|
About 11892 results. 1294 free access solutions
| № |
Condition |
free/or 0.5$ |
| m97560 | Verify that the dot product on R" satisfies axioms P1-P5. |
buy |
| m97563 | Verify that the following blocks constitute a Steiner triple system on nine varieties.
128 147 234 279 389 468
135 169 256 367 459 578 |
buy |
| m97564 | Verify that the polynomial f(x) = x4 + x3 + x + 1 is reducible over every field F (finite or infinite). |
buy |
| m97565 | Verify that the set U of all linear transformations of V into W is a vector space under the operations ⊞ and ⊡. |
buy |
| m97568 | Verify the second distributive law and the identity and inverse laws for Example 15.25.
Example 15.25
Let B be the set of all positive integer divisors of 30: B = {1, 2, 3, 5, 6, 10, 15, 30}. For all x, y ∈ B, define x + y = lcm(x, y); xy = gcd(x, y); and x = 30/x. Then with 1 as the zero element and 30 as the unity element, one can verify that (B, +, ∙, ¯, 1, 30) is a Boolean algebra. |
buy |
| m97570 | Verify Theorem 4.2.
The Principle of Mathematical Induction-Alternative Form. Let S(n) denote an open mathematical statement (or set of such open statements) that involves one or more occurrences of the variable n, which represents a positive integer. Also let no, n e Z+ with n0 < n1.
a) If S(n0), S(n0 + 1), S(n0 + 2), . . ., S(n1 - 1), and S(n1) are true; and
b) If whenever S(n0), S(n0 + 1),..., S(k - 1), and S(k) are true for some (particular but arbitrarily chosen) k ∈ Z+, where k > n1, then the statement S(k + 1) is also true;
then S(n) is true for all n > n0. |
buy |
| m97574 | Waterbury Hall, a university residence hall for men, is operated under the supervision of Mr. Kelly. The residence has three floors, each of which is divided into four sections. This coming fall Mr. Kelly will have 12 resident assistants (one for each of the 12 sections). Among these 12 assistants are the four senior assistants - Mr. DiRocco, Mr. Fairbanks, Mr. Hyland, and Mr. Thornhill. (The other eight assistants will be new this fall and are designated as junior assistants.) In how many ways can Mr. Kelly assign his 12 assistants if
(a) There are no restrictions?
(b) Mr. DiRocco and Mr. Fairbanks must both be assigned to the first floor?
(c) Mr. Hyland and Mr. Thornhill must be assigned to different floors? |
buy |
| m97575 | Wayne tosses an unfair coin - one that is biased so that a head is three times as likely to occur as a tail. How many heads should Wayne expect to see if he tosses the coin 100 times? |
buy |
| m97578 | We first note how the polynomial in the previous exercise can be written in the nested multiplication method:
8 + x(-10 + x{l + x(-2 + x(3 + 12x)))). <br>Using this representation, the following pseudocode procedure (implementing Horner s method) can be used to evaluate the given polynomial. <br><div align="center"><img src="../image/images12/954-M-L-A-L-S (7749).png"/></div>Answer the questions in parts (a) and (b) of Exercise 5 for the new procedure given here. <br> </span> </div> </div> <!-- Google Adword Banner--> <div class="google-adword-banner"> <div class="adword-banner"> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <!-- question_page --> <ins class="adsbygoogle" style="display:inline-block;width:730px;height:90px" data-ad-client="ca-pub-4274030376980924" data-ad-slot="7315349492"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> </div> <!-- Relevant Question Section--> <div class="related-question-section"> <span class="related-question-section-heading">Students also viewed these questions</span> <br> <br> <!--Question--> <div class="related-question-statment"> <span class="question-icon-complete-placement"><img src="includes/images/rewamp/question_membership/supported-images/Q_small.png" class="image-text-positioning"> |
buy |
| m97580 | We have seen that the adjacency matrix can be used to represent a graph. However, this method proves to be rather inefficient when there are many 0 s (that is, few edges) present. A better method uses the adjacency list representation, which is made up of an adjacency list for each vertex v and an index list. For the graph shown in Fig. 7.27, the representation is given by the two lists in Table 7.5.
