I need to express my result as a polynomial, we were given formulas which states the answers however I cannot find the formulas for these last 2 A) C(n+2,n) C) C(C(n,k),(n¦(n-k)))...

I need to express my result as a polynomial, we were given formulas which states the answers however I cannot find the formulas for these last 2 A) C(n+2,n) C) C(C(n,k),(n¦(n-k)))...

Suppose that R is a ring of characteristic n. If addition and multiplication are defined in R x Zn = {(x, a)lx E R; a E Zn} by (x, a) + (y, b) = (x + y, a +n b), (x, a)(y, b)...

Hi I have 2 problems that I need to say whether or not they are true or not and then write a proof for my answer. I am really struggling and could use a little help thank you 1) ...

1. How many different positive integers can be made from the digits {2, 4, 6, 8} if repetitions are allowed? 2. What is the telescoping form of f(x) = x4 + 7x3 - x2 + 2x +...

prove it if it is correct or give counterexample if it is false let d=(a,b) then a|bc if and only if a/d is a divisor of c

Can anyone tell me if: F(n) = 3n^2 + 1 is one-to-one or onto? I'm pretty sure it's neither because n^2 itself isn't onto, but I need second opinions...

Here are four relations defined on R, the set of real numbers: R1 = { (x, y): x ≤ y } R2 = { (x, y): x > y } R3 = { (x, y): x < y } R4 = { (x, y): x = y } Describe...

The Fibonacci sequence F0, F1, F2, F3, ... is an infinite sequence defined by the two initial values F0 =0, F1 =1, and the rule Fk = Fk-2 + Fk-1 for all k ≥ 2. Let Μ...

There are 57 students in a class, how many different ways can you make a group of 5?

f(x) = -(x - 1) g(x) = 2x2 h(x) = 3x + 1 a. What is (f ο g)(-2)? b. What is (g ο f)(-2)? c. What is (f ο h)-1(3)? d. What is (f ο g ο h)(1)? e. What is (h ο h-1)(π)...

Consider the surjective function cos: R → [−1, 1] and let ∼ be the associated equivalence relation x ∼ y ⇐⇒ cos x = cos y. Describe the equivalence classes of ∼...

please I want help with that Consider the ring Mn(R) ofn x n matrices over R, a ring with identity. A square matrix (aij) is said to be upper triangular if aij = 0 for i...

I have a set C: {0,1,3) and set D: {2,8} I have the product of sets CxD and DxC So for example CxD: {(0,2) , (0,8),} {(1,2), (1,8),} {(3,2),...

What I am really looking for here is an explanation as to why this process is actually able to prove that a statement is true for all values of n. Try to make your example non-mathematical and explain...

Suppose we are given the following program segment: F(x) = 0 Input n For x = 1 to x = n y = x*(x+3)+2 Print y Next x 1. Determine the number of steps...

How would you explain to this person why it is that induction actually does work. In my follow up responses to you, I may ask you questions that your friend might as in response to your explanation...

Pigeon hole principle

Twenty distinct integers are arranged in a list in a random order, such that all 20! orderings are equally likely. Going down the list, one marks every number that is larger than all earlier numbers...

security codes are made of 3 letters followed by four single digit numbers. How many different 7 character security codes can be made if none of the letters can repeat and the first digit must be...

suppose that in solving a tsp you use the cheapest link algorithm and find a cheapest link tour with a length of 21400 miles. suppose that you later find out that the length of an optimal tour is...

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