Discrete Mathematics
Which of the following is an isomorphism? 2x + y = 3y * x log ( x * y ) = log x / log y tan x = sin x / cos x x + 1 = x / 2
tan x = sin x / cos x
Evaluate the following sum: SIGMA(4, n=2)(3n-4)
15
What is a set?
A collection of objects
Select the tautology from the statements below. If I got paid, then I order pizza. If I order pizza, then I got paid. I either order pizza or I got paid. I either order pizza or I don't order pizza.
I either order pizza or I don't order pizza.
What is the correct way of denoting (or writing) the cardinality of set Q? Q = {orange, green, pink, red, black} c(Q) = 5 None of these. n|Q|=5 |Q| = 5 Q = 5
|Q| = 5
What is the 83rd term of the sequence 91, 87, 83, 79, ... ( = a1, a2, a3, a4, ...)? -247 -243 -233 -237 -229
-237
If the domain of the function f(x) = x^2 is 0 ≤ x, what is the range of f? -1 to 1 0 to infinity 0 to -0 -infinity to 0 -infinity to infinity
0 to infinity
What is the domain of √(x)? -1 to 1 -infinity to 0 0 to 1 0 to infinity
0 to infinity
Evaluate h(x) = 5x + 1, when x=3. 3 6 x 4 16
16
A brick wall has 60 bricks in the first row, but each row has 3 fewer bricks than the previous one. How many bricks are in the 12th row?
27
Which one of the following pairs of sets is equal? A = {1, 2, 3} B = {a, b, c} A = {0, 1, 2, 3} |A| = 4 A = {3, 5, 7} B = {9, 11, 13} A = {0, 1, 2, 3} n(A) = 4 A = {1, 2, 3} B = {3, 1, 2}
A = {1, 2, 3} B = {3, 1, 2}
If a = c and b = c, what kinds of new statements can you make? A: If a = c and b = c, then a = b. B: If a = 1, then b = 1. C: If b = 2, then a = 1.
A and B
Which of the following is a logic proposition? A: Sam only eats square foods B: Once upon a time C: Circles roll
A and C
If Jimmy does his chores, then Jimmy will get a big scoop of chocolate ice cream. Which of the following represents the conclusion in the above conditional statement? Jimmy does his chores. A big scoop of chocolate ice cream Jimmy will get a big scoop of chocolate ice cream. If Jimmy does his chores If Jimmy does his chores, then Jimmy will get a big scoop of chocolate ice cream.
A big scoop of chocolate ice cream
What's the difference between a sequence and a series? There is no difference because both terms describe the same mathematical expression. A sequence is an ordered list of numbers, and a series is the sum of a sequence's terms. A series is an ordered list of numbers, and a sequence is the sum of a series' terms. A series can be infinite, but a sequence must always be finite.
A sequence is an ordered list of numbers, and a series is the sum of a sequence's terms.
The set of all elements that are under consideration for a particular problem or situation is known as: A notation set A subset A complement set A universal set
A universal set
What kind of reasoning does the statement below illustrate? My phone starts to ring whenever my cat starts to purr. Hasty generalization Circular reasoning Limited choice False cause
False cause
What kind of reasoning uses two unrelated events to prove a point? False cause Valid logic Hasty generalization Limited choice
False cause
Select the tautology from the statements below. I will either pass my English class or not. It is too hot to go outside. His name is either Jack or Josh. Math is awesome.
I will either pass my English class or not.
Which of the following is the inverse of the below argument? If I am in Kansas, then I'm in the United States. If I'm in the United States, then I'm in Kansas. If I am in Kansas, then I'm in the United States. If I'm not in the United States, then I'm not in Kansas. If I'm not in Kansas, then I'm not in the United States.
If I'm not in the United States, then I'm not in Kansas.
Which of the following is a conditional statement whose hypothesis is 'Joe has a red car' and whose conclusion is 'Billy gets to drive it'? If Joe has a red car If Joe has a red car, then Billy gets to drive it. Then Billy gets to drive it. Joe has a red car, so Billy gets to drive it. Joe has a red car and Billy gets to drive it.
If Joe has a red car, then Billy gets to drive it.
Which of the following is a conditional statement? Dogs bark and cats meow. If the dog barks, then the cat will meow. Either the dog barks, or the cat will meow. Dogs bark when cats meow. A dog barks at a cats meow.
If the dog barks, then the cat will meow.
Triangles have 180 degrees in total, and squares are two triangles put together. What can you say about the total degrees of a square? If squares are two triangles put together, then squares equal two triangles. If triangles have 180 degrees in total, then squares have 180 degrees in total. If squares are two triangles put together, then triangles have 180 degrees in total. If triangles have 180 degrees in total, then squares are two triangles put together. If triangles have 180 degrees in total, then squares have 360 degrees in total.
If triangles have 180 degrees in total, then squares have 360 degrees in total.
If x = 1 and y = 2, what can be said about z if z = xy? If x = 1 and y = 2, then x = zy If z = xy, then z = 2. If z = xy, then x = 2. If z = xy, then x = 1. If z = xy, then z = 3.
If z = xy, then z = 2.
