in the game of lucky sevens, the player rolls a pair of dice. if the dots add up to 7, the player wins $4; otherwise, the player loses $1. suppose that, to entice the gullible, a casino tells players that there are many ways to win: (1, 6), (2, 5), and soon. a little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people's eyes glaze over at the first mention of mathematics "wins $4".

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?