The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is less than 50.8 min.P(X < 50.8) = (Report answer accurate to 2 decimal places.)

If a convex function is multiplied by a negative constant, the result: A. is concave B. could be either convex or concave, depending on the value of the constant C. is convex D. is linear

Consider the case of Conrad's Cookie Company, where he and two of his friends (Jared and Jack) are working to make and sell cookies. They have just one oven and can bake up to two dozen cookies at a time. The oven can bake two dozen cookies simultaneously (of similar or different ingredients) or one dozen only. If one dozen is baking in the oven, baking time will not be any different from baking two dozen simultaneously. The sequence of baking steps and respective durations are below. Mixing and Spooning (together) 3 mins/dozen Loading 1 minutte/dozen. Baking 8 mins. baking time for one or two dozens. Cooling 6 minutes Packing 5 mins/dozen cookies Payment (to be done after packing only) 1 minute per order If all orders are 4 dozen cookies, a) What is the best way to assign Conrad and his friends to jobs in order to maximize capacity? Find highest theoretical capacity and bottleneck of the process. b) Once system warms up, is the capacity the same…

A single repairperson looks after both machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate  λi,  i = 1,2. When machine i fails, it requires an exponentially distributed amount of work with rate i to complete its repair. The repairperson will always service machine 1 when it is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop work on machine 2 and start on 1. What proportion of time is machine 2 down? Then compute the probability that machine 2 is down.) There are four possible states in total: no machine is down, only machine 1 is down, only machine 2 is down, and both machines are down. Formulate and solve the balance equations based these four states. Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Do not provide Excel Screet shot rather use tool table