2. The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years. Year Quarter Profit ($1000s) 1 1 45 1 2 51 1 3 72 1 4 50 2 1 49 2 2 45 2 3 79 2 4 54 3 1 42 3 2 58 3 3 70 3 4 56 a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter. b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?

The graph shows the function f(x) = (2.5)x was horizontally translated left by a value of h to get the function g(x) = (2.5)x–h.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Julius sold five times as many computers as sam sold last year. in total, they sold 78 computers. how many computers did julius sell?