Consider functions where the domain is {1,} and the range is {a, b} (a) how many of these functions are there? [hint: if at least one of its inputs is assigned to a different output. how many different outputs are possible for the input 1? what about for the input 2? ] a function is considered different
(b) how many of these functions are onto? hint: take your answer to part (a), and subtract the number of functions that are not onto.]

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.

Which number is located at point a on the number line? a number line is shown from negative 10 to 10 with each interval mark on the number line representing one unit. point a is labeled one interval mark to the right of negative 5.

What is the area of a rectangle with vertices (-8,-2), (-3,-2), (-3,-6), and (-8,-6)? units