Discrete Structures Exam 2 Questions With Detailed Verified Answers 100% Correct Answers Already Passed

How many different 5-digit numbers can be constructed out of the digits {2,2,2,7,7}: - correct answer 10 For the following sequence: 1/5, 1, 5, 25, 125, 625 what is the explicit formula of the sequence. - correct answer (1/5)(5ⁿ) What is the value of a₅₀₀ when aₙ = aₙ₋₁ +6 with a₀ = 3. - correct answer 3003 For the following sequence: 10, 17, 24, 31, 38, ... what is the explicit formula of the sequence. - correct answer aₙ = 10 + 7n How many numbers in the range have no repeating digits: - correct answer 9 * 9 * 8 * 7 For the following sequence: 3, 6, 12, 14, 48, 96, ... what is the explicit formula of the sequence. - correct answer aₙ = 3(2ⁿ) How many license plates with 3 letters followed by 3 digits exist if exactly one of the digit is 1: - correct answer 26 * 26 * 26 * 3 * 9 * 9 For the following sequence: 5, 15, 25, 35, 45, 55... what type of sequence is this: - correct answer Increasing Arithmetric What is the value of a₅ = rⁿ(a₀) where r = ½ and a₀ = 32000. - correct answer 1000 For the following sequence: 3, 6, 12, 14, 48, 96, ... what is the a₀ value. - correct answer 3 A mathematical system consist of the following: A: Axioms, Defintition, Undefined Terms B: Axioms, Algebra, Undefined Terms C: Axioms, Defintition, Algebra - correct answer Axioms, Definition, Undefined Terms What type is the following sequence: 95, 109, 123, 137, 151, 165, ... - correct answer Arithmetric If we wish to proof 1 + 2 + 3 + ... + n = n(n+1)/2 using the proof by induction method, in the induction step we wish to the following ? - correct answer 1 + 2 + 3 + ... (k+1) = (k+1)(k+1+1)/2 For the arithmetic sequence below, what is its d value? 45, 61, 77, 93, 109, 125, ... - correct answer 16 For the following sequence: 95, 109, 123, 137, 151, 165, ... what is the explicit formula of the sequence. - correct answer aₙ = 95 + 14n If you are going to proof 2ⁿ < n! using proof by induction what is the n value for the Base Case. - correct answer 4 How many different 5-digit numbers can be constructed out of the digits {1, 1, 1, 3, 8}: - correct answer 20 What is the value of a₄ when aₙ = rⁿ(a₀) where r = 4 and a₀ = 100. - correct answer 25600 When expanding (x+y)⁶ what is the value of the coefficient of the x⁴y² term: - correct answer 15 What is the value of P(26, 23): - correct answer 26! / 3! What is the formula for the permutation P(n,k): - correct answer n!/(n-r)! What are the main components of Proof by Induction? A. Base Case, Induction Hypothesis, Induction Step. B. Base Case, Induction Step C. Base Case, Induction Hypothesis D. Base Case, Induction Hypothesis - correct answer Base Case, Induction Hypothesis, Induction Step For the following sequence: 95, 109, 123, 137, 151, 165, ... what is the a₀ value? - correct answer 95