Monday, May 14, 2018

Algebra 2 Problems of the Day (open-ended)

Daily Algebra 2 questions and answers.

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August 2017, Part II

All Questions in Part II are worth 2 credits. Work need be shown (or explained or justified) for full credit. Correct numerical answers with no work receive one credit.

25.Explain how (−8)(4/3) can be evaluated using properties of rational exponents to result in an integer answer

A rational exponent, like (4/3), can be re-written as (4) * (1/3), which means to take the fourth power of the cube root of the expression (-8). (The power of a power rule)
The cube root of -8 is -2, which when raised to the 4th power is (-2)4 = 16, which is an integer.

26. A study was designed to test the effectiveness of a new drug. Half of the volunteers received the drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer received the drug?

The probability of two things occurring is 40%. The combined probability can be found by multiplying the two independent probabilities.
Since we know one of those probabilities, we can solve for the other.
P(A) * P(B) = .40
1/2 * P(B) = .40
P(B) = .80
There was an 80% chance that if the volunteer received the drug that he (or she) would get better.

Comments and questions welcome.

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