Consider a nail salon, which only offers manicures, with two nail technicians and one waiting chair.Each nail technician does manicures at a rate of two per hour, and customers arrive at rate 6 perhour, both with exponentially distributed times. Customers arriving to a fully occupied salon leave immediately. (a) Find the stationary distribution for the number of customers. (b) What fraction of customers leave without a manicure on the long run? (c) After it becomes empty, for how long does the shop stay empty on average?

You collect data of average annual returns for Amazon Stock and Microsoft Stock and make the following table: (This data can be copied into Excel.) Year Amazon Return Microsoft Return 2013 0.5896 0.1221 2014 -0.2218 0.2416 2015 1.1778 0.1944 2016 0.1095 0.1200 2017 0.5596 0.3766 2018 0.2843 0.1874 2019 0.3216 0.5526 You use this data to answer the research question: are true population Amazon Returns greater than true population Microsoft Returns?

If actual period demand varies from the forecast by more than 3MAD, this indicates: there is 3% chance that the forecast is wrong. there is a 98% chance that the forecast is wrong. there is a 97% chance that the forecast is wrong. there is a 3% chance that the forecast is correct Moving to the next question prevents changes to this answer:

A certain city's power company charges their residents for electricity usage on a daily basis. There is a basic charge of 11.57 cents. For each day the first 10 kWh cost 4.81 cents per kWh and any additional kWhs are 9.69 per kWh. (A kWh, or kilowatt-hour, is a unit of energy.) (a) Complete the following table using the information provided above. kWhkWh 0 5 10 15 20 cost (dollars)cost (dollars)           kWhkWh 25 30 35 40 cost (dollars)cost (dollars)         (b) We can define a piecewise function f(x)f(x) where xx is the kWh used in a day and f(x)f(x) is the cost, in dollars. This function would have the form   f(x)={g(x)h(x)ififx∈Ax∈Bf(x)={g(x)ifx∈Ah(x)ifx∈B What functions g(x)g(x) and h(x)h(x) make up the piecewise function f(x)f(x)? g(x)=g(x)= for A = h(x)=h(x)= for B = Hint: A and B are intervals. If an interval uses ±∞±∞ write inf or -inf . (c) Using the above function, what is the cost of 26 kWh? dollars. (d) For 3 dollars, what is the maximum kWh usage for one…