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About 11892 results. 1294 free access solutions
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| m96851 | Table 13.1 provides information on the distance (in miles) between pairs of cities in the state of Indiana.
A system of highways connecting these seven cities is to be constructed. Determine which highways should be constructed so that the cost of construction is minimal. (Assume that the cost of construction of a mile of highway is the same between every pair of cities.) |
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| m96852 | Table 6.12 defines v and co for a finite state machine M where
(a) Draw the state diagram for M.
(b) Determine the output for the following input sequences, starting at s0 in each case: (i) x = 111; (ii) x = 1010; (iii) x = 00011.
(c) Describe in words what machine M does.
(d) How is this machine related to that shown in Fig. 6.13? |
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| m96853 | Tables 14.4(a) and (b) make (R, +, •) into a ring, where R = {s, t, x, y}.
(a) What is the zero for this ring?
(b) What is the additive inverse of each element?
(c) What is t(s + xy)?
(d) Is R a commutative ring?
(e) Does R have a unity?
(f) Find a pair of zero divisors. |
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| m96855 | Ten ping-pong balls labeled 1 to 10 are placed in a box. Two of these balls are then drawn, in succession and without replacement, from the box.
(a) Find the sample space for this experiment.
(b) Find the probability that the label on the second ball drawn is smaller than the label on the first.
(c) Find the probability that the label on one ball is even while the label on the other is odd. |
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| m96857 | Ten students take a physics test in a certain room. When the test is over the students take a break and then return to the room to discuss their answers to the test questions. If there are 14 chairs in this room, in how many ways can the students seat themselves after the break so that no one is in the same chair he, or she, occupied during the test? |
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| m96858 | Ten women attend a business luncheon. Each woman checks her coat and attache case. Upon leaving, each woman is given a coat and case at random.
(a) In how many ways can the coats and cases be distributed so that no woman gets either of her possessions?
(b) In how many ways can they be distributed so that no woman gets back both of her possessions? |
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| m96865 | The 50 members of Nardine s aerobics class line up to get their equipment. Assuming that no two of these people have the same height, show that eight of them (as the line is equipped from first to last) have successive heights that either decrease or increase. |
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| m96866 | The (5m, m) five-times repetition code has encoding function E: Zm2 → Z5m2, where E(w) = wwwww. Decoding with D: Z5m2 → Zm2 is accomplished by the majority rule. (Here we are able to correct single and double errors made in transmission.)
(a) With p = 0.05, what is the probability for the transmission and correct decoding of the signal 0?
(b) Answer part (a) for the message 110 in place of the signal 0.
(c) For m = 2, decode the received word
r = 0111001001.
(d) If m = 2, find three received words r where D(r) = 00.
(e) For m = 2 and D: Z102 → Z22, what is | D-1(w) | for each w ∈ Z22? |
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| m96867 | The accompanying table is a sample set of seasonal farm employment data (t1. yi) over about a two-year period, where t, represents months and y, represents millions of people. A plot of the data is given in the figure. It is decided to develop a least squares mathematical model of the form
y(t) = x1 + x2t + x3 cost.
Determine the least squares model. Plot the resulting function y(t) and the data set on the same coordinate system. |
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| m96870 | The adjacency list representation of a directed graph G is given by the lists in Table 7.6. Construct G from this representation. |
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| m96896 | The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members).
(a) How many different slates consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval?
(b) Three members of the board of directors are physicians. How many slates from part (a) have
(i) A physician nominated for the presidency?
(ii) Exactly one physician appearing on the slate?
