The values of Alabama building contracts (in millions of dollars) for a 12-month period follow:240 350 230 260 280 320 220 310 240 310 240 230a. Construct a time series plot. What type of pattern exists in the data?b. Compare a three-month moving average forecast with an exponential smoothing forecast. Use alpha =0.2 Which provides the better forecasts based on MSE?c. What is the forecast for the next month?

Check the explanation

Step-by-step explanation:

Kindly check the attached image below for the full explanation.

Based on the preceding MBE values in the attached image below, the 3-Month moving averages appear better; however, exponential smoothing was penalized by including month 2 which was difficult for any method to forecast; using only the errors for months 0 to 12, the MBE for exponential smoothing is

MSE  = 14694/9= 1632.72

exponential smoothing was better considering months 4 to 12.

(-5,-28)

i graphed to on desmos.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc