An engineering professor acquires a new computer once every 2 years. The professor can choose from three models: M1, M1, and M3. If the present model is M1, the next model can be M2 with probability 0.2, or M3 with probability 0.15. If the present model is M2, the probabilities of switching to M1 and M3 are 0.6 and 0.25, respectively. And, if the present model is M3, then the probabilities of purchasing M1 and M2 are 0.5 and 0.1, respectively. Represent the situation as a Markov chain.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."