Which is the correct definition of a conjunction? It is when two statements are connected with an 'OR'; only when both statements are true is the resulting compound statement true. It is when two statements are connected with an 'OR'. The resulting compound statement can be labeled as true when just one of the statements is true. It is when two statements are connected with an 'AND'. The resulting compound statement can be labeled as true when just one of the statements is true. It is when two statements are connected with a 'NOT'. The resulting compound statement can be labeled as true when just one of the statements is true. It is when two statements are connected with an 'AND'; only when both statements are true is the resulting compound statement true.
It is when two statements are connected with an 'AND'; only when both statements are true is the resulting compound statement true.
Which is the correct definition of a disjunction? It is when two statements are connected with an 'AND''; only when both statements are true is the resulting compound statement true. It is when two statements are connected with an 'OR'. The combined compound statement can be labeled as true when just one of the statements is true. It is when two statements are connected with an 'OR''; only when both statements are true is the resulting compound statement true. It is when two statements are connected with an 'AND'. The resulting compound statement can be labeled as true when just one of the statements is true. It is when two statements are connected with a 'NOT''. The resulting compound statement can be labeled as true when just one of the statements is true.
It is when two statements are connected with an 'OR'. The combined compound statement can be labeled as true when just one of the statements is true.
What does the statement, 'We will go get ice cream if and only if you clean your room' mean? It means no clean room, then no ice cream. It means getting ice cream for a dirty room. It means we get ice cream. It means cleaning a room does not affect getting ice cream.
It means no clean room, then no ice cream.
What does ii mean when a set of pairs are equivalent?
It means they have the same number of items in theirs sets.
Which of the following is NOT true about a bijection? The sizes of the domain and codomain must be equal. it includes all possible outputs of a given function. It will be graphed in the Cartesian plane. It is both an injection and a surjection.
It will be graphed in the Cartesian plane
Select the tautology from the statements below. If it rains on Friday, then I will go to the movies. My name is Andrew. It will either rain or not rain. I have a cat or I have a goldfish.
It will either rain or not rain.
If someone asked you to choose between two candidates for president, but there were still five candidates running for president, what kind of logical fallacy is that? False cause Circular reasoning Hasty generalization Limited choice
Limited Choice
Which of the following connectors is the logical disjunction? AND BUT Both OR
OR
The amount of money you spend on coffees every month can be calculated as a function of the number of drinks you order every month. What are the independent and dependent variables in this function? The independent variable is the amount of money you spend on coffee per month and the dependent variable is the number of drinks you order per month. The independent variable and dependent variable cannot be determined from the given situation. The independent variable is the number of drinks you order per month and the dependent variable is the amount of money you spend on coffee per month. The independent variable is the number of months and the dependent variable is the amount of money you spend on coffee per month. The independent variable is the number of drinks you order every month and the dependent variable is the number of months.
The independent variable is the number of drinks you order per month and the dependent variable is the amount of money you spend on coffee per month.
Which statement is an example of circular reasoning? Anything that possesses 360 degrees must be a circle. I like cheesecake, and you are the same age as me, so you must like cheesecake too. The moon is made of cheese because the moon is made of cheese. You can only pick from a car or a motorcycle as your mode of transportation.
The moon is made of cheese because the moon is made of cheese.
Which rule represents the nth term in the sequence 9, 16, 23, 30...? an = 7n + 2 an = 9n + 2 an = 2n + 7 an = 7n + 9 an = 9n + 7
an = 7n + 2
What is the rule for the nth term of the sequence with a7 = 53 and a13 = 101? an = 8n + 3 an = 5n + 8 an = 8n + 5 an = 8n - 3 an = -3n + 8
an = 8n - 3
What is the rule for the nth term of the geometric sequence if the third term is 96 and the fifth term is 1,536?
an= 6(4)^n-1
Find the rule for this series: 2 + 6 + 18 + 54 + ...
an=2(3)^n-1
Which of the following functions is NOT a surjection going from the set of real numbers to the set of real numbers? f(x) = 3x f(x) = 2x / 3 f(x) = x + 1 f(x) = x2
f(x) = x2
What is the hypothesis in the following statement? 'If p is an even integer and q is an odd integer, then p + q is an odd integer.' q If p is an even integer p is an even integer and q is an odd integer p then p + q is an odd integer
p is an even integer and q is an odd integer
p: The pond is not frozen over. q: The fish are not jumping. For the combination p AND (NOT q), for which truth values of p and q is the combination true?
p: T q: F
p: The dog rolls over on command. q: The dog gets a treat. For the combination p AND q, for which truth values of p and q is the combination true? p: F q: T p: T q: T p: T q: F p: F q: F
p: T q: T
Suppose you play a game with two six-sided dice, where if you get doubles, you win $10, but for anything else you lose $5. If you continue to play this game, how much do you expect to win or lose per roll in the long run? In other words, what is the expected value of this game? $1.75 -$3.25 -$1.67 +$5.00 -$2.50
-$2.50
You play a game with two six-sided dice. If you roll a sum of 6 or 8, you win $3. If you roll a sum of 11, you win $1, but for anything else, you lose $2. If you continue to play this game, what do you expect to win in the long run? $0.75 per roll $1.45 per roll -$1.50 per roll -$2.44 per roll -$0.44 per roll
-.$044
According to Fleury's algorithm, how many odd vertices does a graph with an Euler circuit in it have?
