An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane. If 2 swimmers are in a lane, each swims up and down one side of the lane. Swimmers always join the lane with the fewest number of swimmers. If all 3 lanes are occupied by 2 swimmers, a prospective swimmer becomes disgusted and goes running.

a. What fraction of the time will 3 people be swimming laps?

b. On the average, how many people are swimming laps in the pool?

c. How many lanes does the YMCS need to allot to lap swimming to ensure that at most 5% of all prospective swimmers will become disgusted and go running?

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

Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). suppose your car averages 33 miles per gallon on the highway if your average speed is 54 miles per hour, and it averages 22 miles per gallon on the highway if your average speed is 75 miles per hour. answer parts (a) and (b) below. a. what is the driving time for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the driving time at 75 miles per hour? the driving time at 54 miles per hour is nothing hours. (type an integer or decimal rounded to two decimal places as needed.) the driving time is at 75 miles per hour is nothing hours. (round to two decimal places as needed.) b. assume a gasoline price of $3.33 per gallon. what is the gasoline cost for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the gasoline cost at 75 miles per hour? the gasoline cost at 54 miles per hour is $ nothing. (round to two decimal places as needed.) the gasoline cost at 75 miles per hour is $ nothing. (round to two decimal places as needed.)

Find the scale factor and ratio of perimeters for a pair of similar trapezoids with areas 49 cm squared and 36 cm squared.