Let n be an even integer where n>0. How many bitstrings have more ones than zeros with a length n? The answer does not have to be in a closed form

Let a and b be integers. Then a divides b if and only if: O ab-k for som integer k you can't divide integers O a=bk for some integer k O b=ak for some integer k

The function f(n)= n2.5+ no log n + 10 is a. O(log n) O b. 0(n5) O(n5 log n) C. O d. O(n2.5) O e. O(n logn)

Algorithm for Conversion from an Arabic number to a modern Roman number.in: decimal number n (0 ≤ n)out: sequence R =
s0, s1,...,s12 representing the structure of the Roman number (Ri = number of primitives Vi in n for i ∈ [0, 12])

158400= (DL) + (DL x 1.5)

. Prove that n2 + 1  2n, where n is a positive integer with 1  n  4.

Given an n-element sequence of integers, an algorithm executes an O(n)-time computation for each even number in the sequence, and an O(logn)-time computation for each odd number in the sequence. What are the best-case and worst-case running times of this algorithm? Why? Show with proper notations.

Let n be an integer. If 3n+ 4 is odd, then n is odd.

find a counterexmaple.

Given that a,b,c,d,e are distinct whole numbers from 1 to 9 inclusive, along with the equalityab=c⋅100+d⋅10+e where c⋅100+d⋅10+e is the largest possible value, find the value ofa+b+c+d+e

6. Prove: For all integers n, if n2 is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1.

Given that x and y are integers such that 0 < x < y < 9 and that the integer 77265x597y is divisible by 12, find x and y.

Design an algorithm for computing for any positive integer n. Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations.