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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.

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?

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.

Which of the following data values is best represented with a floating point variable?

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

15 _____ 3 = 5.0

Which following change in the coffee market would shift the supply curve to the right?