How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have more outcomes? Why? Provide an example in your explanation.

(please provide detailed answer with no less than 100 characters)

true or false. The solution to a rational inequality will be a single value?

what are the possible rational zeros of the function: f(x)=x^3+2x^2-x+6?

Let X = {1, 2, 3}. Find all topologies T on X such that (X, T ) is regular.

1. Let A = R x R, and let a relation S be defined as: “(x​1,​ y​1)​ S (x​2,​ y​2)​ ⬄ points (x​1,​ y​1)​ and (x​2,​ y​2)​are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you ​must​ give a counterexample.

MAXIMIZATION BY THE SIMPLEX METHOD

Maximize z = x₁ + 2x₂ + x₃

subject to

x₁ + x₂ ≤ 3

x₂ + x₃ ≤ 4

x₁ + x3 ≤ 5

x₁, x₂, x₃ ≥0

(1 point) Use the method of undetermined coefficients to find a solution of

y′′−4y′+33y=64e2tcos(5t)+64e2tsin(5t)+2e1t.y″−4y′+33y=64e2tcos⁡(5t)+64e2tsin⁡(5t)+2e1t.

Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term.
y=yh+yp=

Consider the differential equation x′=[2 4

-2 −2],

with x(0)=[1 1]

Solve the differential equation where x=[x(t)y(t)].

x(t)=

y(t)=

please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

A manager of an inventory system believes that inventory models are important decision-making aids. The manager has experience with the EOQ policy, but has never considered a backorder model because of the assumption that backorders were “bad” and should be avoided. However, with upper management's continued pressure for cost reduction, you have been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. For a specific product with D = 800 units per year, Co = $150, Ch = $5, and Cb = $30, what is the difference in total annual cost between the EOQ model and the planned shortage or backorder model? If the manager adds constraints that no more than 25% of the units can be backordered and that no customer will have to wait more than 15 days for an order, should the backorder inventory policy be adopted? Assume 250 working days per year.

Let S ⊆ R be a nonempty compact set and p ∈ R. Prove that there exists a point x_0 ∈ S which is “closest” to p. That is, prove that there exists x0 ∈ S such that |x_0 − p| is minimal.

1. Let (an) be a real sequence in the standard metric. Prove that (an) is bounded if and only if every subsequence of (an) has a convergent subsequence.

Explore the change of mathematics due to interactions with different cultures. What cultures made the biggest impacts on mathematics? Which cultures benefited the most from this interaction?

Prove or Disprove: that Z^x_mn is isomorphic to Z^x_m x Z^x_n  if gcd (n, m) = 1