A piano instructor examined student progress. she noticed that when students spend less time playing video games, their memorization ability does not tend to change . what can she conclude A. there is no correlation

B. there is a correlation between amount of time spent playing video games and memorization ability. there is probably also causation. this is because there is an increase in memorization ability with a decrease in the amount of time spent playing video games.

C. there is a correlation between amount of time spent playing video games and memorization ability. there may or may not be causation. further studies would have to be done to determine this

There is a correlation between amount of time spent playing video games and memorization ability. There may or may not be causation. Further studies would have to be done to determine this.

Step-by-step explanation:

A piano instructor examined student progress. She noticed that when students spend less time playing video games, their memorization ability tends to increase. What can she conclude?

There is a correlation between amount of time spent playing video games and memorization ability. There may or may not be causation. Further studies would have to be done to determine this.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!