Podcast
Questions and Answers
Which of the following describes if the graph has a Euler path or circuit?
Which of the following describes if the graph has a Euler path or circuit?
- The graph has no Euler path or circuit.
- There are more than 2 odd vertices.
- The graph has a circuit because there are no odd vertices.
- The graph has a path because there are exactly 2 odd vertices. (correct)
Which of these statements must be true?
Which of these statements must be true?
- There are 6 vertices so there must be 6 edges.
- There are 6 edges so the degree of each vertex must add up to 6.
- There are 6 vertices so there must be 12 edges.
- There are 6 edges so the degree of each vertex must add up to 12. (correct)
For a graph with seven edges, what is the sum of its degrees?
For a graph with seven edges, what is the sum of its degrees?
14
Which of the following combination of degrees (vertices) for a graph is not possible?
Which of the following combination of degrees (vertices) for a graph is not possible?
If the sum of the degrees for a graph is 16, how many edges does the graph have?
If the sum of the degrees for a graph is 16, how many edges does the graph have?
Is it possible to have a connected graph with two vertices, one with a degree of 1 and the other with a degree of 2?
Is it possible to have a connected graph with two vertices, one with a degree of 1 and the other with a degree of 2?
Hamilton paths and circuits must go through every _______ exactly one time.
Hamilton paths and circuits must go through every _______ exactly one time.
Euler paths and circuits must go through every ______ exactly one time.
Euler paths and circuits must go through every ______ exactly one time.
How many combinations are possible for a 4 digit combination for an alarm code with specific restrictions?
How many combinations are possible for a 4 digit combination for an alarm code with specific restrictions?
How many combinations are possible for a password that is a 5 digit code with specific restrictions?
How many combinations are possible for a password that is a 5 digit code with specific restrictions?
About how much weight is the elevator supporting if it has about 90 square feet of space?
About how much weight is the elevator supporting if it has about 90 square feet of space?
How many different combinations can there be for a combination locker using a three number combination?
How many different combinations can there be for a combination locker using a three number combination?
What is the estimation method to calculate vet bills over the course of a dog's life?
What is the estimation method to calculate vet bills over the course of a dog's life?
What are the dimensions of a television screen measured at 46" (on the diagonal) with an aspect ratio of 16:9?
What are the dimensions of a television screen measured at 46" (on the diagonal) with an aspect ratio of 16:9?
What is the height of the image for a movie shown on a 46" television with an aspect ratio of 2.25:1?
What is the height of the image for a movie shown on a 46" television with an aspect ratio of 2.25:1?
What is the height of the black border at the top and bottom for a movie with an aspect ratio of 2.25:1 when shown on a 46" television?
What is the height of the black border at the top and bottom for a movie with an aspect ratio of 2.25:1 when shown on a 46" television?
What percent of the screen is utilized if a movie with an aspect ratio of 2.25:1 is shown on a 46" television screen?
What percent of the screen is utilized if a movie with an aspect ratio of 2.25:1 is shown on a 46" television screen?
What is the batter's average for a baseball player after 285 times at bat?
What is the batter's average for a baseball player after 285 times at bat?
Determine the inflation rate by comparing the CPI from the year 2000 to the CPI of 2016.
Determine the inflation rate by comparing the CPI from the year 2000 to the CPI of 2016.
Determine the slugging average based on a baseball player's statistics.
Determine the slugging average based on a baseball player's statistics.
What does a price index of 71% signify compared to the year 2000?
What does a price index of 71% signify compared to the year 2000?
State the number of significant digits for each of the following values: 427.01, 0.00052, 2301.0, 320,000, 2.75 x 10^4.
State the number of significant digits for each of the following values: 427.01, 0.00052, 2301.0, 320,000, 2.75 x 10^4.
What is the distance of a plane from the airport after 3.00 hours of travel?
What is the distance of a plane from the airport after 3.00 hours of travel?
What are the missing angle measures in the triangle regarding the airplane problem?
What are the missing angle measures in the triangle regarding the airplane problem?
What describes the accuracy of a gym scale measuring weight to be 137.20 pounds?
