Stored on a flash memory device is a 200-megabyte (MB) message to be transmitted by an e-mail from one server to another, passing three nodes of a connectionless network. This network forces packets to be of size 10KB, excluding a packet header of 40 bytes. Nodes are 400 miles apart, and servers are 50 miles away from their corresponding nodes. All transmission links are of type 100Mb/s. The processing time at each node is 0.2 seconds. (a) Find the propagation delays per packet between a server and a node and between nodes.
(b) Find the total time required to send this message.

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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)?

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