With reference to time series data patterns, a cyclical pattern is the component of the time series that: a. is characterized by a linear variation of the dependent variable with respect to time.

b. shows a periodic pattern lasting more than one year.

c. shows a periodic pattern lasting one year or less.

d. does not vary with respect to time.

b. shows a periodic pattern lasting more than one year.

Step-by-step explanation:

A cyclical pattern is the component of the time series that exhibit fluctuations in the data pattern. The frequency at which the data rises and falls is not fixed. The fluctuations occurring in the cyclical pattern can last up to 2 years or more.

Time series patterns are of three types, namely, trend, seasonal, and cyclical. The trend is associated with an increase in data that lasts a long period of time. The seasonal increase in data occurs at a definite frequency.

y=−9/2x+10

step-by-step explanation:

let's solve for y.

0−9x−2y=−20

step 1: add 9x to both sides.

−9x−2y+9x=−20+9x

−2y=9x−20

step 2: divide both sides by -2.

−2y

−2

=

9x−20

−2

y=

−9

2

x+10

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2