Please provide explanation! For each of the following statements, give a T (true

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Please provide explanation!

For each of the following statements, give a T (true) or F (false) answer. (True or False) Given a function f(n) = 3n3 + 2n2 + 10n + 100, we have that f(n) = theta(n3). (True or False) Given a function f(n) = 3n3 + 2n2 + 10n + 100, we have that f(n) = O(n5). (True or False) Given a function /(n) = 3n3 + 2n2 + 10n + 100, we have that f(n) = theta(n2). (True or False) Given a function f(n) = (logn)3 + log n+11n, we have that f(n) = theta((logn)3). (True or False) Given a function f(n) = (logn)3 + logn+11n, we have that f(n) = theta(n). (True or False) Both Merge Sort and Quicksort are in-place sorts. True or False) An algorithm with theta(n3) best-case running time will run more quickly than a 0(n3) worst-case running time algorithm, for large enough inputs.

Explanation / Answer

1) True

2) False

3) True

4) False

5) False

6) True

7) True

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