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Suppose five points are randomly placed inside a square that measures 2 inches by 2 inches. Use the pigeonhole principle to prove that there must at least two points that are within V2 inches of...
From a Course on the Introduction to Abstract Algebra 4. Use pigeonhole principle to show that...
From a Course on the Introduction to Abstract Algebra
4. Use pigeonhole principle to show that ·Out of 15 people there are at least two that have their birthdays in the same month. ·Out of five points inside a square with the side length two there are at least two that are at most of distance of V2.
Suppose there is a square dartboard that is 8 inches by 8 inches. If you throw 65 darts at the bo...
Suppose there is a square dartboard that is 8 inches by 8 inches. If you throw 65 darts at the board (and hit the board every time), prove that at least 2 of them will be less than 1.5 inches apart. (You may use the fact that the longest distance between two points in a 1 × 1 square is √ 2 ≈ 1.41).
1. Use Pigeon hole principle to prove that any graph with at least 2 vertices contains...
1. Use Pigeon hole principle to prove that any graph with at
least 2 vertices contains two vertices of the same degree. (Hint:
Prove by contradiction. (4 points)
2. Given (6 Points)
a. Prove the above equation using binomial theorem. (3
Points)
b. Give a combinatorial proof for the given equating. (3
Points)
4n = (0)2" + (1)2" +...+)2"-
#3 and 5 only 3. Prove that if six natural numbers are chosen at random, then...
#3 and 5 only
3. Prove that if six natural numbers are chosen at random, then the sum or difference of two of them is divisible by 9. 4. Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within 2 units of each other. 5. Prove that any set of seven distinct natural numbers contains a pair of numbers whose sum or difference is...
2. Five starting basketball players were randomly selected from two teams. The heights, in inches, of...
2. Five starting basketball players were randomly selected from two teams. The heights, in inches, of five players on Team I are 72, 73, 76, 76, and 78; the heights of those on Team Il are 67, 72,76, 76 and 84, (please use the correct symbols in your answers, for example, x # orus#.) (1) Find the mean, median, mode and range of each team, respectively. (2) Are the four numbers you found in (1) statistics or parameters? (3) Calculate...
Five starting basketball players were randomly selected from two teams. The heights, in inches, of five...
Five starting basketball players were randomly selected from two teams. The heights, in inches, of five players on Team I are 72, 73, 76, 76, and 78; the heights of those on Team II are 67, 72, 76,76, and 84" (please use the correct symbols in your answers, for example, x : # or μ4. ) 2. (1) Find the mean, median, mode and range of each team, respectively. (2) Are the four numbers you found in (1) statistics or...
Use the Internet to research at least two (2) accounting scandals within the past five (5)...
Use the Internet to research at least two (2) accounting scandals within the past five (5) years. Based on the accounting scandals you researched, identify the accounts that the fraud had affected, and analyze the auditor’s responsibility to detect fraud. Next, suggest key internal controls that would have either prevented or detected the fraudulent behavior or transactions. Justify your response
2. Suppose A and B are two events. Use the axioms of probability to prove the...
2. Suppose A and B are two events. Use the axioms of probability to prove the following (a) P(AnB) 2 P(A) P(B) 1 (b) Show that the probability that one and only one of the events A or B occurs is P(A)+ P(B) -2P(AnB). 3. There are 9 lights labeled 1 to 9, and they are lined up in a row in Boelter Hall. or budget reasons, we are going to turn off 3 of them. For security purposes, we...
TU U L, within ne last three to five years. Students must post a minimum of...
TU U L, within ne last three to five years. Students must post a minimum of twice (an initial posting and at least one additional posting) per Discussion Board: 1. Make initial (student's original post-not copied or based on another student's post) post by 2400 EST Thursday. 2. Respond to at least one other classmate's post by 2400 EST Sunday. American Psychological Association (APA) is required for writing, citing, and referencing. Please post a response specific to each of the...
osUniPhys1 19.1.P.01 9. Ask Your Teacher 0.67/1 points Previous Answers My Notes 2. Suppose a gas-filled...
osUniPhys1 19.1.P.01 9. Ask Your Teacher 0.67/1 points Previous Answers My Notes 2. Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure (absolute pressure) when the bulb has a temperature of 18.0°c. (Enter your answers to at least four significant figures.) (a) Find the gauge pressure inside such a bulb in atmospheres when it is hot, assuming its average temperature is 55.0°C (an approximation) and neglecting any change in volume...
From a Course on the Introduction to Abstract Algebra
4. Use pigeonhole principle to show that ·Out of 15 people there are at least two that have their birthdays in the same month. ·Out of five points inside a square with the side length two there are at least two that are at most of distance of V2.
1. Use Pigeon hole principle to prove that any graph with at
least 2 vertices contains two vertices of the same degree. (Hint:
Prove by contradiction. (4 points)
2. Given (6 Points)
a. Prove the above equation using binomial theorem. (3
Points)
b. Give a combinatorial proof for the given equating. (3
Points)
4n = (0)2" + (1)2" +...+)2"-
#3 and 5 only
3. Prove that if six natural numbers are chosen at random, then the sum or difference of two of them is divisible by 9. 4. Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within 2 units of each other. 5. Prove that any set of seven distinct natural numbers contains a pair of numbers whose sum or difference is...
2. Five starting basketball players were randomly selected from two teams. The heights, in inches, of five players on Team I are 72, 73, 76, 76, and 78; the heights of those on Team Il are 67, 72,76, 76 and 84, (please use the correct symbols in your answers, for example, x # orus#.) (1) Find the mean, median, mode and range of each team, respectively. (2) Are the four numbers you found in (1) statistics or parameters? (3) Calculate...
Five starting basketball players were randomly selected from two teams. The heights, in inches, of five players on Team I are 72, 73, 76, 76, and 78; the heights of those on Team II are 67, 72, 76,76, and 84" (please use the correct symbols in your answers, for example, x : # or μ4. ) 2. (1) Find the mean, median, mode and range of each team, respectively. (2) Are the four numbers you found in (1) statistics or...
2. Suppose A and B are two events. Use the axioms of probability to prove the following (a) P(AnB) 2 P(A) P(B) 1 (b) Show that the probability that one and only one of the events A or B occurs is P(A)+ P(B) -2P(AnB). 3. There are 9 lights labeled 1 to 9, and they are lined up in a row in Boelter Hall. or budget reasons, we are going to turn off 3 of them. For security purposes, we...
TU U L, within ne last three to five years. Students must post a minimum of twice (an initial posting and at least one additional posting) per Discussion Board: 1. Make initial (student's original post-not copied or based on another student's post) post by 2400 EST Thursday. 2. Respond to at least one other classmate's post by 2400 EST Sunday. American Psychological Association (APA) is required for writing, citing, and referencing. Please post a response specific to each of the...
osUniPhys1 19.1.P.01 9. Ask Your Teacher 0.67/1 points Previous Answers My Notes 2. Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure (absolute pressure) when the bulb has a temperature of 18.0°c. (Enter your answers to at least four significant figures.) (a) Find the gauge pressure inside such a bulb in atmospheres when it is hot, assuming its average temperature is 55.0°C (an approximation) and neglecting any change in volume...
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