The following is the list of MAD statistics for each of the models you have estimated from time-series data:

Model MAD
Linear Trend 2.38
Quadratic Trend 3.66
Exponential Trend 4.33
AR(2) 1.97

Based on the MAD criterion, the most appropriate model is:

a) linear trend.
b) quadradic trend.
c) exponential trend.
d) AR(2).

b) quadratic trend.

Step-by-step explanation:

The Mean Absolute Deviation MAD is the value which is calculated by taking sum of deviation of the observations from the mean and divides it by the total number of observations. The quadratic trend is analysis of values over time series, the values will not be constant and will either fall or rise. The quadratic trend gives the lowest value for MAD. The low value for MAD is preferable so the best model which should be used for MAD is quadratic trend.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)