Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.

Question

x 1 2 5 10
y 6 12 30 60
A. direct variation; y equals one-sixth x
B. inverse variation; x y equals 6
C. direct variation; y equals 6 x
D. inverse variation; x y equals one-sixth

Answer 1

C. direct variation; y equals 6x

Answer 2

Dorothy and Rosanne are baking cookies for a party. Working alone, Rosanne can finish the cookies in 6 hours. Dorothy can finish them in 8 hours if she is working alone. How long will it take them to bake the cookies if they are working together? Round your answer to the nearest hundredth if necessary.
A. 7.00 hours
B. 3.43 hours
C. 0.29 hours
D. 14.00 hours

Answer 3

Let's use the formula for working together:

Time to complete task together = (time for person 1 to complete task * time for person 2 to complete task) / (time for person 1 to complete task + time for person 2 to complete task)

Plugging in the values we get:

Time to complete task together = (6 hours * 8 hours) / (6 hours + 8 hours)

Time to complete task together = 48 / 14

Time to complete task together ≈ 3.43 hours

Therefore, the answer is B. 3.43 hours.