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About 11892 results. 1294 free access solutions
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free/or 0.5$ |
| m96710 | Suppose that G = (V, E) is a loop-free undirected graph. If G is 5-regular and |V| = 10, prove that G is nonplanar. |
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| m96715 | Suppose that in Example 16.35 we 2-color the faces of the cube, which is free to move in space.
(a) How many distinct 2-colorings are there for this situation?
(b) If the available colors are red and white, determine the pattern inventory.
(c) How many nonequivalent colorings have three red and three white faces? |
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| m96723 | Suppose that p(x, y) is ∧n open statement where the universe for each of x, y consists of only three integers: 2, 3, 5. Then the quantified statement ∃y p(2, y) is logically equivalent to p(2, 2) ∨ p(2, 3) ∨ p(2, 5). The quantified statement ∃x ∀y p(x, y) is logically equivalent to [p(2, 2) ∧ p(2, 3) ∧ P(2, 5)] ∨ [p(3, 2) ∧ p(3, 3) ∧ p(3, 5)] ∨ [p(5, 2) ∧ p(5, 3) ∧ p(5, 5)]. Use conjunctions and/or disjunctions to express the following statements without quantifiers.
(a) ∀x p(x, 3)
(b) ∃x ∃y p(x, y)
(c) ∀y 3x p(x, y) |
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| m96725 | Suppose that S = [v1, v2, v3} is a linearly dependent set of vectors in a vector space V. Is T = {w1, w2, w3}, where w1 = v1, w2 = v1, + v3, w3 = v1, + v2 + v3, linearly dependent or linearly independent? Justify your answer. |
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| m96726 | Suppose that S = {v1, v2, v3} is a linearly independent set of vectors in a vector space V. Prove that T = {w1, w2, w3} is also linearly independent, where w1 = v1 + v2 + v3, w2 = v2 + v3, and w3 = v3. |
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| m96738 | Suppose that the linear system Ax = b, where A is m ( n, is consistent (i.e., has a solution). Prove that the solution is unique if and only if rank A = n. |
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| m96739 | Suppose that the number of boxes of cereal packaged each day at a certain packaging plant is a random variable - call it X-with E(X) = 20,000 boxes and Var(X) = 40,000 boxes2. Use Chebyshev s Inequality to find a lower bound on the probability that the plant will package between 19,000 and 21,000 boxes of cereal on a particular day. |
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| m96761 | Suppose that the three points (1, - 5), (- 1, 1), and (2, 7) lie on the parabola p(x) = ax2 + bx + c.
(a) Determine a linear system of three equations in three unknowns that must be solved to find a, b, and c.
(b) Solve the linear system obtained in part (a) for a, b, and c. |
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| m96770 | Suppose that {v1, v2, ( ( ( ( vn} is a basis for Rn. Show that if A is an n ( n nonsingular matrix, then
{Av1, Av2, ( ( ( ( Avn}
is also a basis for Rn. |
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| m96771 | Suppose that {v1, v2, vn} is a linearly independent set of vectors in Rn. Show that if A is an n ( n non-singular matrix, then {Av1, Av2, Ayn} is linearly independent. |
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| m96772 | Suppose that {v1, v2.... vn} is an orthonormal set in Rn with the standard inner product. Let the matrix A be given by A = [v1 v2 ∙ ∙ ∙ vn]. Show that A is non-singular and compute its inverse. Give three different examples of such a matrix in R2 or R3. |
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| m96776 | Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains x(t) pounds of salt in 200 gallons of brine, and tank B contains y(t) pounds of salt in 300 gallons of brine. The mixture in each tank is kept uniform by constant stirring. When t = 0, brine is pumped from tank A to tank B at 20 gallons/minute and from tank B to tank A at 20 gallons/minute. Find the amount of salt in each tank at time t if x(0) = 10 and y(0) = 40. |
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| m96788 | Suppose that X is a binomial random variable where Pr(X = x) = (n/x)px(l - p)n-x, x = 0, 1, 2, . . ., n. If E(X) = 70 and Var(X) = 45.5, determine n, p. |
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| m96790 | Suppose that X is a discrete random variable with probability distribution given by
where k is a constant. Determine (a) the value of k;
(b) Pr (X = 3), Pr (X < 3), Pr (X > 3), Pr (X > 2); and
(c) Pr (X > 4X > 2), Pr (X > 104X > 102). |
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| m96791 | Suppose that X is a random variable defined on a sample space and that a, b are constants. Show that
(a) E(aX + b) = aE(x) + b.
(b) Var(aX + b) = a2Var(X). |
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| m96808 | Suppose that Y is a geometric random variable where the probability of success for each Bernoulli trial is p. If m, n ∈ Z+ with m > n, determine Pr (Y > mY > n). |
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| m96823 | Suppose the probability that the integer key is in the array a1, a2, a3, ..., an (of ft distinct integers) is 3/4 and that each array element has the same probability of containing this value. If the linear search algorithm of Example 5.70 is applied to this array and value of key, what is the average number of array elements that are examined? |
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| m96830 | Suppose we have seven different colored balls and four containers numbered I, II, III, and IV. (a) In how many ways can we distribute the balls so that no container is left empty? (b) In this collection of seven colored balls, one of them is blue. In how many ways can we distribute the balls so that no container is empty and the blue ball is in container II? (c) If we remove the numbers from the containers so that we can no longer distinguish them, in how many ways can we distribute the seven colored balls among the four identical containers, with some container(s) possibly empty? |
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| m96831 | Suppose we have two dice - each loaded as described in the previous exercise. If these dice are rolled, what is the probability the outcome is
(a) 10.
(b) At least 10.
(c) A double? |
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| m96832 | Suppose we try to construct an affine plane AP (Z6) as we did in this section.
a) Determine which of the conditions (Al), (A2), and (A3) fail in this situation.
b) Find how many lines contain a given point P and how many points are on a given line i, for this "geometry." |
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