## Tuesday, October 04, 2016

### August 2016 Common Core Algebra II Regents Part 2, continued

I don't usually post the answers to the Algebra II exam, but I've received enough requests that I've decided to post some of the open-ended questions.
Some questions were posted earlier here and here.

### August 2016, Algebra II Part 2 (continued)

31. The distance needed to stop a car after applying the brakes varies directly with the square of the car’s speed. The table below shows stopping distances for various speeds.

Determine the average rate of change in braking distance, in ft/mph, between one car traveling at 50 mph and one traveling at 70 mph.
Explain what this rate of change means as it relates to braking distance.

32. Given events A and B, such that P(A) = 0.6, P(B) = 0.5, and P(A ∪ B) = 0.8, determine whether A and B are independent or dependent.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
0.8 = 0.6 + 0.5 - P(A ∩ B)
0.8 = 1.1 - P(A ∩ B)
-0.3 = - P(A ∩ B)
0.3 = P(A ∩ B)

If A and B are independent, then P(A ∩ B) = P(A) * P(B)
0.3 = (0.6)(0.5)
0.3 = 0.3
Therefore, A and B are independent.

End of Part II.

to be continued.

Any questions?