Let O be the origin of the plane. Imagine that five points, not equal to O, are

Q: Let O be the origin of the plane. Imagine that five points, not equal to O, are

Answer 3 . Let A be the set of bit positions that are 11; the sum is even or odd according as |A|is even or odd, so the problem really amounts to comparing the numbers of even- and odd-sized subsets of {1,…,N}. It's known that for N>0 the set {1,…,N} has equal numbers of even- and odd-sized subsets, so the probability is indeed 1/2in both cases.

ID: 3695320 • Letter: L

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Let O be the origin of the plane. Imagine that five points, not equal to O, are placed on the plane. Prove that there are two of those points, P and Q, such that the angle anglePOQ is acute. View this problem as an application of the pigeonhole principle. What are the pigeonholes? What are the pigeons? Complete the argument. You generate a random N-bit string, and compute X = summation i to N x_i, where x_i are the 0 and 1 entries of the string. What is the probability that X is odd, if N is odd?

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Answer 3 .

Let A be the set of bit positions that are 11; the sum is even or odd according as |A|is even or odd, so the problem really amounts to comparing the numbers of even- and odd-sized subsets of {1,…,N}. It's known that for N>0 the set {1,…,N} has equal numbers of even- and odd-sized subsets, so the probability is indeed 1/2in both cases.

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Let O be a measurement operator for the of dots facing upwards on a 6-sided \'qu

Let O represent the set of odd natural numbers less than 10. Represent 0 in set

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Let O be the origin of the plane. Imagine that five points, not equal to O, are

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