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How many ways can you assign 4 caretakers each of which look after 2 lighthouses for a year (for a total of 8 lighthouses), and then assign each two lighthouses in the next year so that none of them tend the same two lighthouses both years?
How many ways can you assign 4 caretakers each of which look after 2 lighthouses for a year (for a total of 8 lighthouses), and then assign each two lighthouses in the next year so that none of them tend the same two lighthouses both years?
Find a generating function in closed form for the sequence:
{1,2,3,4,1,2,3,4,1,2,3,4,...}
How many permutations of the 26 letters of our alphabet do not contain any of the three strings "US", "AIM", and "DONKEY"?
I need to program an tic tac toe game on MSP432 with the booster board programming in c.
Exactly 100 ml of 0.15 M acetic acid (HC2H3O2,Ka = 1.8x 10^-5) are titrated with a 0.20 M NaOH solution. Calculate the pH for (a) the initial solution (the HC2H3O2), (b) the point at which 37.5 ml of the base has been added, (c) the equivalence point (d) after adding 80.0 ml of 0.20 M NaOH
New domain of the function f given by f x is equal to under root 2 - X upon X is zero one is it true or false give reason
A chemist must prepare 875.mL

of 3.00M

aqueous nickel(II) chloride NiCl2

working solution. He'll do this by pouring out some 3.43M

aqueous nickel(II) chloride stock solution into a graduated cylinder and diluting it with distilled water.
Calculate the volume in mL

of the nickel(II) chloride stock solution that the chemist should pour out.
Find the indicated limit, if it exists.

limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Let X be a non-empty set, and let R be an equivalence relation on X. Let C be the set of all equivalence classes of R. So C={A⊆X such that A=[x] for some x ∈ X}.

Now, define f : X → C by the rule f(x) = [x] for all x ∈ X.

Prove that if x ∈ X, then there is one and only one equivalence class which contains x.

Suppose X = {1, 2, 3, 4, 5} and that R is an equivalence relation for which 1 R 3, 2 R 4 but 1 R̸ 2,1 R̸ 5,and 2 R̸ 5.

Write down the equivalence classes of R and draw a diagram to represent the function f.
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