Q18-5 points Solve the recurrence relation: b1​ = 3 b2​ = 5 bn​ = 2​bn-1​ −​ b​n-2

Q13-5 points Jim has a drawer with 6 red socks, 6 blue socks, and 10 black socks. If he picks them out without looking, how many socks must Jim pull out of the drawer to guarantee that he has a matching color pair?

Q12-5 points Jamar’s Donut Shop sells 6 flavors of doughnuts each day. If repeat flavors are allowed, how many different ways can a three-doughnut box be filled?

Q14-5 points 19,596 people attended the second game of the 2017 NBA Finals between the Golden State Warriors and the Cleveland Cavaliers. Is it a certainty that at least two of those people shared the same three-letter set of initials (such as JFK or LBJ)? Justify your reasoning.

The pediatric nurse is aware of the maturation of organ systems in the school-age child. What does not accurately describes these changes? Select 1 option.

Q16-5 points Use the Binomial Theorem to write out the expansion of (a + b)4 .

Q7-8 points Decide why the argument is valid or invalid. Explain your reasoning.               If he goes hiking, then he will put on boots.             He puts on boots.       .          ∴              He goes hiking.    

Q11-8 points Prove that the sum of any three consecutive ​even​ integers is divisible by 6.                                              

Q12-8 points Let ​n be an integer. Use a proof by contrapositive to prove that if ​3n²​ is odd, then ​n​ is odd. 

Q20-5 points Prove that for any sets A and B, (A ∪ B) ∩ B  =  B.