At a coffee shop, 70% of the customers buy a coffee drink, 30% buy food, and 20% buy both a coffee drink and food. Are buying food and buying a coffee drink independent events? How do you know?

No

Step-by-step explanation:

For events to be independent:

P(A^B) = P(A)×P(B)

P(Food & Coffee) = 0.2

P(Food) = 0.3

P(Coffee) = 0.7

Since,

0.2 = 0.3×0.7

0.2 = 0.21 is a false statement. They are not independent

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

68719476736

step-by-step explanation:

8*8*8*8*8*8*8*8*8*8*8*8=68719476736