0
Consider the following probability distribution (see table below) of the number of firearms in a household, constructed from a survey of 25,000 randomly selected households. Let X = the number of firearms in a household, and assume that the probability of a household having more than 6 firearms in the home is negligible. If a household is selected at random, then how many firearms would you expect them to have? 0.68 of a gun. 0.468 of a gun. 0.20 of a gun. 1.148 guns. 0.753 of a gun.
0.468 of a gun
How many times do you visit a vertex when traveling either a Hamilton circuit or path? 4 0 1 3 2
1
Which of the following sequences is NOT a geometric sequence? 2, 4, 8, 16, 32, ... 5, 15, 45, 135, 405, ... 100, 50, 25, 25/2, 25/4, ... 1, 8, 15, 22, 29, ... 9, 27, 81, 243, 729, ...
1, 8, 15, 22, 29, ...
A television channel conducts a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. How many TVs does each household have on average? 2.0 1.51 1.83 1.94 2.5
1.83
When you roll two six-sided dice, what is the probability of getting a sum of 11? 1/9 1/12 1/18 1/36
1/18
When two six-sided dice are rolled, what is the probability of getting doubles? (two ones, two twos, etc.) 1/36 1/2 1/9 1/6
1/6
The total number of degrees in a graph is 20. How many edges does it have?
10
A man is deciding what to wear to work. He is considering an outfit from among 5 shirts, 3 pairs of pants, and 7 ties. How many possible outfits are there? 105 120 15 30
105
A sandwich shop offers 3 types of meat, 3 types of cheeses, 3 types of bread, and 4 types of condiments for its sandwiches. If you select one of each of the four ingredients, how many possible sandwiches can you create? 108 36 9 13
108
A vehicle license plate uses three numbers and three letters on each plate. The numbers are listed first and then the letters. The numbers used range from 0-9 and the letters used can be any letter of the 26 letters of the alphabet. On any given license plate, the letters can be repeated, but the numbers cannot be repeated. How many different plates are possible? 108 17,576,000 11,232,000 12,654,720
12,654,720
A complete graph with 6 vertices has how many Hamilton circuits? 60 40 100 120 720
120
Jimmy is making multi-flavored ice cream cones by scooping in different flavors one at a time. Jimmy has 6 different flavors but can only put 3 flavors in each cone. The order of the flavors is important to him as it affects how he tastes each ice cream. How many different arrangements of cones can Jimmy make? 60 18 30 120
120
Six people are going to sit at a round table. How many different ways can this be done?
120
Solve the following combination: 10C7 86,400 120 6 604,800 720
120
If 55 and 89 are two sequential terms of the Fibonacci sequence, what term would come next?
144
If 55 and 89 are two sequential terms of the Fibonacci sequence, what term would come next? 165 123 178 110 144
144
If a2 = 5 and a8 = 35, what is the value of a30? 185 145 150 158 245
145
The value at time n is the value at time (n - 1) plus 6. If the start value at time n = 0 is 4, the value at time n = 2 is _____. 10 0 16 4
16
From mortality tables it has been determined that the probability of a 20-year old male non-smoker dying within the year is 0.0035. Suppose an insurance company wants to sell a $50,000 1-year life insurance policy to a 20-year old non-smoking male. What should they charge for the policy to break even? $175 $180 $125 $210 $200
175
In the sequence 9, 14, 19, 24, 29,.... Say we're using a to describe the terms. What is the value of the term below? 24 9 14 29 19
19
A complete graph with 3 vertices has how many Hamilton circuits? 1 8 None 2 6
2
According to Fleury's algorithm, how many odd vertices does a graph with an Euler path in it have?
2
How many odd vertices can a graph have in order to use Fleury's algorithm? 1 4 3 2 6
2
Suppose you have a circular arrangement of three items. If the circle is free, in how many ways can the items be arranged? 3 2 4 1
2
Calculate 4! (factorial) 12 24 9 48 6
24
Evaluate f(x) = √(x), when x = 9. 1 0 10 3 9
3
How many propositions are there in the statement below? I will buy you a huge bacon cheeseburger and she will wash your car if and only if you give me your big screen television. 1 2 3 4
3
How many rows would a matrix that represents a system of 5 variables and 3 equations have? 6 3 5 8 2
3
Suppose you have a drawer full of white socks and black socks. What is the minimum number of socks you would need to pull out of the drawer to guarantee a pair of matching socks? 1 4 3 2
3
Suppose you toss three coins. What is the probability that you get two heads and one tail if the order in which you get them does not matter? 7/8 3/8 1/8 1/4 1/6
3/8
If a graph has 15 edges, what must the degrees of the vertices add up to?
30
Assuming that an ace counts as a one, calculate the number of combinations of straight flushes for a poker hand. (In other words, disregard the royal flush.) There are 4 possible combinations of straight flushes. There are 10 possible combinations of straight flushes. There are 71,193 possible combinations of straight flushes. There are 36 possible combinations of straight flushes. There are 1287 possible combinations of straight flushes.
