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When the government places a tax on the producer of a good or service

Using the definition of divides, prove the following statement or provide a counterexample to disprove: “For all a, b, c ∈ ℤ with a ≠ 0, if a|b and a|c then a|(b + c).”  Use good proof technique.  Note:  To avoid the need to type special symbols, use ‘does not equal’ for ≠. Grading rubric: 1 pt. State the definition of divides at the beginning. 1 pt. State any givens and assumptions.  1 pt. Clearly explain your steps and reasoning. 1 pt. State the final conclusion at the end of the proof.

The decimal expansion of the hexadecimal number A916 is _______________ten. Only type the digits; do not include the base.

Source code, like Python .py files, can be edited with Notepad.

What is the least integer n such that the function 2×4 + 5×3 + 10x + 3 is O(xn)?

Prove, or provide a counterexample to disprove, the following statement:             “The function f : ℕ ⟶ ℕ  be defined by f(n) = n(mod 5) is onto.” Use good proof technique. Grading rubric:1 pt. State the definition of onto at the beginning, then prove or disprove.1 pt. State any givens and assumptions.1 pt. Clearly explain your reasoning.1 pt. Remember to state the final conclusion at the end of the proof.

A subsidy

Prove that 3×2 + x + 6 is O(x2), by identifying values for C and k and demonstrating that they do satisfy the definition of big-O for this function.  Show your work. Note:  To avoid the need for typing superscript exponents, you may use the notation ‘x^2′ to represent x2.

S, a subset of integers, is defined recursively below. Initial Condition:  2 ∈ S Recursive Step: If n ∈ S, then 3n ∈ S. Which of the sets below is equal to S?

Assigning a value to a floating point variable that is too large for the computer to represent is a condition called _____ .