The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature x1, the number of days in the month x2, the average product purity X3, and the tons of product produced x4. The past year's historical data are available and are presented in the following table. 240 236 25 31 45 24 21 24 91 90 100 95 290 88 110 274 60 25 25 87 88 65 72 301 91 94 316 26 94 87 99 300 296 267 276 80 84 75 25 25 24 97 86 96 88 110 60 25 91 105 288 50 38 25 23 90 100 98 261 89 If y = ao + a1x1+a2X2+a3X3+ a4X4 represents the regression model. What is the value of a0? Use 2 decimal places.

For the data set, perform exponential smoothing with alpha = 0.1 to determine the forecast for week 20.   week Sales (1000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 13 31 14 34 15 31 16 33 17 28 18 32 19 30

A researcher wants to know how long it takes, on average, for a certain species of bacteria to divide. She watches 17 cells through a microscope and times how long it takes them to divide. She obtains the following data, in hours:8.1, 7, 7.4, 7.4, 6.6, 7.3, 7.5, 7, 7.7, 6.9, 7.9, 6.7, 6.7, 6.9, 7.5, 7.1, 7.3Assuming the population standard deviation is σ=0.4, construct a 89% confidence interval for the average time it takes this species of bacteria to divide.xˉ=α2=zα2=Margin of Error: E=We are 89% confident that this species of bacteria takes, on average, between ___hours and ___hours to divide.

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