Algebra 2 Problems of the Day

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June 2017, Part II

All Questions in Part II are worth up tp 2 credits. Partial credit is possible.


25. Given r(x) = x³ - 4x² + 4x - 6, find the value of r(2).

What does your answer tell you about x - 2 as a factor of r(x)? Explain.

Answer:
r(2) = (2)³ - 4(2)x² + 4(2) - 6
r(2) = 8 - 4(4) + 8 - 6 = 8 - 16 + 8 - 6 = -6
Therefore, x - 2 is not a factor of r(x) because r(2) =/= 0. If you divide r(x) / (x - 2) there will be a remainder.

26. The weight of a bag of pears at the local market averages 8 pounds with a standard deviation of 0.5 pound. The weights of all the bags of pears at the market closely follow a normal distribution. Determine what percentage of bags, to the nearest integer, weighed less than 8.25 pounds.

Answer:
Use your calculator to find a normal distribution. "less than 8.25" means that the endpoints are 0 and 8.25. The mean is 8 and the standard deviation is 0.5.
On your paper, write normalcdf(0,8.25,8,.50) to show work to get full credit. Then enter this into your calculator.
You will get an answer of .6915, which is 69% to the nearest integer.



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