(iii) At least one physician appearing on the slate? |
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| m96913 | The ciphertext
RWJWQTOOMYHKUXGOEMYP
was encrypted with an affine cipher. Given that the plaintext letters e, t are encrypted as the ciphertext letters W, X, respectively, determine (a) the encryption function E; (b) the decryption function D and (c) the original (plaintext) message. |
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| m96918 | The complete binary tree T = (V, E) has V = {a, b, c, ...,i, j, k}. The post order listing of V yields d, e, b, h, i, f, j, k, g, c, a. From this information draw T if
(a) The height of T is 3;
(b) The height of the left subtree of T is 3. |
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| m96921 | The connective "Nor" or "Not ... or ..." is defined for any statements p, q by (p ↑ q) ⇔ ¬ (p ∨ q). Represent the statements in parts (a) through (e) of Exercise 15, using only this connective. |
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| m96973 | The directed graph G for a relation R on set A = {1, 2, 3, 4} is shown in Fig. 7.24.
(a) Verify that (A, R) is a poset and find its Hasse diagram.
(b) Topologically sort (A, R).
(c) How many more directed edges are needed in Fig. 7.24 to extend (A, R) to a total order? |
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| m96983 | The encoding function E: Z22 → Z52 is given by the generator matrix
(a) Determine all code words. What can we say about the error-detection capability of this code? What about its error- correction capability?
(b) Find the associated parity-check matrix H.
(c) Use H to decode each of the following received words,
(i) 11011
(ii) 10101
(iii) 11010
(iv) 00111
(v) 11101
(vi) 00110 |
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| m96986 | The exit door at the end of a hallway is open half of the time. On a table by the entrance to this hallway is a box containing 10 keys, but only one of these keys opens the exit door at the end of the hallway. Upon entering the hallway Mario selects two of the keys from the box. What is the probability she will be able to leave the hallway via the exit door, without returning to the box for more keys? |
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| m97003 | The following data show the size of the U.S. debt per capita (in dollars). This information was constructed from federal government data on public debt (http://www.publicdebt.treas.gov/opd/opd.htm#history) and (estimated) population data (http://www.censi.is. gov.popest/archives/).
(a) Determine the line of best fit to the given data.
(b) Predict the debt per capita for the years 2008, 2010, and 2015.
Year Debt per Capita (in $)
1996......................20,070
1997......................20,548
1998......................20,774
1999......................21,182
2000......................20,065
2001......................20,874
2002......................22,274
2003......................24,077
2004......................25,868
2005......................27,430 |
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| m97004 | The following data showing U.S. per capita health care expenditures (in dollars) is available from the National Center for Health Statistics (http://www/cdc.gov/nchs/ hus.htm) in the 2002 Chartbook on Trends in the Health of Americans.
Year Per Capita Expenditures (in $)
I960......................................143
1970......................................348
1980...................................1,067
1990...................................2,738
1995...................................3,698
1998...................................4,098
1999...................................4,302
2000...................................4,560
2001...................................4,914
2002...................................5,317
Determine the line of best fit to the given data.
Predict the per capita expenditure for the years 2008, 2010, and 2015. |
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| m97005 | The following exercise provides a combinatorial proof for a summation formula we have seen in four earlier results: (1) Exercise 22 in Section 1.4; (2) Example 4.4; (3) Exercise 3 in Section 4.1; and (4) Exercise 19 in Section 4.2.
Let A = {a, b, c}, B = {1, 2, 3, . . . , n, n + 1}, and S = {/: A ->- Bf(a) < f(c) and f(b) < /(c)}.
(a) If S1 = {f: A → B| f ∈ 5 and f(c) = 2}, what is |S1|?
(b) If S2 - {f: A → B | f ∈ S and f(c) = 3}, what is |S2|?
(c) For 1 < i < n, let St = { f : A → B| f ∈ S and f(c) = i + 1}. What is |S,|?
(d) Let T1 = { f : A → B | f ∈ S and f(a) = f(b)}. Explain Why T1, I = (n+12).
(e) LetT2 = {f : A → B | f ∈ Sand | (a) < f(b)}and T3 = {f : A → B | f ∈ S and f(a) > f(b)}. Explain why | T2| = (n+12)
(f) What can we conclude about the sets
S1 ∪ S2 ∪ S3 ∪ ......... ∪ Sn and T1 ∪ T2 ∪ T3?
(g) Use the results from parts (c), (d), (e), and (f) to verify that |
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