After a brief hiatus, the Algebra 2 Problems of the Day are back. Hopefully, daily.
More Algebra 2 problems.
January 2019, Part I
All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.
10. A random sample of 100 people that would best estimate the computations.
proportion of all registered voters in a district who support
improvements to the high school football field should be drawn from
registered voters in the district at a
(1) football game
(2) supermarket
(3) school fund-raiser
(4) high school band concert
Answer: (2) supermarket
At the supermarket, you will encounter a more random set of people.
If you want to improve a high school football field, then football games and school functions will give you biased results.
11. Which expression is equivalent to (2x - i)2 - (2x - i)(2x + 3i),
where i is the imaginary unit and x is a real number?
(1) -4 - 8xi
(2) -4 - 4xi
(3) 2
(4) 8x - 4i
Answer: (1) -4 - 8xi
First method: multiply and combine like terms:
4x2 - 4xi + i2 - ( 4x2 + 6xi - 2xi - 3i2)
4x2 - 4xi + i2 - 4x2 - 4xi + 3i2)
4x2 - 4xi - 1 - 4x2 - 4xi - 3
-8xi - 4
-4 - 8xi
Second method: Factor out (2x - i) from each term first.
(2x - i) ( ( 2x - i) - (2x + 3i) )
(2x - i) ( 2x - i - 2x - 3i )
(2x - i) (-4i)
-8xi + 4i2
-8xi - 4
-4 - 8xi
12. Suppose events A and B are independent and P(A and B) is 0.2.
Which statement could be true?
(1) P(A) = 0.4, P(B) = 0.3, P(A or B) = 0.5
(2) P(A) = 0.8, P(B) = 0.25
(3) P(A|B) = 0.2, P(B) = 0.2
(4) P(A) = 0.15, P(B) = 0.05
Answer: (2) P(A) = 0.8, P(B) = 0.25
If A and B are independent then P(A and B) = P(A) * P(B)
Choice (1): P(A) * P(B) = 0.4 * 0.3 = 0.12 =/= 0.2.
Choice (2): P(A) * P(B) = 0.8 * 0.25 = 0.2.
Choice (4): P(A) * P(B) = 0.15 * 0.05 = 0.0075 =/= 0.2
In Choice (3), if A and B are independent, then P(A|B) = P(A). So 0.2 * 0.2 = 0.04 =/= 0.2.
Comments and questions welcome.
More Algebra 2 problems.
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