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nature of mathematics

Questions and Answers of Nature Of Mathematics

Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Show the result of the moves on Rubik's cube indicated in Problems 3-29. Remember that R, F, L, B, T, and U mean rotate \(90^{\circ}\) clockwise the right, front, left, back, top, and under faces,
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle. +++
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Determine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(F\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(U\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(L^{-1}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(B^{-1}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(T^{2}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(U^{2}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(F^{3}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(B^{3} B\)\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(T U\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(B U\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(F B^{-1}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(F T^{-1}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(U^{-1} T^{-1}\)
Name the move or moves that will return the Rubik's cube to standard position after making the move shown in Problems 38-51.\(F^{-1} B^{-1}\)
Are two consecutive moves \(M_{1}\) and \(M_{2}\) on Rubik's cube commutative; that is,\[M_{1} M_{2}=M_{2} M_{1} ?\]
Are three consecutive moves \(M_{1}, M_{2}\), and \(M_{3}\), associative; that is,\[M_{1}\left(M_{2} M_{3}ight)=\left(M_{1} M_{2}ight) M_{3} \text { ?}\]
Does each move have an inverse move?
We saw in Example 2 that \(R^{-1} T^{-1}\) reversed the move \(T R\). Would \(T^{-1} R^{-1}\) also reverse the move \(T R\) ? Why or why not?
Does the move \(L^{-1} R^{-1}\) reverse the move \(L R\) ? Would it also reverse the move \(R L\) ? Why or why not?
Find the number of different arrangements for the Instant Insanity blocks.
The most difficult part of understanding a solution to Rubik's cube is understanding the notation used by the author in stating the solution. In one solution, the Ledbetter-Nering algorithm (see the
David Singmaster, in his book Notes on Rubik's "Magic Cube" (see the references in the Individual Research Projects), describes a sequence of moves to put the upper corners in place (after certain
In The Simple Solution to Rubik's Cube (see the references in the Individual Research Projects), James Nourse describes a process to orient the bottom corner cubes. Using our notation, this set of
Simplify each expression in Problems 1-5.8 ! -3 !
Simplify each expression in Problems 1-5.\(8-3\) !
Simplify each expression in Problems 1-5.\((8-3)\) !
Simplify each expression in Problems 1-5.\(\left(\frac{8}{2}ight)\) !
Simplify each expression in Problems 1-5.\(\left(\begin{array}{l}8 \\ 2\end{array}ight)\) !
Find the numerical value of each expression in Problems 6-10.\(\left(\begin{array}{l}5 \\ 3\end{array}ight)\)
Find the numerical value of each expression in Problems 6-10.\({ }_{8} P_{3}\)
Find the numerical value of each expression in Problems 6-10.\({ }_{12} P_{0}\)
Find the numerical value of each expression in Problems 6-10.\({ }_{14} C_{4}\)
Find the numerical value of each expression in Problems 6-10.\({ }_{100} P_{3}\)
In how many ways can a three-member committee be chosen from a group of 12 people?
In how many ways can five people line up at a bank teller's window?
How many distinguishable permutations are there of the letters of the words HAPPY and COLLEGE?
A jar contains four red and six white balls. Three balls are drawn at random. In how many ways can at least one red ball be drawn?
If the Senate is to form a new committee of five members, in how many different ways can the committee be chosen if all 100 senators are available to serve on this committee?
Advertisements for Wendy's Old Fashioned Hamburgers claim that you can have your hamburgers 256 ways. If Wendy's offers catsup, onion, mustard, pickles, lettuce, tomato, mayonnaise, and relish, is
Bob has one pair of shabby slacks, forty ties, seven shirts, and five sports jackets, but has absolutely no sense of style.In how many ways can Bob dress for the day?
a. A certain mathematics test consists of 10 questions. In how many ways can the test be answered if the possible answers are "true" and "false"?b. Answer the question if the possible answers are
a. One variation of Instant Insanity is a puzzle with five blocks instead of four. How many arrangements are possible?b. If you carry out one arrangement every second, how much time is required to
The Wednesday Luncheon Club, consisting of ten members, decided to celebrate its first anniversary by having lunch at a fancy restaurant. When the members arrived and were ready to take their seats,
Write a paper on the famous Tower of Hanoi problem.
How can all the constructions of Euclidean geometry be done by folding paper? What assumptions are made when paper is folded to construct geometric figures? What is a hexaflexagon? How many flexes
Find a solution for the Instant Insanity puzzle.
A puzzle sold under the name The Avenger is pictured in Figure 12.10.There are four problems posed in the article shown in the reference. Write a report on this article.PROJECT 12.
