Astudent measuring how gasoline prices change records the cost of gas at 10 randomly selected stations in her hometown. one week later, she records the price again at the same 10 stations. are these data paired or independent?

Independent- meaning that the probabilities are not changing
Dependent- meaning that the probabilities are changing
I would guess paired because the prices are changing, meaning that the probabilities are also changing. 

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.