Finding the probability of rolling doubles: There are 6 sets of doubles (1,1: 2,2: 3,3: 4,4: 5,5: 6,6) 6 = 1 6 chances of rolling doubles 36 6 36 total outcomes The probability of rolling doubles is 1/6, or .167 or 16.7% chance.

In uniform auctions, the following is an equilibrium: (i) one of the shorts bids R h for Q − 1 units and R 0 for 1 unit (and all other shorts are passive); (ii) long player n bids (a) R 0 for Q units if z n,0 < Q or (b) R h for Q units if z n,0 ≥ Q. Thus if Q > Z, there is no short squeeze and all units trade at R 0. If Q ≤ Z, there is a ...

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1. Letter representation: There are actually standard letters used as symbols for transformations in math. Since your direction is to use a different letter for each, I will suggest using M for reflection since they make mirror images (normally it is a lower case r).

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In uniform auctions, the following is an equilibrium: (i) one of the shorts bids R h for Q − 1 units and R 0 for 1 unit (and all other shorts are passive); (ii) long player n bids (a) R 0 for Q units if z n,0 < Q or (b) R h for Q units if z n,0 ≥ Q. Thus if Q > Z, there is no short squeeze and all units trade at R 0. If Q ≤ Z, there is a ...

In this unit, students expand and deepen their prior understanding of expressions, equations, and inequalities. Students reason about equations, inequalities, and systems of equations and inequalities as ways to represent constraints, and they reason about the process of solving equations and inequalities in terms of finding values that satisfy those constraints.