187 cm tall. his son, ralph, is 142 cm tall. who casts the longer shadow. george when the sun is 65° above the horizon, or ralph when the sun is 56° above the horizon? how much longer? (nearest centimeter)

Rob spent 25%, percent more time on his research project than he had planned. he spent an extra h hours on the project. which of the following expressions could represent the number of hours rob actually spent on the project? two answers