Thursday, May 10, 2018

Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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August 2017, Part I

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

22. A public opinion poll was conducted on behalf of Mayor Ortega's reelection campaign shortly before the election. 264 out of 550 likely voters said they would vote for Mayor Ortega; the rest said they would vote for his opponent.
Which statement is least appropriate to make, according to the results of the poll?

1) There is a 48% chance that Mayor Ortega will win the election.
2) The point estimate (ˆp) of voters who will vote for Mayor Ortega is 48%.
3) It is most likely that between 44% and 52% of voters will vote for Mayor Ortega.
4) Due to the margin of error, an inference cannot be made regarding whether Mayor Ortega or his opponent is most likely to win the election.

Answer: There is a 48% chance that Mayor Ortega will win the election.
Analysis of data. While 48% of the likely voters in this poll said that they would vote for Mayor Ortega, this is only a sample of all the voters and there is a margin of error. It is more appropriate to say that the point estimate is 48% than to say that this is his chance of winning.

23. What does ( (-54x9) / y4 )2/3 equal?

Check your work against the image below.
We need to take the cube root of the expression. We can factor -54 into (-27)(2) because -27 is a perfect cube. The cube root of x9 is x3. The y4 term can be broken into y3 times y, and the cube root of y3 is y.
After that we can square all the terms. (You could have done that sooner, if you don't mind squaring -54 and then finding the largest perfect cube that's a factor.)
(-3x3) squared is 9x6, over y2, times the cube root of 4 over y2. Split up the radical into a fraction of two radicals and you have choice 4.

The Rickerts decided to set up an account for their daughter to pay for her college education. The day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. Beginning with her first birthday, they deposit an additional $750 into the account on each of her birthdays. Which expression correctly represents the amount of money in the account n years after their daughter was born?

1) an = 1000(1.018)n + 750
2) an = 1000(1.018)n + 750n
3) a0 = 1000; an = an - 1 (1.018) + 750
4) a0 = 1000; an = an - 1 (1.018) + 750n

Answer:3) a0 = 1000; an = an - 1 (1.018) + 750
The initial value was $1000. Each year the value of the account will by 1.8% greater plus another $750 will be added to the balance. So the previous value, an - 1, times (1.018) then add 750.

Choice 1 doesn't work because the $750 is only added once, instead of every year, and it isn't earning any interest.
Choice 2 doesn't work because the $750, while being added each year, isn't earning the 1.8% interest.
Choice 4 shows a recursive formula, so no variable is needed at $750. The parents aren't adding, for example, $1500 on her second birthday or $3000 on her fourth.

Comments and questions welcome.

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