36
8 different novels are to be placed side-by-side on a shelf. How many ways can the 8 novels be arranged on the shelf? 8 40,320 56 20,160
40,320
Solve 8! (factorial) 37 362,880 40,320 5,040 840
40,320
Solve the expression 7P2 (P = permutation) 120 42 2,640 5,040
42
Calculate the probability of getting a single pair in a hand of poker. Round that probability to the nearest percent. 35% 52% 42% 8% 92%
42%
A brick wall contains 52 bricks in its bottom row and 49 bricks in the next row up from the bottom row. Each subsequent row contains 3 fewer bricks than the row immediately below it. If the wall contains 16 rows, how many bricks total make up the wall? 518 944 720 360 472
472
Asia is conducting an experiment for her psychology class. She asks 80 students if they believe in hypnosis. Previous studies show that 60% of the population believes in hypnosis. Based on the expected value, how many people should answer yes, they do believe in hypnosis, in Asia's study? 48 people 60 people 40 people 32 people 43 people
48
Find the sum 1 + 8 + 15 + 22 + 29 using the formula for an arithmetic series. What number should you use to replace the variable n in the formula (n/2)(a1 +an)? 1 29 7 5
5
Jane is attempting to unlock her locker but has forgotten her locker combination. The lock uses 3 numbers and includes only the numbers 1 to 9. The digits cannot be repeated in the combination. How many possible locker combinations can be formed? 504 locker combinations 252 locker combinations 27 locker combinations 362,880 locker combinations
504 locker combinations
Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. Let X = the number of firearms in a household. From the survey of 30,000 households it was determined that the empirical probability of X = 1 was 0.2. How many of the households in the survey had one firearm in their home? 6,000 20% 11,000 20,000 9,000
6,000
Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. If the sample size was 25,000 and 17,000 households reported that they had no firearms in their home, what would be the empirical probability that a randomly selected household had no firearms in their home? 17% 25% 68% 0% 100%
68%
A couple wants to plant some shrubs around a circular walkway. They have seven different shrubs. How many different ways can the shrubs be planted? 720 1440 120 5040
720
A horse race includes 10 participants. How many possible finishes are there for the top three positions: first (win), second (place), and third (show)? 5,040 720 3,628,800 1,000
720
The local bowling team plays in a 7-team league where each team plays other teams 4 times in a season. Using the combination formula, how many different games will be played in a season? 35 105 320 84 420
84
A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). On one spin of the roulette wheel, what is the probability that the ball lands on a red slot? 9/19 1/19 9/38 19/38 1/2
9/19
Which of the following is the 14th term of the sequence below? 11, 22, 44, 88, 176, ... 90,112 180,224 45,056 8,192 16,384
90,112
Find the sum of the arithmetic series 106 +100 + 94 + ... + 28 + 22. 768 1,792 896 1536 960
960
Which graph in discrete mathematics has a path of edges between every pair of vertices in the graph? A bipartite graph A disconnected graph A connected graph A directed graph
A connected graph
What is the difference between a directed and an undirected graph? A directed graph can contain weights on the edges, but an undirected graph cannot. A directed graph can contain multiple edges and loops, but an undirected graph cannot. There is no difference between directed and undirected graphs. A directed graph uses arrows to indicate one-way relationships, but an undirected graph does not.
A directed graph uses arrows to indicate one-way relationships, but an undirected graph does not.
Which of the following is NOT a property of a random variable? The sum of the probabilities of a random variable is equal to 1. A random variable represents numerical outcomes for different situations or events. A random variable can be discrete or continuous. A random variable cannot be negative.
A random variable cannot be negative.
What is a tautology? A statement that is sometimes true A statement that is always false A statement that is always true A statement that is sometimes false
A statement that is always true
What is a tautology?
A statement that is always true by logical structure (I believe..., I think...)
What is a proposition?
A statement that is true or false
Which of the following connectors is the logical conjunction? AND BOTH BUT OR
AND
What is the ratio of successful outcomes and the total number of trials? Randomized experiment Theoretical probability Parameter percentage Actual probability
Actual probability
Which is a correct logical disjunction formed with the following phrases? Algebra is easy. Geometry is a breeze. Algebra and geometry are either easy or a breeze. Algebra is easy and geometry is a breeze. Algebra is easy or geometry is a breeze. Algebra and geometry are both easy and a breeze. Neither is algebra easy nor geometry a breeze.
Algebra is easy or geometry is a breeze.
A complete graph is a graph where each vertex is connected to how many of the other vertices? Some Half None All 2
All
Which of the following conditions is necessary in order to have isomorphic graphs? All are correct V(G1)=V(G2) E(G1)=E(G2) Equal number of vertices of a particular degree.
All are correct
Which of the following occurs with a direct proof? A series of statements are made. All are correct A conditional statement is proven. Statements are supported by known facts and definitions.
All are correct
In the following statement, which part is the hypothesis? If all mammals are animals, then dogs are animals.
All mammals are animals
How many vertices in a graph do you visit by traveling a Hamilton path or circuit? All of them. 2 1 Half of them. 1/3 of them.
All of them.
Which of the following statements about the pigeonhole principle is TRUE? If we are placing 7 pigeons in 5 pigeonholes, it must be the case that at least one of the pigeonholes has more than one pigeon in it. All of these statements about the pigeonhole principle are true. The pigeonhole principle is a simple yet extremely useful concept used in combinatorics. The pigeonhole principle states that if we are placing pigeons in pigeonholes, and there are more pigeons than pigeonholes, it must be the case that at least one pigeonhole has more than one pigeon in it.
