A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and services time averages six minutes per machine. What is the probability that a machine will have to wait for service with two operators

Lems1. the following data set represents the scores on intelligence quotient(iq) examinations of 40 sixth-grade students at a particular school: 114, 122, 103, 118, 99, 105, 134, 125, 117, 106, 109, 104, 111, 127,133, 111, 117, 103, 120, 98, 100, 130, 141, 119, 128, 106, 109, 115,113, 121, 100, 130, 125, 117, 119, 113, 104, 108, 110, 102(a) present this data set in a frequency histogram.(b) which class interval contains the greatest number of data values? (c) is there a roughly equal number of data in each class interval? (d) does the histogram appear to be approximately symmetric? if so, about which interval is it approximately symmetric?

The height of a flare fired from the deck of a ship in distress can be modeled by h(t)= -2(8t^2-52t-28), where h is the height of the flare above water and t is the time in seconds. a. find the time it takes the flare to hit the water.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .