## Saturday, March 21, 2020

### Algebra 2 Problems of the Day (Jan 2020)

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

January 2020, Part I

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

11. Consider the data in the table below

 Right Handed Left Handed Male 87 13 Female 89 11

What is the probability that a randomly selected person is male given that the person is left-handed?

(1) 13/200
(2) 13/100
(3) 13/50
(4) 13/24

There are a total of 24 left handed students. Of those 13 are male. So the probability is 13/24 of selecting a male if we know the person is left-handed.

12. The function N(x) = 90(0.86)x + 69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0, 6]?

(1) -8.93
(2) -0.11
(3) 0.11
(4) 8.93

The hot chocolate is cooling, so the temperature change is negative. Choices (3) and (4) are incorrect.

Find N(0) and N(6)
N(0) = 90(0.86)0 + 69 = 90(1) + 69 = 159
N(6) = 90(0.86)6 + 69 = 90(0.405) + 69 = 105.45

The average rate of change = (105.45 - 159) / 6 = -8.925

13. A recursive formula for the sequence 40, 30, 22.5, … is

(1) gn = 40(3/4)n
(2) g1 = 40 ; gn = gn-1 - 10
(3) gn = 40(3/4)n-1
(4) g1 = 40 ; gn = (3/4)gn-1 - 10

Answer: (4) g1 = 40 ; gn = (3/4)gn-1 - 10
Choices (1) and (3) are not recursive formulas.
Choice (2) indicates that the sequence is decreasing by 10. However, that would make g3 = 20, which it does not.
Choice (4) says that each term is 3/4 of the prior term, with the first term being 40. This is correct.

14. The J & B candy company claims that 45% of the candies it produces are blue, 30% are brown, and 25% are yellow. Each bag holds 65 candies. A simulation was run 200 times, each of sample size 65, based on the premise that 45% of the candies are blue. The results of the simulation are shown below.

Bonnie purchased a bag of J & B’s candy and counted 24 blue candies. What inference can be made regarding a bag of J & B’s with only 24 blue candies?
(1) The company is not meeting their production standard.
(2) Bonnie’s bag was a rarity and the company should not be concerned.
(3) The company should change their claim to 37% blue candies are produced.
(4) Bonnie’s bag is within the middle 95% of the simulated data supporting the company’s claim.

Answer: (4) Bonnie’s bag is within the middle 95% of the simulated data supporting the company’s claim.
The mean is 29.270, the standard deviation is 3.936.
The mean - 2 SD = 21.398, which is less than 24, so it is within the middle 95% of the data.

15. Which investigation technique is most often used to determine if a single variable has an impact on a given population?

(1) observational study
(2) random survey
(3) controlled experiment
(4) formal interview