All of these statements about the pigeonhole principle are true.
What must a conditional statement contain?
An IF (Hypothesis) and a THEN (Conclusion)
The name one-to-one describes which function? An exponential function A surjective function A bijective function An injective function
An injective function
When using Fleury's algorithm with a graph that has 0 odd vertices, at which vertex must you start? Any vertex will work. The vertex with the least degree. The vertex with the largest degree. The top-most vertex. The vertex at the way bottom.
Any vertex will work.
Which type of logical fallacy is illustrated in the example below? I will get an A in math class because I spent many sleepless nights studying. Appeal to ignorance Appeal to wisdom Appeal to emotion Appeal to popularity
Appeal to emotion
Which type of logical fallacy is illustrated below? The moon is made of cheese because it looks like cheese and no one has ever eaten the moon. Appeal to ignorance Appeal to popularity Appeal to wisdom Appeal to emotion
Appeal to ignorance
Which type of logical fallacy is illustrated below? Everyone in the class agrees that if x = 2 and y = 2, then x must equal y. Appeal to popularity Appeal to wisdom Appeal to ignorance Appeal to emotion
Appeal to popularity
Which type of logical fallacy is illustrated below? This chocolate pie must be bad because nobody is taking it. Appeal to emotion Appeal to ignorance Appeal to wisdom Appeal to popularity
Appeal to popularity
If you're placing pigeons in pigeonholes, and there are more pigeons than pigeonholes, which of the following must be TRUE? At least one pigeonhole will contain more than one pigeon. The pigeons that have the same coloring will need to be placed together. No pigeonhole will contain more than one pigeon. All of the pigeons will need to be placed in one hole.
At least one pigeonhole will contain more than one pigeon.
A decision tree has only two options at each node. What is this called? Two-noded decision tree Binary decision tree Two-edged decision tree Two options at each node is not a possibility in decision trees.
Binary decision tree
What is an experiment that contains a fixed number of trials that results in only one of two independent outcomes: success or failure? Systematic random sampling Cluster sampling Randomized experiment Binomial experiment
Binomial experiment
What is an experiment that contains a fixed number of trials that results in only one of two outcomes: success or failure? Statistical probability Experimental design trials and outcomes Binomial experiment
Binomial experiment
What is the number of successes in a binomial experiment called? Binomial experiment Standard deviation Expected value Binomial random variable
Binomial random variable
Which method is optimal for finding the most efficient Hamilton circuit? Nearest neighbor Brute force None Repeated nearest neighbor Cheapest link
Brute force
What is the brute force method? Choose the nearest city using different starting points. Choose the edges starting with the cheapest and going to the most expensive. Choose the next closest city. Connect the dots randomly. Calculate each Hamilton circuit to see which one is best.
Calculate each Hamilton circuit to see which one is best.
Which is the nearest neighbor method? Calculate each Hamilton circuit to see which is best. Choose the next closest city with different starting points. Choose the edges starting with the cheapest and going to the most expensive. Choose the next closest city. Connect the dots.
Choose the next closest city.
What is a probability formula that uses factorials to find the number of possible combinations of all the outcomes in an experiment? Combination formula Coefficient formula Permutation formula Correlation formula
Combination formula
What is a probability formula that uses factorials to find the number of possible combinations of all the outcomes in an experiment? Student t formula Correlation formula Permutation formula Combination formula Coefficient formula
Combination formula
Which statement best describes combinatorics? Combinatorics is a fancy name for the study of counting. Combinatorics is an idea that mathematicians have yet to prove. Combinatorics is the study of shapes. Combinatorics is theoretical and can't be applied to actual probabilities.
Combinatorics is a fancy name for the study of counting.
What is a database NOT required to do? Correct Data. Retrieve Data. Preserve Data Store Data.
Correct Data
What is the difference of discrete vs continues variables?
Discrete are whole numbers 1,2,3,etc. Continuous can be a decimal such 2.53
What do we call data that cannot be divided, which is distinct, and can only occur in certain values? Continuous data Random data Discrete data Quantitative data Qualitative data
Discrete data
You conduct an experiment where you want to measure the number of rolls it takes to get two 6's in a row when you roll a fair six-sided die. State whether the random variable is discrete or continuous and give a summary of its values. Discrete with values 2, 3, 4, 5, 6, etc. Discrete with values ranging from 1 to 6 Discrete with values ranging from 0 to 1 Continuous with values ranging from 1 to 6
Discrete with values 2, 3, 4, 5, 6, etc.
Which of the following is not a valid matrix operation? Division Addition Subtraction Multiplication
Division
Which one is the correct denotation of an empty set? E = {0} |E| = 1 n(E) = 1 E = { } E = {none}
E = { }
Which statement is false? The elements of a universal set are based on the context of a problem. A universal set is a subset of itself. A subset cannot have more elements than the set from which it is created. Every universal set has the same number of elements.
Every universal set has the same number of elements.
