Disreet Math help

Question 1 (4 points} Select the description that ts the sequence below: 8, 5, 2, 2, 'I, 1 a. Nondecreasing but not increasing b. Nonincreasing and decreasing c. Nonincreasing but not decreasing d. Nondecreasing and increasing Question 2 (4 points} What is the common ratio ofthe following geometric sequence? 27, 9, 3, l, a. 27 Question 3 (4 points) A population of mice increases by 10% every year. Define In to be the number of mice after n years. Select the recurrence relation that describes the sequence {gn } a. gn = (1.01) . gn-1 b. gn = (1.1) . gn-1 C. In = (.01) . gn-1 + gn-2 d. In = (.1) . gn-1 + gn-2 Oa Ob Oc Od Question 4 (4 points) Select the mathematical expression that is equivalent to the sum in-4 a. _1 2 jit7 + (n - 4)n+3 2i=_2 jit7 + (n - 4) n+3 1= -2 ji+7 + in+ 3 Liz-2j3+7 + in+3 Ob Oc OdQuestion 5 (3.5 points) The inductive step of an inductive proof shows that for k 2 4, if k! > 2k, then (k + 1)! > 2k+1 However the lines are not labeled with the proper justification. Which line should be labeled "Inductive Hypothesis"? (k + 1)! _ (k + 1) . k. (k - 1) ...2 . 1 (Step 1) ( k + 1)! > (k + 1) . k! (Step 2) ( k + 1)! > (k + 1). 2k (Step 3) (k + 1)! > 2. 2k (Step 4) ( k + 1)! > 2k+1 (Step 5) a. Step 2 b. Step 3 c. Step 4 d. Step 5 Oa Ob Oc Od Question 6 (3.5 points) Select the correct value for 74 div 11. a. 6-8 b. 6 C. 7 d. 8 Oa Ob Oc OdQuestion 3 (3.5 points) 92:23-52-7-133 9222-54247 What is the prime factorization for Icm(x, y)? a. 22 - 5 - 7 b.23-52 7133-17 c.23 .52 -72 . 133 - 17 d.25-53-73-133-17 Question 9 (3.5 points) ;.~:=34-53-7-114 3,232.547134 What is the prime factorization for gcd(x, y)? a. 32 _ 53 b. 32 -53 - 7 c. 32 . 53 .72 d.32-53.7-114 -134 Question 11 (3.5 points) How many 10-bit strings begin with "101" or "00"? a. 27 + 28 b. 210 + 210 C. 27 . 28 d. 210 . 210 Oa Ob Oc Od Question 12 (3.5 points) A bank PIN is a string of four digits, each digit 0-9. How many choices are there for a PIN if the last digit must be odd? a. 104 b. 410 c. 5 . 310 d. 5 . 103 Oa Ob Oc Od