Reference no: EM131084341
1: Place a knight on each square of a 7x7 chessboard. Is it possible for each knight to simultaneously make a legal move?
2: Suppose n is an odd integer. The numbers 1, 2, . . . , 2n are written on a blackboard. I pick two arbitrary numbers on the blackboard, say a, b with b ≥ a, erase them, and write down b - a on the blackboard. I repeat this process until only one integer is left. Is the number at the end odd or even?
3: At first, a room is empty. Each minute, either four people enter or one person leaves. After exactly 1 hour, could the room contain 101 people?
4: There is one stone at each vertex of a square. In any move, you can change the number of stones at each corner according to this rule: you may take away any number of stones at one vertex and add twice as many stones to the pile at an adjacent vertex. Is it possible to get 2003, 2004, 2005, 2006 stones at consecutive vertices after a finite number of moves?
5: Consider an 8 × 8 × 8 cube with two diagonally opposite corners removed. For which n is it possible to completely fill this object with 1 × 1 × n boxes?
6: Are you Positive about this Polynomial? Suppose f(x) is an unknown polynomial with unknown degree and non-negative integer coefficients. Your goal is to determine f(x), but you are only allowed to ask questions of the following form: for a specific number k, "what is f(k)?". What is the fewest number of questions needed to determine f(x)?
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What is the main purpose of gram staining
: What is the main purpose of gram staining?
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Every laptop returned to a repair center
: Every laptop returned to a repair center is classified according its needed repairs: (1) LCD screen, (2) motherboard, (3) keyboard, or (4) other. A random broken laptop needs a type i repair with probability pi = 24-i /15. Let Ni equal the number ..
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Use the degree of financial leverage formula
: DFL and graphical display of financing plans: Wells and Associates has EBIT of $65,000. Interest costs are $16,700, and the firm has 14,300 shares of common stock outstanding. Assume a 40% tax rate. Use the degree of financial leverage (DFL) formula ..
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Stereotype of conventional public opinion
: The stereotype of conventional public opinion on gender is the most source of bias, having more or less relationship to the religion. Stereotype is usually acquired though interactions with parents, peers, teachers and mass media.
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What is the fewest number of questions
: Are you Positive about this Polynomial? Suppose f(x) is an unknown polynomial with unknown degree and non-negative integer coefficients. Your goal is to determine f(x), but you are only allowed to ask questions of the following form: for a specifi..
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Write a brief summary of the history of hip hop
: What are your views of the author major points and what do you think it mean to you people today ? Write a brief summary of the history of Hip Hop and why it came into existence, and at least one major event that led to Hip Hop's presence in mains..
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Random variables described by the probability vectors
: Let X and Y denote independent finite random variables described by the probability vectors px and py and range vectors sx and sy. Write aMatlab function n[pw,sw]=sumfinitepmf(px,sx,py,sy) such that finite random variable W = X + Y is described by..
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Does the convertible issues lower coupon rate
: Suppose a company simultaneously issues $50 million of convertible bonds with a coupon rate of 10% and $50 million of straight bonds with a coupon rate of 14%. Both bonds have the same maturity. Does the convertible issue's lower coupon rate suggest ..
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Why many religious people feel compelled to remake society
: Analyze the relationship between religion and reform in the decades from 1800 to 1860. Why did many religious people feel compelled to remake society? How successful were they? Do you see any parallels with social movements today?
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