Penelope has a points card for a movie theater. She receives 50 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs 65 points for a free movie ticket. Which equation or tape diagram could be used to represent the context if vv represents the number of visits Penelope must make to earn a free movie ticket?

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.