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August 2016 Common Core Algebra II Regents Part 3 (continued)

August 2016, Algebra II Part 3

35. Solve the equation SQRT(2x - 7) + x = 5 algebraically, and justify the solution set.

Look at the image below. The procedure is to subtract x from both sides to isolate the radical expression. Next, square both sides of the equation, leaving 2x - 7 on the left side and a quadratic on the right. Subtract (2x - 7) from both sides to set up the quadratic equation that you are going to solve.

Once you solve it, you must check both answers to see that they are in fact solutions.
You can see from the check that 4 is a solution, but 8 is not, so it is rejected. 36. Ayva designed an experiment to determine the effect of a new energy drink on a group of 20 volunteer students. Ten students were randomly selected to form group 1 while the remaining 10 made up group 2. Each student in group 1 drank one energy drink, and each student in group 2 drank one cola drink. Ten minutes later, their times were recorded for reading the same paragraph of a novel. The results of the experiment are shown below. a) Ayva thinks drinking energy drinks makes students read faster. Using information from the experimental design or the results, explain why Ayva’s hypothesis may be incorrect.

Using the given results, Ayva randomly mixes the 20 reading times, splits them into two groups of 10, and simulates the difference of the means 232 times. b) Ayva has decided that the difference in mean reading times is not an unusual occurence. Support her decision using the results of the simulation. Explain your reasoning.

Anya's hypothesis may be incorrect because some of the students in Group 2 read faster than students in Group 1. The means for Groups 1 and 2 are listed as 17.7 and 19.1, respectively. If you find the standard deviation (put the data into Lists in the graphing calculator and do 1-Var Stats on each) you will find the standard deviations for Groups 1 and 2 are 1.396... and 3.720... So there is overlap between the groups.

The difference between the two means is 17.7 - 19.1 = -1.4. Since scores less than this happen 10% of the time, this is not an unusual occurrence.

To be continued


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