Children born after the turn of the century have a 60% probability of needing braces. What are the expected value and standard deviation for a group of 30 children surveyed? Expected Value: 18 Standard Deviation: 2.7 Expected Value: 12 Standard Deviation: 2.7 Expected Value: 12 Standard Deviation: 7.2 Expected Value: 18 Standard Deviation: 7.2
Expected Value: 18 Standard Deviation: 2.7
What do we call the number of successful outcomes expected in an experiment? Qualitative data Random data Discrete data Continuous data Expected value
Expected value
What is the number of successful outcomes expected in an experiment called? Binomial experiment Standard deviation Variance Expected value
Expected value
Which of the following does a graph search NOT include? Finding a vertex Finding the chromatic number Finding a path Finding an edge
Finding the chromatic number
Which of the following words means that a circle cannot be flipped over when determining the number of different possible arrangements of items? friendly fixed fickle free
Fixed
What kinds of graphs does Fleury's algorithm work for? Graph with an even number of edges. Graphs with an Euler path or circuit in it. A graph with 4 odd vertices. A graph with 1 odd vertex. Any graph.
Graphs with an Euler path or circuit in it.
What kind of logic is presented below? Your dog loves rock and roll music because my dog loves rock and roll music. Limited choice Circular reasoning Hasty generalization False cause
Hasty generalization
If he eats a hamburger, then he will eat two bags of fries. Which of the following represents the hypothesis in the above conditional statement? He eats a hamburger. If he eats a hamburger, then he will eat two bags of fries. He will eat two bags of fries. Then he will eat two bags of fries Hamburger
He eats a hamburger.
Suppose you play a game where you spin a spinner (see picture below) with areas of the colors on the spinner broken down as shown: 10% blue, 60% green, and 30% red. In addition, if the spinner lands on red you win 6 points, if it lands on blue you win 1 point, and if it lands on green you lose 5 points. If you keep spinning, how many points can you expect to win or lose per game? I expect to lose 2.3 points per game. I expect to lose 1.1 points per game. I expect to win 2 points per game. I expect to lose 1.5 points per game. I expect to break even.
I expect to lose 1.1 points per game.
You play a game where you toss a coin. On each toss if it lands with heads up, you win $1. However, if it lands with tails up, you lose $2. If you continue to play this game, how much can you expect to win or lose per game? I expect to make $1 per game. I expect to make 25 cents per game. I expect to break even. I expect to lose 50 cents per game. I expect to lose $1 per game.
I expect to lose 50 cents per game.
A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). Suppose that for a bet of $1 on red, the casino will pay you $2 if the ball lands on a red slot (a net gain of $1), and otherwise you lose your dollar. What can you expect to win or lose in this game? I expect to break even in this game. I expect to lose about 5 cents per game. I expect to lose 50 cents per game. I expect to lose $1 per game. I expect to make about 50 cents per game.
I expect to lose about 5 cents per game.
If the following two propositions are true, which is a true statement? Theresa loves dogs. Spot is a dog. If Spot is a dog, then Theresa loves Spot. If Spot is a dog, then Theresa hates Spot. If Theresa loves dogs, then Spot hates Theresa. If Theresa loves dogs, then Spot loves Theresa. If Spot is a dog, then Theresa loves dogs.
If Spot is a dog, then Theresa loves Spot.
Which of the following is a conditional statement? A square is a rectangle, so therefore, a triangle is a shape. Squares are rectangles, but triangles are shapes. If a square is a rectangle, then a triangle is a shape. If a square is a rectangle, triangles will have shape. A square is a rectangle and a triangle is a shape.
If a square is a rectangle, then a triangle is a shape.
Which of these is the logical contrapositive to the following statement? If killing in any sense is wrong, then murder is wrong. If killing in any sense is wrong, then murder is not wrong. If murder is not wrong, then killing in any sense is not wrong. If murder is wrong, then killing in any sense is wrong. If killing in any sense is not wrong, then murder is not wrong.
If murder is not wrong, then killing in any sense is not wrong.
All of the following statements could be proven with a direct proof EXCEPT: If c is an even integer, then 5c + 6 is even. If m is an even integer, then -m is an even integer. If n is an odd integer, then m is an even integer. If q is an even integer, then q^2 is an even integer. If x and y are integers and x is odd and y is even, then xy is even.
If n is an odd integer, then m is an even integer.
What is the most specific term that describes the numbers 5, 10, 15, 20, 25, ...?
Infinite arithmetic sequence
What is a range?
Is the expected possible outputs of Y
Suppose you are at a small get-together at a friend's house, and there are 13 people there, including yourself. When it comes to birthdays of the people at the party and the pigeonhole principle, which of the following statements must be true? It must be true that at least two people were born at the same hour of day. It must be true that at least two people share the same birthday month. It must be true that at least two people have the same birthday. None of these statements must be true.
It must be true that at least two people share the same birthday month.
The best Hamilton circuit in a weighted graph is the one where the total cost is what? 20 Least 100 Most 10
Least
Suppose you play a game with two 4-sided dice with sides numbered 1 through 4. If you roll a sum of 8 (face down), you win $10. If you roll anything else, you lose $1. What can you expect to win or lose in this game? Lose $0.67 per game Lose 31 cents per game Lose 12 cents per game Lose 40 cents per game Win $1.50 per game
Lose 31 cents per game
After finding the number of ways to get four-of-a-kind for four cards in a poker hand, should you use: a. 48 choose 1 or b. 12 choose 1 x 4 choose 1 to describe all possible ways for getting the 5th card? Explain your reasoning. There is not enough information given, because the last calculation depends on the four-of-a-kind values. Neither calculation is correct, because they don't take the order of the cards into account. 1 x 12 choose 1 x 4 choose 1, because there are 12 possible values and 4 possible suits for the 5th card. Either way is correct, because both calculations describe all possible ways for getting the 5th card. 1 choose 48, because there are 48 possible cards remaining for the 5th card and the value doesn't matter.
