Determine the availability ratio (percentage) of the two following different cluster systems: A failover cluster with the ability to detect a failed node in 10 seconds on average, migrate the workloads to another node in 30 seconds. Such a cluster fails 10 times on average in a year. Also, it will be taken down two hours every week for maintenance (not running any applications during this time)

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)?