AQR A Final Flashcards

Questions and Answers

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?

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?

Which of the following combination of degrees (vertices) for a graph is not possible?

2, 3, 4, 4 Signup and view all the answers

If the sum of the degrees for a graph is 16, how many edges does the graph have?

8 Signup and view all the answers

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?

No Signup and view all the answers

Hamilton paths and circuits must go through every _______ exactly one time.

vertex Signup and view all the answers

Euler paths and circuits must go through every ______ exactly one time.

edge Signup and view all the answers

How many combinations are possible for a 4 digit combination for an alarm code with specific restrictions?

1,350 Signup and view all the answers

How many combinations are possible for a password that is a 5 digit code with specific restrictions?

4,200 Signup and view all the answers

About how much weight is the elevator supporting if it has about 90 square feet of space?

5,400 pounds Signup and view all the answers

How many different combinations can there be for a combination locker using a three number combination?

59,280 Signup and view all the answers

What is the estimation method to calculate vet bills over the course of a dog's life?

Average vet bill x # of visits per year x average lifespan for a dog Signup and view all the answers

What are the dimensions of a television screen measured at 46" (on the diagonal) with an aspect ratio of 16:9?

40" by 23" Signup and view all the answers

What is the height of the image for a movie shown on a 46" television with an aspect ratio of 2.25:1?

17.78 Signup and view all the answers

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?

2.61" Signup and view all the answers

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?

77% Signup and view all the answers

What is the batter's average for a baseball player after 285 times at bat?

0.330 Signup and view all the answers

Determine the inflation rate by comparing the CPI from the year 2000 to the CPI of 2016.

39.4% Signup and view all the answers

Determine the slugging average based on a baseball player's statistics.

0.588 Signup and view all the answers

What does a price index of 71% signify compared to the year 2000?

The price today is about 71% of the price in 2000. Signup and view all the answers

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.

5, 2, 5, 2, 3 Signup and view all the answers

What is the distance of a plane from the airport after 3.00 hours of travel?

753.1 miles Signup and view all the answers

What are the missing angle measures in the triangle regarding the airplane problem?

x=30.9; y=74.1 Signup and view all the answers

What describes the accuracy of a gym scale measuring weight to be 137.20 pounds?

The scale is accurate to the nearest hundredth of a pound. Signup and view all the answers

Identify the variables from David's survey on swimming ability in students.

Grade level and swimming ability Signup and view all the answers

Identify the variables from Andrew's survey on cell phone and gaming device ownership.

Cell phone and gaming device Signup and view all the answers

What is the probability of not selecting an AP course from the given math course options?

0.67 Signup and view all the answers

What is the probability George will draw two blue marbles in two tries?

4/25 Signup and view all the answers

How many females purchased vegetables based on the grocery chain's survey?

90, 45% Signup and view all the answers

What represents the probability of selecting a randomly chosen customer who is male or purchased vegetables?

P(X) + P(Y) - P(X and Y) Signup and view all the answers

What is the probability that Mrs. Rosie Soto picks a non-elective course?

0.96 Signup and view all the answers

What expression gives the probability that both volunteers chose a Queen?

(4/52) (3/51) dependent Signup and view all the answers

How many customers live in the U.S. but did not buy clothes according to an online retail survey?

55, 28% Signup and view all the answers

What represents the probability that a randomly selected customer lives in the U.S. or bought clothing?

P(X) + P(Y) - P(X and Y) Signup and view all the answers

What must be true regarding independent events?

I, II, and III Signup and view all the answers

What is the probability that a randomly selected summer school student is not in Biology and not in Algebra 2?

29% Signup and view all the answers

Which statement uses the condition that event A already occurred?

P(B | A) Signup and view all the answers

What is the probability that player 3 loses his or her turn given the first two players did not?

2/5 Signup and view all the answers

How to set up a Venn Diagram for Stanley's grocery store situation?

Write 25 in the intersection. Subtract to find the values for only fruits and only vegetables and calculate the remainder. Signup and view all the answers

What interpretation is made from the formula P(A/B) = P(A and B) / P(B)?

The probability that event A happens, given that event B happens is found by dividing the probability that both A and B happen together, by the probability of event B. Signup and view all the answers

How to calculate the probability that a randomly selected student is in neither Algebra 2 nor Biology?

Count students in Algebra or Biology, subtract from total, divide by total students. Signup and view all the answers

What is the probability that the athlete breaks his swimming record given he breaks his running record?

0.23 Signup and view all the answers

What percentage of all teenagers are online and have NOT posted a picture on a social networking site?

0.39 Signup and view all the answers

What is the probability that an expert archer hits 5 consecutive marks?

0.73 Signup and view all the answers

What can be said about events A and B if P(B/A) = P(B) and P(A/B) = P(A)?

Events A and B are independent. Signup and view all the answers

What describes the probability of flipping a coin four times and never getting any heads?

(1/2)^4 ; independent events Signup and view all the answers

What percentage of American teens own a cell phone and have not posted a picture on a social networking site?

31% Signup and view all the answers

What is the probability of Michael Jordan missing 5 shots in a row?

(1 - 0.497)^5 Signup and view all the answers

What is the probability that when Joellen removes a cookie with chocolate chips, it also has peanuts?

0.33 Signup and view all the answers

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.

Z, Y, X Signup and view all the answers

Which stock investment has a better expected value based on given options?

Stock 1 because the expected value is larger. Signup and view all the answers

Determine the truth value for the following given p = true and q = true: i) p ∨ q, ii) p ∧ q, iii) ∼ q.

<ol> <li>true, 2. true, 3. false</li> </ol> Signup and view all the answers

Determine the truth value for the following given p = false and q = true: i) p ∨ q, ii) p ∧ q, iii) p → q.

<ol> <li>true, 2. false, 3. true</li> </ol> Signup and view all the answers

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.

Z, X, Y Signup and view all the answers

What is the expected value of stock 1 investments?

Stock 1: The expected value is (0.15)(1,000) + (0.85)(40) Signup and view all the answers

What is the expected value of stock 2 investments?

Stock 2: The expected value is (0.8)(200) + (0.1)(125) + (0.1)(40) Signup and view all the answers

How to choose the best investment between stock 1 and stock 2?

Compare expected values to find the higher return opportunity. Signup and view all the answers

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?

The probability of winning can be explained by the odds given in the game scenario. Signup and view all the answers

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).

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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.