Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
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
C. direct variation; y equals 6x
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
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.
To determine if the data represents direct variation or inverse variation, we can check if the ratio of y to x remains constant.
Let's calculate the ratios for each pair of values:
For x = 1, y = 6, the ratio of y to x is 6/1 = 6.
For x = 2, y = 12, the ratio of y to x is 12/2 = 6.
For x = 5, y = 30, the ratio of y to x is 30/5 = 6.
For x = 10, y = 60, the ratio of y to x is 60/10 = 6.
Since the ratio of y to x is constant, the data represents a direct variation.
The equation that models the data in the table is y = 6x.
Therefore, the correct answer is C. direct variation; y equals 6x.