Neither calculation is correct, because they don't take the order of the cards into account.
Justin is conducting an experiment. He wants to know which type of pet is most preferred among 2nd graders. He asks them if they prefer dogs, cats, or hamsters. Is this a binomial experiment? No, the outcomes are independent. Yes, there are fixed number of trials. Yes, the outcomes are independent. No, there are more than two possible outcomes.
No, there are more than two possible outcomes.
In a tree structure, the point at which a discrete decision is made is called a _____. root corner block node
Node
Which of the methods is both optimal and efficient?
None
Work to sort, organize the data, or maintain the Tree Sort is referred to as _____. overhead through-put system margin sunk costs
Overhead
What variable represents the probability of success on an individual trial? t P x n y
P
A binomial experiment must have two possible outcomes: success and failure. Select the answer that is an example of a binomial experiment. Picking an ace (success) or not an ace (failure) out of a deck of cards. Replacing each of the cards before drawing again. Drawing 20 cards total. Picking an ace (success) or not an ace (failure) out of a deck of cards. Replacing each of the cards before drawing again. Drawing until all of the aces are out of the deck. Picking an ace (success) or not an ace (failure) out of a deck of cards. Not replacing each of the cards before drawing again. Drawing 20 cards total. Picking an ace (success) or not an ace (failure) out of a deck of cards. Replacing each of the cards before drawing again.
Picking an ace (success) or not an ace (failure) out of a deck of cards. Replacing each of the cards before drawing again. Drawing 20 cards total.
If a universal set is defined as all the countries of South America, which of the following is not an element of the universal set? Chile Poland Argentina Brazil
Poland
The decision tree structure begins at a node called the _____. branch span root top
Root
Express this series using sigma notation: 3 + 5 + 9 + 17 + 33.
SIGMA(5,n=1)(2^n)+1
Express this series using sigma notation: 5 + 6 + 7 + 8 + 9 + 10...
SIGMA(infinite, n=1)(4+n)
What is an example of a logical fallacy? Writing a correct mathematical equation Saying something is true or false based on emotions Making a logical argument about an emotional subject Reasoning that is based on pure facts
Saying something is true or false based on emotions
What is the degree in which the variables are different from the mean called? Binomial random variable Median Binomial experiment Standard deviation
Standard deviation
The converse of a logical statement is found by doing what? Negating the hypothesis and conclusion, then switching them. Negating the conclusion, but not the hypothesis. Switching the hypothesis and the conclusion. Negating both the hypothesis and conclusion.
Switching the hypothesis and the conclusion.
Let the universal set U be the set of Mr. Salada's 5th grade class of 17 boys and 13 girls. Let set A be the set of all the girls in Mr. Salada's class, and let set B be the set of all the boys in Mr. Salada's class. Which set has the most elements? The complement of B A The complement of A The complement of U
The complement of A
Which of these is always logically equivalent to the inverse? The counterexample The conditional The converse The contrapositive
The converse
What is a domain?
The domain are those values that you can put as input (as the x variable) into the function.
What is the ratio of the desired outcome and the total number of possible outcomes? Theoretical probability Parameter percentage Randomized experiment Actual probability
Theoretical probability
Jeanette asks 20 people in her history class to answer either yes or no to this question, "Are you comfortable using technology?" Seven out of the 20 answer yes, the remainder answer no. Calculate the theoretical and the actual probability of this scenario. Theoretical: 50% Actual: 35% Theoretical: 35% Actual: 50% Theoretical: 70% Actual: 50% Theoretical: 50% Actual: 70%
Theoretical: 50% Actual: 35%
Jeanette asks 50 students in her math class if they are comfortable using technology. Thirty-eight say they are comfortable using technology. Calculate the theoretical and actual probability of this scenario. Theoretical: 25% Actual: 50% Theoretical: 50% Actual: 76% Theoretical: 25% Actual: 76% Theoretical: 50% Actual: 83%
Theoretical: 50% Actual: 76%
Calculate the number of combinations of royal flushes. There are 10 combinations of royal flushes. There are 13 combinations of royal flushes, one for each value. There are 2,598,960 combinations of royal flushes. There are 649,740 combinations of royal flushes. There are 4 combinations of royal flushes, one for each suit.
There are 4 combinations of royal flushes, one for each suit.
How many different combinations of flushes are there in a fair deck of cards? There are 1,277 combinations of flushes in a deck. There are 1,287 combinations of flushes in a deck. There are 36 combinations of flushes in a deck. There are 5,108 combinations of flushes in a deck. There are 10,240 combinations of flushes in a deck.
There are 5,108 combinations of flushes in a deck.
Calculate the number of combinations and the probability of getting a three-of-a-kind hand in poker. There are 54,912 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 47 chance of getting a three-of-a-kind hand in poker. There are 674 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 47 chance of getting a three-of-a-kind hand in poker. There are 123,552 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 21 chance of getting a three-of-a-kind hand in poker. There are 54,912 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 624 chance of getting a three-of-a-kind hand in poker. There are 47 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 624 chance of getting a three-of-a-kind hand in poker.
