Questions and Answers
Which of the following describes if the graph has a Euler path or circuit?
Which of these statements must be true?
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?
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If the sum of the degrees for a graph is 16, how many edges does the graph have?
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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?
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Hamilton paths and circuits must go through every _______ exactly one time.
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Euler paths and circuits must go through every ______ exactly one time.
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How many combinations are possible for a 4 digit combination for an alarm code with specific restrictions?
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How many combinations are possible for a password that is a 5 digit code with specific restrictions?
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About how much weight is the elevator supporting if it has about 90 square feet of space?
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How many different combinations can there be for a combination locker using a three number combination?
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What is the estimation method to calculate vet bills over the course of a dog's life?
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What are the dimensions of a television screen measured at 46" (on the diagonal) with an aspect ratio of 16:9?
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What is the height of the image for a movie shown on a 46" television with an aspect ratio of 2.25:1?
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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?
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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?
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What is the batter's average for a baseball player after 285 times at bat?
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Determine the inflation rate by comparing the CPI from the year 2000 to the CPI of 2016.
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Determine the slugging average based on a baseball player's statistics.
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What does a price index of 71% signify compared to the year 2000?
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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.
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What is the distance of a plane from the airport after 3.00 hours of travel?
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What are the missing angle measures in the triangle regarding the airplane problem?
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What describes the accuracy of a gym scale measuring weight to be 137.20 pounds?
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Identify the variables from David's survey on swimming ability in students.
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Identify the variables from Andrew's survey on cell phone and gaming device ownership.
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What is the probability of not selecting an AP course from the given math course options?
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What is the probability George will draw two blue marbles in two tries?
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How many females purchased vegetables based on the grocery chain's survey?
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What represents the probability of selecting a randomly chosen customer who is male or purchased vegetables?
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What is the probability that Mrs. Rosie Soto picks a non-elective course?
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What expression gives the probability that both volunteers chose a Queen?
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How many customers live in the U.S. but did not buy clothes according to an online retail survey?
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What represents the probability that a randomly selected customer lives in the U.S. or bought clothing?
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What must be true regarding independent events?
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What is the probability that a randomly selected summer school student is not in Biology and not in Algebra 2?
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Which statement uses the condition that event A already occurred?
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What is the probability that player 3 loses his or her turn given the first two players did not?
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How to set up a Venn Diagram for Stanley's grocery store situation?
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What interpretation is made from the formula P(A/B) = P(A and B) / P(B)?
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How to calculate the probability that a randomly selected student is in neither Algebra 2 nor Biology?
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What is the probability that the athlete breaks his swimming record given he breaks his running record?
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What percentage of all teenagers are online and have NOT posted a picture on a social networking site?
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What is the probability that an expert archer hits 5 consecutive marks?
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What can be said about events A and B if P(B/A) = P(B) and P(A/B) = P(A)?
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What describes the probability of flipping a coin four times and never getting any heads?
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What percentage of American teens own a cell phone and have not posted a picture on a social networking site?
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What is the probability of Michael Jordan missing 5 shots in a row?
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What is the probability that when Joellen removes a cookie with chocolate chips, it also has peanuts?
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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.
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Which stock investment has a better expected value based on given options?
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Determine the truth value for the following given p = true and q = true: i) p ∨ q, ii) p ∧ q, iii) ∼ q.
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Determine the truth value for the following given p = false and q = true: i) p ∨ q, ii) p ∧ q, iii) p → q.
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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.
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What is the expected value of stock 1 investments?
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What is the expected value of stock 2 investments?
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How to choose the best investment between stock 1 and stock 2?
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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?
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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.