For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. Click on the datafile logo to reference the data. (a) Choose the correct time series plot. (i) (ii) (iii) (iv) - Select your answer - What type of pattern exists in the data? - Select your answer - (b) Compare a three-month moving average forecast with an exponential smoothing forecast for α = 0.2. Which provides the better forecasts using MSE as the measure of model accuracy? Do not round your interim computations and round your final answers to three decimal places. Three-month Moving Average Exponential smoothing MSE - Select your answer - (c) What is the forecast for next month? If required, round your answer to two decimal places.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.