Discrete Mathematics Answers

Which of the following expressions are equivalent to: (-171 x 77) mod 16 Select all that applies

a) 1

b) (5 x 13) mod 16

c) 2

d) 65 mod 16

e) 18 mod 16

What is 6 mod 9 + 11 mod 9 congruent to?

a) 8 mod 9

b) 6 mod 9

c) 7 mod 9

d) 0 mod 9

What is 7 mod 3?

a) 1 mod 3

b) 2 mod 3

c) 3 mod 3

d) 0 mod 3 

Draw a graph having the given properties

(a) Four vertices each of degree 1

(b) Six vertices each of degree 3 

When drawing one card out of a deck of 52 playing cards, what is the probability of getting heart or a face card? There are 13 hearts and a total of 12 face cards (3 of each suit: spades, hearts, diamonds and clubs), but only 3 face cards of hearts.

45% of the children in a school have a dog, 30% have a cat, and 18% have a dog and a cat. What percentage of those who have a cat also have a dog? 

In a hamster breeder's experience the number X of live pups in a litter has the probability distribution of 

x 3 4 5 6 7 8 9

P(x) 0.04 0.1 0.26 0.31 0.22 0.05 0.02 

(a) Find the probability that the next litter will produce five to seven live pups.

(b) Find the probability that the next litter will produce at least six live pups. 

Two fair dice are rolled.

(a) What is the probability of getting a sum of 7?

(b) What is the probability that the sum of the numbers on the dice is odd? 

Refer to the menu below, how many dinners at Kay’s Quick Lunch consist of an optional appetizer, one main course, and an optional beverage? 

Appetizers

Nachos 2.15

Salad 1.90

Main courses

Hamburger 3.25

Cheeseburger 3.65

Fish filet 3.15

Beverages

Tea .70

Milk .85

Cola .75

Root Beer .75

There are a selection of Action Comics, Superman, Captain Marvel, Archie, X-Man, and Nancy comics.

(a) How many ways are there to select 10 comics?

(b) How many ways are there to select 10 comics if we choose at least one of each book?