One of Madison's hobbies is to locate hidden geocaches. To find yesterday's cache, Madison was instructed to start at a water fountain at a local park. Then, the directions had her walk 30 yards due west and 16 yards due south. If this was the location of the cache, how far was it from the water fountain where she started? A.
14 yards
B.
34 yards
C.
23 yards
D.
46 yards

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. what is the probability you will roll a brown on your next toss of the die? express your answer as a simplified fraction or a decimal rounded to four decimal places.

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis

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.