**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?

Comments, corrections welcome.

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