Explanation Approach: The 90 ∘ clockwise rotation position of Rubik’s cube of R, F L, B, T and U is given below. Given: Here, R, F L, B, T and U denotes the rotation of the Rubik’s cube 90 ∘ clockwise to the right, front, left, back, top, and under faces, respectively. Consider each clockwise rotation is the first turning of the cube. The Rubik’s cube is, Calculation: The given rotation can be written as B 5 = B 4 B

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

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Chapter 12.4, Problem 28PS

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The result of the moves on Rubik’s cube of B5.

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Chapter 12.4, Problem 27PS

Chapter 12.4, Problem 29PS

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Divide an equilateral triangle into a number of triangles that are similar to the original triangle (ie similar in shape but possibly different size and possibly rotated) so that they lie in k rows in the original triangle. If you select k = 2, 4, 8 you get the following figures (for eg k = 6 you remove the two bottom rows in the right figure, for k = 3 you delete the bottom row in the middle figure, etc.). Let ak be the number of triangles when you have k rows and consider the case k = 2n, n ≥ 0. A. Determine the values for a2m where n = 1, 2, 3, and 4. B. Using the results in task A, determine a recurrence relation for a2n, where n ≥ 0.

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10. Which series of transformation will return the rectangle to its original position? Select the three correct answers. A. A reflection along one diagonal followed by a reflection along another diagonal. B. A 90° clockwise rotation about one vertex followed by a reflection along on of the short sides. C. A 90° clockwise rotation about the intersection of the diagonals followed by a second 90° clockwise rotation about the intersection of the diagonals. D. A reflection along one of the long sides followed by a second reflection along that same side. E. A reflection along one of the short sides followed by a 180° rotation about one of the vertices of the previously reflected short side.

Chapter 12 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

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