Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...
Prove that if the integers 1, 2, 3, . . . , 65 are arranged in
any order, then it is possible to look either left to right or
right to left through the list and find nine numbers that are in
increasing order
Prove these scenarios by mathematical induction:
(1) Prove n2 < 2n for all integers
n>4
(2) Prove that a finite set with n elements has 2n
subsets
(3) Prove that every amount of postage of 12 cents or more can
be formed using just 4-cent and 5-cent stamps
Prove that there exists integers m and n such that 15m + 12n =
3
Please do not prove by assuming m=1 and n=-1, I'd like to prove
by not assuming any actual numbers.
Assume that there are a sequence of consecutive integers 1, 2, 3,
4, 5, ... 15. Tom and Jim respectively select a number from the
sequence randomly (no repetition). Given that Tom’s number is
divisible by 5, what’s the probability that Tom’s number is greater
than Jim’s number ?
Consider the set of integers A = {1, 2, 3, 4, 5}. Pairs of
numbers are constructed where each number of the pair comes from
set A. Construct the sampling distribution of sample ranges. Apply
the Empirical Rule to this distribution.