The following exercises (unless otherwise specified) take place in a geometry with axioms (11)-(13), (B1)-(B4), (C1)-(C3). 8.1 (a) Show that addition of line segments is associative: Given segments AB, CD, EF, and taking A, B in order, then (AB+CD) + EF = AB+ (CD+EF). (This means that we obtain the same segment as the sum, not just congruent segments.) (b) Show that addition of line segments is commutative up to congruence: Given segments AB, CD, then AB+CD= CD + AB.

Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…

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