What describes the accuracy of a gym scale measuring weight to be 137.20 pounds?
Identify the variables from David's survey on swimming ability in students.
Identify the variables from David's survey on swimming ability in students.
Identify the variables from Andrew's survey on cell phone and gaming device ownership.
Identify the variables from Andrew's survey on cell phone and gaming device ownership.
What is the probability of not selecting an AP course from the given math course options?
What is the probability of not selecting an AP course from the given math course options?
What is the probability George will draw two blue marbles in two tries?
What is the probability George will draw two blue marbles in two tries?
How many females purchased vegetables based on the grocery chain's survey?
How many females purchased vegetables based on the grocery chain's survey?
What represents the probability of selecting a randomly chosen customer who is male or purchased vegetables?
What represents the probability of selecting a randomly chosen customer who is male or purchased vegetables?
What is the probability that Mrs. Rosie Soto picks a non-elective course?
What is the probability that Mrs. Rosie Soto picks a non-elective course?
What expression gives the probability that both volunteers chose a Queen?
What expression gives the probability that both volunteers chose a Queen?
How many customers live in the U.S. but did not buy clothes according to an online retail survey?
How many customers live in the U.S. but did not buy clothes according to an online retail survey?
What represents the probability that a randomly selected customer lives in the U.S. or bought clothing?
What represents the probability that a randomly selected customer lives in the U.S. or bought clothing?
What must be true regarding independent events?
What must be true regarding independent events?
What is the probability that a randomly selected summer school student is not in Biology and not in Algebra 2?
What is the probability that a randomly selected summer school student is not in Biology and not in Algebra 2?
Which statement uses the condition that event A already occurred?
Which statement uses the condition that event A already occurred?
What is the probability that player 3 loses his or her turn given the first two players did not?
What is the probability that player 3 loses his or her turn given the first two players did not?
How to set up a Venn Diagram for Stanley's grocery store situation?
How to set up a Venn Diagram for Stanley's grocery store situation?
What interpretation is made from the formula P(A/B) = P(A and B) / P(B)?
What interpretation is made from the formula P(A/B) = P(A and B) / P(B)?
How to calculate the probability that a randomly selected student is in neither Algebra 2 nor Biology?
How to calculate the probability that a randomly selected student is in neither Algebra 2 nor Biology?
What is the probability that the athlete breaks his swimming record given he breaks his running record?
What is the probability that the athlete breaks his swimming record given he breaks his running record?
What percentage of all teenagers are online and have NOT posted a picture on a social networking site?
What percentage of all teenagers are online and have NOT posted a picture on a social networking site?
What is the probability that an expert archer hits 5 consecutive marks?
What is the probability that an expert archer hits 5 consecutive marks?
What can be said about events A and B if P(B/A) = P(B) and P(A/B) = P(A)?
What can be said about events A and B if P(B/A) = P(B) and P(A/B) = P(A)?
What describes the probability of flipping a coin four times and never getting any heads?
What describes the probability of flipping a coin four times and never getting any heads?
What percentage of American teens own a cell phone and have not posted a picture on a social networking site?
What percentage of American teens own a cell phone and have not posted a picture on a social networking site?
What is the probability of Michael Jordan missing 5 shots in a row?
What is the probability of Michael Jordan missing 5 shots in a row?
What is the probability that when Joellen removes a cookie with chocolate chips, it also has peanuts?
What is the probability that when Joellen removes a cookie with chocolate chips, it also has peanuts?
Rank these outcomes from least likely to most likely when rolling a pair of dice: X = rolling a 6, Y = rolling a 9, Z = rolling a 12.
Rank these outcomes from least likely to most likely when rolling a pair of dice: X = rolling a 6, Y = rolling a 9, Z = rolling a 12.
Which stock investment has a better expected value based on given options?
Which stock investment has a better expected value based on given options?
Determine the truth value for the following given p = true and q = true: i) p ∨ q, ii) p ∧ q, iii) ∼ q.
Determine the truth value for the following given p = true and q = true: i) p ∨ q, ii) p ∧ q, iii) ∼ q.
Determine the truth value for the following given p = false and q = true: i) p ∨ q, ii) p ∧ q, iii) p → q.
