I would like help with this homework, if possible please show all work so I can understand.

 

 

Answer the following problems. Work will get you partial credit if incorrect. (2 pts
each)
1. 9 mod 4=¿ 4. 47 div 6 = 5. −73÷9=¿ 2. −24 mod 7=¿ 6. 32÷16=¿ 3. 28 mod 12=¿ Solve the problems. Show your work for full credit: (2 pts each)
7. 32+24∈Z7 =¿ 8. 6 ×3∈Z7 =¿ Find the following values. Final answer should be a number and not an expression.
Show your work for full credit. (2 pts each)
9. gcd ( 72, 60 )=¿ 10. lcm ( 72,60 ) =¿ Convert the following binary number: (1 pt each) 1101
101¿
11.
¿
¿ to decimal 1101
101¿
12.
¿
¿ to hexadecimal 13.Convert the hexadecimal 0x4B53A to decimal. Show work for full credit. (3
pts) 14.The Hulk takes pictures and videos of his kittens and stores them on his
computer. He doesn’t want his friends Tony and Steve to see them, so he
decides that locking the computer with a password to protect his secret
obsession with his kittens. If the Hulk only uses a password which each
character is a digit (0-9), a lowercase letter (a-z), or an uppercase letter (AZ), how many different 8 character passwords could he create? There is no
limit to the amount of times a character appears in a password. Show work
for full credit. (5 pts) 15.The Hulk has 6 kittens that he loves to dress up and show off to the world
online. How many photographs can he take of the kittens if there are 3
different kittens in each photograph? Show work for full credit. (Hint:
Order doesn’t matter in this instance) (5 pts) 16.For meals, the Hulk’s kittens don’t like eating in the same spot every meal.
All 6 food bowls are along a line. If each kitten is paired with a food bowl,
how many different ways can the kittens be arranged for a meal? Show
work for full credit. (Hint: Order matters) (5 pts) Solve the following problems. Show work for full credit: (2 pts each) 17. P ( 8,5 )=¿ 18. P ( 9,7 )=¿ 21.Use the Binomial Theorem to expand 19. (85) 20. (83) ( 2 x +3 y )4 . Show work for full credit. (5 pts) For each permutation of {1, 2, 3, 4, 5, 6, 7}, give the next largest permutation or
indicate that the permutation is the last one in lexicographic order. (1 pts each
problem)
22. (1,2,3,4,5,6,7)
23. (2,3,1,5,6,7,4)
24. (7,2,3,4,5,6,1)
25. (1,7,6,4,2,3,5)
26. (5,4,7,6,3,2,1) 27.While drinking a coffee at his favorite coffee shop, the Hulk notices the shop
offers 17 different kinds of drinks offered. What is the least amount of customers buying a single drink must the store have in order for at least 3 of
those customers buy the same drink. Explain your answer. (10 pts) 28.The pet store the Hulk buys his kittens their food, sells 5 different types of
pets: rodents, fish, cats, dogs, and reptiles. If 7 people purchased a single
pet, were there 2 people that purchased the same type of pet? Explain your
answer? (10 pts) 29.The Hulk rolls two dice and adds the two values. What is the probability
that the sum of the two dice is 6 or 8? Express the answer as a simplified
fraction and show work for full credit. (11 pts) 30.The Hulk flips 4 coins. What is the probability that he flips 3 of the same
side? Express the answer as a simplified fraction and show your work for
full credit. (11 pts)