More Algebra 2 problems.

__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
*

**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?
*

**Answer: **

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.

More Algebra 2 problems.

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