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?

Yes.

70% of the customers buy a coffee drink and 30% buy food.

The sum of it is 100% already.

So 20% of it just another addition of information since it cannot exceed 100% of percentage (100% + 20% = 120%).

It also contains a subset for both percentage.

No

Step-by-step explanation:

If independent,

P(C^F) = P(C) × P(F)

0.2 = 0.3×0.7

0.2 = 0.21 is not a true statement

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2