Consult one of the references listed below and learn to solve Rubik's cube. Demonstrate your skill to the class. Nourse names the following categories:20 minutes: WHIZ 10 minutes: SPEED DEMON 5
What is the difference between empirical and theoretical probabilities?
Define probability.
Write a simple argument to convince someone why all probabilities must be between 0 and 1 (including 0 and 1 ).
What do we mean by " 100 -year storms" or a "1,000-year earthquake"? How do these expressions relate to probability?
For the spinners in Problems 5-8, assume that the pointer can never lie on a border line.a. \(P(A)\)b. \(P(B)\)c. \(P(C)\)
For the spinners in Problems 5-8, assume that the pointer can never lie on a border line.a. \(P(D)\)b. \(P(E)\)c. \(P(F)\)
For the spinners in Problems 5-8, assume that the pointer can never lie on a border line.a. P(G)b. P(H)c. P(1 or J)
For the spinners in Problems 5-8, assume that the pointer can never lie on a border line.a. P(1)b. P(J)c. P(G or H)
Give the probabilities in Problems 9-11 in decimal form (correct to two decimal places). A calculator may be helpful with these problems.Last year, 1,485 calculators were returned to the
Give the probabilities in Problems 9-11 in decimal form (correct to two decimal places). A calculator may be helpful with these problems.Last semester, a certain professor gave 13 A's out of 285
Give the probabilities in Problems 9-11 in decimal form (correct to two decimal places). A calculator may be helpful with these problems.Last year in Ferndale, California, it rained on 75 days. What
Consider the bowl containing marbles shown in Figure 13.7. Suppose each marble has an equal chance of being picked from the bowl.Figure 13.7Find:a. \(P(\) yellow)b. \(P\) (blue)c. \(P(\) green \()\)
Poker is a common game in which players are dealt five cards from a deck of cards. We found there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in
Poker is a common game in which players are dealt five cards from a deck of cards. We found there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in
Poker is a common game in which players are dealt five cards from a deck of cards. We found there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in
Poker is a common game in which players are dealt five cards from a deck of cards. We found there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in
Poker is a common game in which players are dealt five cards from a deck of cards. We found there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in
Some numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from.Table 13.1The four possible hands called "royal flush" Royal flush 4 hands Other straight flush 36 hands
Some numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from.Table 13.1The 36 hands called "other straight flush" Royal flush 4 hands Other straight flush 36 hands
Some numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from.Table 13.1The 624 hands called "four of a kind" Royal flush 4 hands Other straight flush 36 hands Four of
Some numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from.Table 13.1The 3,744 hands called a "full house" Royal flush 4 hands Other straight flush 36 hands Four of
Some numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from.Table 13.1The 5,108 hands called a "flush" Royal flush 4 hands Other straight flush 36 hands Four of a
a. One airline has six across seating in coach. If seats are assigned randomly, what is the probability that a person will be stuck in a middle seat?b. Another airline has five across seating. If
A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. Find the probabilities in Problems 24-27.Figure 12.2a. \(P\) (five of clubs)b. \(P\) (five)c.
A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. Find the probabilities in Problems 24-27.Figure 12.2a. \(P(\) jack \)b. \(P\) (spade)c. \(P\)
A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. Find the probabilities in Problems 24-27.Figure 12.2a. \(P\) (five and a jack)b. \(P\) (five or a
A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. Find the probabilities in Problems 24-27.Figure 12.2a. \(P(\) heart and a jack)b. \(P\) (heart or
Suppose that you toss a coin and roll a die in Problems 28-31. The sample space is shown in Figure 13.1.Figure 13.1What is the probability of obtaining:a. Tails and a five?b. Tails or a five?c.
Suppose that you toss a coin and roll a die in Problems 28-31. The sample space is shown in Figure13.1.Figure 13.1What is the probability of obtaining:a. Tails?b. Heads or a two?c. One, two, three,
Suppose that you toss a coin and roll a die in Problems 28-31. The sample space is shown in Figure 13.1.Figure 13.1What is the probability of obtaining:a. Heads and an odd number?b. Heads or an odd
Suppose that you toss a coin and roll a die in Problems 28-31. The sample space is shown in Figure 13.1.Figure 13.1What is the probability of obtaining:a. Heads and a five?b. Heads or a five? Quest
Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) five \()\) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) six \()\) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) seven \()\) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) eight \()\) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\mathrm{two})\) THE 36 WAYS DICE CAN ROLE O 8

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