AQR A Final Flashcards

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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?

14

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

<p>2, 3, 4, 4</p> Signup and view all the answers

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

<p>8</p> 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?

<p>No</p> Signup and view all the answers

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

<p>vertex</p> Signup and view all the answers

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

<p>edge</p> Signup and view all the answers

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

<p>1,350</p> Signup and view all the answers

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

<p>4,200</p> Signup and view all the answers

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

<p>5,400 pounds</p> Signup and view all the answers

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

<p>59,280</p> Signup and view all the answers

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

<p>Average vet bill x # of visits per year x average lifespan for a dog</p> 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?

<p>40&quot; by 23&quot;</p> 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?

<p>17.78</p> 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?

<p>2.61&quot;</p> 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?

<p>77%</p> Signup and view all the answers

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

<p>0.330</p> Signup and view all the answers

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

<p>39.4%</p> Signup and view all the answers

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

<p>0.588</p> Signup and view all the answers

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

<p>The price today is about 71% of the price in 2000.</p> 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.

<p>5, 2, 5, 2, 3 (B)</p> Signup and view all the answers

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

<p>753.1 miles</p> Signup and view all the answers

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

<p>x=30.9; y=74.1</p> Signup and view all the answers

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

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

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

<p>Grade level and swimming ability</p> Signup and view all the answers

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

<p>Cell phone and gaming device</p> Signup and view all the answers

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

<p>0.67</p> Signup and view all the answers

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

<p>4/25</p> Signup and view all the answers

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

<p>90, 45%</p> Signup and view all the answers

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

<p>P(X) + P(Y) - P(X and Y)</p> Signup and view all the answers

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

<p>0.96</p> Signup and view all the answers

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

<p>(4/52) (3/51) dependent</p> 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?

<p>55, 28%</p> Signup and view all the answers

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

<p>P(X) + P(Y) - P(X and Y)</p> Signup and view all the answers

What must be true regarding independent events?

<p>I, II, and III</p> 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?

<p>29%</p> Signup and view all the answers

Which statement uses the condition that event A already occurred?

<p>P(B | A)</p> 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?

<p>2/5</p> Signup and view all the answers

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

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

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

<p>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.</p> Signup and view all the answers

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

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

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

<p>0.23</p> Signup and view all the answers

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

<p>0.39</p> Signup and view all the answers

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

<p>0.73</p> 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)?

<p>Events A and B are independent.</p> Signup and view all the answers

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

<p>(1/2)^4 ; independent events</p> 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?

<p>31%</p> Signup and view all the answers

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

<p>(1 - 0.497)^5</p> Signup and view all the answers

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

<p>0.33</p> 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.

<p>Z, Y, X</p> Signup and view all the answers

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

<p>Stock 1 because the expected value is larger.</p> 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.

<p>Z, X, Y</p> Signup and view all the answers

What is the expected value of stock 1 investments?

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

What is the expected value of stock 2 investments?

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

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

<p>Compare expected values to find the higher return opportunity.</p> 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?

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

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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).

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