During the course of a day, the vehicle traffic at a certain location varies randomly, changing among light, medium, and heavy. imagine a three-state continuous time markov process where changes in traffic density are represented by transitions. assume the only way to get from light to heavy or vice versa is by way of medium. the transition times are exponentially distributed. assume the parameter values are λlm = 4, λml = 3, λmh = 2, λhm = 1 in units of transitions per hour. find the percentages of time that the traffic is light, medium, and heavy.

Arectangle has an area of 54 square feet. if the length is 3 feet more than the width, find the dimensions of the rectangle.

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

Any is very appreciated! (picture is provided below)not sure how to do this at all won't lie