The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is

Jobs arrive at a facility at an average rate of $$5$$ in an $$8$$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $$40$$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be

The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}} = - 8\,\,MPa.$$ The maximum tensile stress (in MPa) at the point is ____________.

A pair of spur gears with module $$5$$ $$mm$$ and a center distance of $$450mm$$ is used for a speed reduction of $$5:1$$. The number of teeth on pinion is _________