## Tuesday, August 21, 2018

### Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.

13. A student studying public policy created a model for the population of Detroit, where the population decreased 25% over a decade. He used the model P = 714(0.75)d, where P is the population, in thousands, d decades after 2010. Another student, Suzanne, wants to use a model that would predict the population after y years. Suzanne’s model is best represented by
Which explanation is appropriate for Miles and his dad to make?
1) P = 714(0.6500)y
2) P = 714(0.8500)y
3) P = 714(0.9716)y
4) P = 714(0.9750)y

There are 10 years to 1 decade, so d = 10y
So P = 714(0.75)d = 714(0.75)10y = 714(0.7510)y
And P = 714(0.9716)y

14. The probability that Gary and Jane have a child with blue eyes is 0.25, and the probability that they have a child with blond hair is 0.5. The probability that they have a child with both blue eyes and blond hair is 0.125. Given this information, the events blue eyes and blond hair are

I: dependent
II: independent
III: mutually exclusive

1) I, only
2) II, only
3) I and III
4) II and III

They are independent because P(A and B) = P(A) * P(B). That is 0.125 = 0.5 * 0.25.
This eliminates choices 1 and 3.
The events are not mutually exclusive, because P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.5 - 0.125 = 0.625, but 0.625 =/= 0.5 + 0.25.

15. Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x) = 23.914sin(0.508x - 2.116) + 55.300. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) = 20.238sin(0.525x - 2.148) + 86.729.
Which statement can not be concluded based on the average monthly temperature models x months after starting data collection?
1) The average monthly temperature variation is more in Bar Harbor than in Phoenix.
2) The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix.
3) The maximum average monthly temperature for Bar Harbor is 79° F, to the nearest degree.
4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.

Answer: 4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.
If you graph both of these functions you will find the following information:
For Bar Harbor: the minimum value is 31.39, the midline 55.3, the maximum is 79.21 and the range is 47.83.
For Phoenix, min is 66.49, mid is 86.73, max is 106.97 and range is 40.48.
Choices 1, 2, and 3 can be seen in the data. Choice 4 is incorrect, the minimum average monthly temperature for Phoenix is approximately 66° F, to the nearest degree.