For each vertex v in the graph, we list, preferably in numerical order, each vertex w that is adjacent from v. Hence for 1, we list 1, 2, 3 as the first three adjacencies in our adjacency list. Next to 2 in the index list we place a 4, which tells us where to start looking in the adjacency list for the adjacencies from 2. Since there is a 5 to the right of 3 in the index list, we know that the only adjacency from 2 is 6. Likewise, the 7 to the right of 4 in the index list directs us to the seventh entry in the adjacency list - namely, 3 -and we find that vertex 4 is adjacent to vertices 3 (the seventh vertex in the adjacency list) and 5 (the eighth vertex in the adjacency list). We stop at vertex 5 because of the 9 to the right of vertex 5 in the index list. The 9 s in the index list next to 5 and 6 indicate that no vertex is adjacent from vertex 5. In a similar way, the 11 s next to 7 and 8 in the index list tell us that vertex 7 is not adjacent to any vertex in the given directed graph.
In general, this method provides an easy way to determine the vertices adjacent from a v |
buy |
| m97581 | We make a child s bracelet by symmetrically placing four beads about a circular wire. The colors of the beads are red, white, blue, and green, and there are at least four beads of each color,
(a) How many distinct bracelets can we make in this way, if the bracelets can be rotated but not reflected?
(b) Answer part (a) if the bracelets can be rotated and reflected. |
buy |
| m97584 | We use s(m,n) to denote the number of ways to seat m people at n circular tables with least one person at each table. The arrangements at any one table are not distinguished if one can be rotated into another (as in Example 1.16). The ordering of the tables is not taken into account. For instance, the arrangement in parts (a),(b),(c) of Fig.5.6 are considered the same; those in parts (a),(d),(e) are distinct (in pairs).
The number s (m,n) are referred to as the stirling numbers of the first kind.
a) If n > m, what is s(m, n)?
(b) For m > 1, what are s(m, m) and s(m, 1)?
(c) Determine s(m, m - 1) for m > 2.
(d) Show that for m > 3, |
buy |
| m97590 | What can you say about the solutions to the consistent nonhomogeneous linear system Ax = b if the rank of A is less than the number of unknowns? |
buy |
| m97605 | What is the generating function for the number of partitions of n ∈ N into summands that (a) cannot occur more than five times; and (b) cannot exceed 12 and cannot occur more than five times? |
buy |
| m97606 | What is the length of a longest path in each of the following graphs?
(a) K1,4
(b) K3,7
(c) K7,12
(d) Km,n, where m,n ∈ Z+ with m < n. |
buy |
| m97608 | What is the minimum number of times we must toss a fair coin so that the probability that we get at least two heads is at least 0.95? |
buy |
| m97619 | What type of matrix is a linear combination of scalar matrices? Justify your answer. |
buy |
| m97620 | What type of matrix is a linear combination of symmetric matrices? Justify your answer. |
buy |
| m97622 | When a coin is tossed three times, for the outcome HHT we say that two runs have occurred - namely, HH and T. Likewise, for the outcome THT we find three runs: T, H, and T. (The notion of a run was first introduced in Example 1.41.) Now suppose a biased coin, with Pr(H) = 3/4, is tossed three times and the random variable X counts the number of runs that result. Determine
(a) The probability distribution for X.
(b) E(X).
(c) crx- |
buy |
| m97637 | When one examines the units digit of each Fibonacci number Fn, n ≥ 0, one finds that these digits form a sequence that repeats after 60 terms. [This was first proved by Joseph-Louis Lagrange (1736-1813).] Write a computer program (or develop an algorithm) to calculate this sequence of 60 digits. |
buy |
|