In a school of 685 students, there are 385 students involved in sports teams, and there are 450 involved with the music program. There are 87 students that are not involved in either program.
There are some students involved in both programs.
a) Draw a Venn diagram to represent this situation.
b) Use the additive principle of non-mutually exclusive sets to determine the number of students that
are involved in both team sports and music.
c) Use the additive principle for the probability of non-mutually exclusive events to determine the
probability of a student being involved in team sports OR involved in music.

Scott’s bank account showed a balance of $750 on sunday. during the next five days, he made one deposit of $140 and numerous withdrawals of $180 each. let x represent the number of withdrawals that scott made. write an inequality that can be used to find the maximum number of withdrawals that scott could have made and maintain a balance of at least $100. do not use a dollar sign ($) in your response.

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.

In a rectangle klmn, km = 6x + 16 and ln = 49. find the value of x