Describe an efficient algorithm that, given a set \{x_1, x_2, \ldots, x_n\}{x 1 ,x 2 ,…,x n} of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points. argue that your algorithm is correct.

The triangles in the diagram are congruent. if mzf = 40°, mza = 80°, and mzg = 60°, what is mzb?

Pepe and leo deposits money into their savings account at the end of the month the table shows the account balances. if there pattern of savings continue and neither earns interest nor withdraw any of the money , how will the balance compare after a very long time ?

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.