There are 54,912 different combinations of three-of-a-kind hands in poker. There is approximately a 1 in 47 chance of getting a three-of-a-kind hand in poker.
Calculate the number of combinations of getting a four-of-a-kind hand in poker. There is a 1 in 2,598,960 probability of getting a four-of-a-kind. There is a 1 in 4,165 probability of getting a four-of-a-kind. There are 4,165 different combinations of four-of-a-kind hands in poker. There are 624 different combinations of four-of-a-kind hands in poker. There is a 1 in 624 probability of getting four-of-a-kind.
There are 624 different combinations of four-of-a-kind hands in poker.
Which of the following statements is NOT true? There are only three types of graphs in discrete mathematics. A graph is a collection of points and lines between those points. The points in a graph are called vertices. The lines between points in a graph are called edges.
There are only three types of graphs in discrete mathematics.
Calculate the probability of getting a straight in a hand of poker. There is approximately a 1 in 10,240 chance of getting a straight in poker. There is approximately a 1 in 36 chance of getting a straight in poker. There are 10,200 different combinations of straights in poker. There are 5,108 different combinations of straights in poker. There is approximately a 1 in 255 chance of getting a straight in poker.
There is approximately a 1 in 255 chance of getting a straight in poker.
Why are inverses important when it comes to isomorphisms?
They allow you to find the other value regardless of which value you are given
What is the negation of 'Triangles are not squares'? Triangles are squares. Triangles don't have four sides. Triangles are not circles. Triangles are three sided.
Triangles are squares.
A statement can be determined to be which of the following through a direct proof? Only true Never false True or false Only false Never true
True or false
Let the universal set U be all the letters of the English alphabet. What is the complement of the empty set? (Note: the empty set is a subset of every set.) Ø - U U {a, b, c, d} Ø
U
You decide to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values? Yes, it is a random variable, and its values can be 1 and 2. No, it is not a random variable, since it is not random. Yes, it is a random variable, and its values are 0, 1, or 2. Yes, it is a random variable, and its values can be 2 or 4.
Yes, it is a random variable, and its values are 0, 1, or 2.
What is an example of a generalized tree in discrete math? all of these are correct a non-spanning tree a tree with loops a simple spanning tree
all of these are correct
What is a universal set?
all the elements, or members, of any group under consideration. (Finite)
Deleting unused data is called _____. data compression garbage collection data recycling linear sorting
garbage collection
What variable represents the number of trials in an experiment? P y n t x
n
What is the combination formula? i.e. 10C7
n!/r!(n-r)!
The number of comparisons required to sort n items linearly varies as _____. n-squared nlog(n) n n-cubed
n-squared
The number of comparisons required to sort n items into a tree structure varies as _____. n-squared nlog(n) n n-cubed
nlog(n)
Searching from left to right is a(n) _____ search strategy . reorder inorder preorder postorder
preorder
A search which starts at the tips (leaves) of the tree and works toward the root is the _____ strategy. preorder postorder reorder inorder
reorder
Standard Deviation Formula
sgrt(n*P*(1-P)
What is the formula for the standard deviation of a binomial random variable? P * x n* P sqrt (n * P * (1-P)) a^2 + b^ = c^2
sqrt (n * P * (1-P))
What is cardinality?
the number of elements in a set written as |P| or n(P)
What is the conclusion in the following statement? 'If p and q are odd integers, then pq is odd.' odd integers If p and q are odd integers, If p and q then pq is odd.
then pq is odd.
Data sorted in a tree structure may occasionally need to be resorted to maintain _____. dynamic tension entropy tree asymmetry tree symmetry
tree symmetry
An example of a recurrence relation is _____. un = 3 n un = 3 un = 3 un-1 un = 3 n2
un = 3 un-1
If a value today is 6 times the value it was yesterday, the recurrence relation is _____. un = 6 + un-1 un = 2 un-1 + 4 un-2 un = 6 un+1 un = 6 un-1
un = 6 un-1
Which of the following is a first-order recurrence? un = sin un - 1 un = 6 un = 2un - 1 + 3 un - 2 un = vn - 1
un = sin un - 1
Discrete math deals with problems concerning options that can be expressed as _____. fractions all real numbers odd numbers whole numbers
whole numbers
An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x? x is a discrete random variable. x is a continuous random variable. x is both discrete and continuous. x is not a random variable. x is a binomial random variable.
x is a continuous random variable.
You decide to collect a bunch of cans of soda and measure the volume of soda in each can. Let x = the number of mL of soda in each can. What type of variable is x? x is a discrete random variable. x is a continuous random variable. x is a constant. x is not a random variable.
x is a continuous random variable.
If a universal set is {1, 2, 3, 4, 5, 6, 7} and set C equals {1, 2, 3}, What is the complement of the complement of C? {1, 2, 3} {1, 2, 3, 4, 5, 6, 7} Ø {4, 5, 6, 7}
{1, 2, 3}
If U = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} and A = {12, 13, 14, 20}, what is the complement of A?
{11, 15, 16, 17, 18, 19}
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Which of the following is not a subset of the universal set? {1, 6, 9} U {1, 2, 3} {8, 9, 10}
{8, 9, 10}
