Consider a single-server queue in which customers arrive according to a Poisson process with rate 1 per minute. The service time is according to a general distribution with mean 0.5 minutes. Assume that 50% of the time system is idle (no customer is in the system). (a) what is the average number of busy servers? (b) what is the average amount of time that the system is busy?

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

Aretha wanted to gather data about the cost of local bowling leagues in her area. she plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20. identify and interpret the y-intercept in this model. the y-intercept is 20. this is the cost per month. the y-intercept is 20. this is the cost of registration. the y-intercept is 15. this is the cost of registration. the y-intercept is 15. this is the cost per month.

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 + 4x + 5 = 0