Determine the truth value for the following given p = false and q = true: i) p ∨ q, ii) p ∧ q, iii) p → q.
Rank these outcomes from least likely to most likely when rolling a pair of dice: X = rolling a 3, Y = rolling a 6, Z = rolling a 12.
Rank these outcomes from least likely to most likely when rolling a pair of dice: X = rolling a 3, Y = rolling a 6, Z = rolling a 12.
What is the expected value of stock 1 investments?
What is the expected value of stock 1 investments?
What is the expected value of stock 2 investments?
What is the expected value of stock 2 investments?
How to choose the best investment between stock 1 and stock 2?
How to choose the best investment between stock 1 and stock 2?
What is the probability of drawing a red marble from a bag of 6 red and 9 blue marbles plus the odds of winning a large prize?
What is the probability of drawing a red marble from a bag of 6 red and 9 blue marbles plus the odds of winning a large prize?
Study Notes
Graph Theory Concepts
- A graph has a Euler path if it has exactly 2 odd vertices.
- The sum of the degrees of a graph is equal to twice the number of edges; if there are 6 edges, the sum of degrees must equal 12.
- For a graph with 7 edges, the sum of its degrees is 14.
- The combination of degrees 2, 3, 4, 4 is not possible in a graph.
- If the sum of degrees is 16, the graph has 8 edges.
- A connected graph cannot have a single vertex with a degree of 1 and another vertex with a degree of 2 due to degree sum inconsistencies.
Hamiltonian and Eulerian Paths
- Hamilton paths visit every vertex exactly once.
- Euler paths visit every edge exactly once.
Combinatorial Problems
- A 4-digit alarm code with restrictions leads to 1,350 possible combinations.
- A 5-digit password with restrictions results in 4,200 combinations.
- A combination locker using three numbers from 00 to 39 results in 59,280 unique combinations.
Elevator Capacity and Statistics
- An elevator with 90 sq ft of space supports a full load weight of approximately 5,400 pounds without exceeding space limits.
Aspect Ratios and Measurements
- A 46" TV with a 16:9 aspect ratio has dimensions of 40" by 23".
- For a TV with a 2.25:1 aspect ratio, the height of the image on a 46" TV is 17.78 inches.
- The black border at the top and bottom for the aforementioned aspect ratio is 2.61 inches.
- 77% of the screen is utilized when displaying the movie.
Sports Statistics
- A baseball player's average after 285 at bats is 0.330.
- The slugging average for a player with assorted hits totals 0.588.
Inflation and Price Index Calculation
- The inflation rate between a CPI of 172.200 in 2000 and 240.008 in 2016 is 39.4%.
- A price index of 71% indicates current prices are about 71% of what they were in 2000.
Probability and Statistics
- Identified variables in surveys include grade level and swimming ability, cell phone and gaming device ownership.
- For a high school with 6 math courses, the probability of selecting a non-AP course is 0.67.
- The probability of selecting a male who does not purchase or of buying vegetables can be calculated using the principles of addition and conditional probability.
- Students not registered in Biology or Algebra 2 make up about 29% of the summer school population.
Independent and Dependent Events
- Events A and B are independent if the occurrence of one does not influence the other.
- The probability of multiple flips of a coin resulting in no heads is calculated using (1/2)^4.
Expected Value and Financial Decisions
- Stock 1 is expected to earn $136; Stock 2 is expected to earn $192.50 in one year.
- In game value comparisons, Game 2 is more favorable, leading to a loss of only about $1.50 compared to Game 1.
Truth Values in Logic
- Evaluating logical statements using truth values reveals consistent outcomes for given conditions.
- The compound statement includes conditions that highlight relationships and dependencies among events.
Theory of Randomness
- When rolling dice, outcomes are ranked based on their likelihood: Z (rolling a 12) is least likely, followed by Y (rolling a 9) and X (rolling a 6).
Studying That Suits You
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Description
Test your understanding of Euler paths and circuits in graphs through these flashcards. Each card presents a question focused on the properties of vertices and edges, vital for grasping graph theory concepts. Perfect for AQR students reviewing for finals.
