The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.5, 2). The finishing point will be at (2, −5.5). A four-quadrant coordinate grid is drawn from negative 4 to positive 4. Quadrant I is labeled Quadrant P, Quadrant II is labeled Quadrant Q, Quadrant III is labeled Quadrant R, and Quadrant IV is labeled Quadrant S.

Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points)

Part B: A checkpoint will be at (5.5, 2). In at least two sentences, describe the differences between the coordinates of the starting point and the checkpoint, and explain how the points are related. (4 points)

If the table of the function contains exactly two potential turning points, one with an input value of –1, which statement best describes all possible values of m? m ≥ –12 –12 < m < 4 m ≤ 4 m ≥ 4 or m ≤ –12

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)

Atravel agent is booking a trip to england, scotland, ireland, and france for a group of senior citizens. the agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (e = england, i = ireland, s = scotland, f = france). which country is the condorcet winner? number of votes 15 12 16 19 1st f e e i 2nd e s i s 3rd s i s e 4th i f f f 1. scotland 2. england 3. france 4.ireland