All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
advanced engineering mathematics

Questions and Answers of Advanced Engineering Mathematics

Suppose that a telephone switchboard of some company on the average handles 300 calls per hour, and that the board can make at most 10 connections per minute. Using the Poisson distribution, estimate
Represent the data by a stem-and-leaf plot, a histogram, and a boxplot:Foundrax test of Brinell hardness (2.5 mm steel ball, 62.5 kg load, 30 sec) of 20 copper plates (values in kg/mm2)86
Explain the use of the tables of the normal distribution. If you have a CAS, how would you proceed without the tables?
Find the mean and variance of the random variable X with probability function or density f(x).X = Number of times a fair coin is flipped until the first Head appears. (Calculate μ only.)
Let X [cm] and Y [cm] be the diameters of a pin and hole, respectively. Suppose that (X, Y) has the densityf(x, y) = 625 if 0.98 < x < 1.02, 1.00 < y < 1.04and 0 otherwise.(a) Find the
If the standard deviation in Prob. 5 were smaller, would that percentage be larger or smaller?Data from Prob. 5If the lifetime X of a certain kind of automobile battery is normally distributed with a
Graph a sample space for the experiments:Recording the lifetime of each of 3 light bulbs
Suppose that 4% of steel rods made by a machine are defective, the defectives occurring at random during production. If the rods are packaged 100 per box, what is the Poisson approximation of the
Represent the data by a stem-and-leaf plot, a histogram, and a boxplot:Gasoline consumption [miles per gallon, rounded] of six cars of the same model under similar conditions15.0
Find the mean and variance of the random variable X with probability function or density f(x).f(x) = k(1 - x2) if -1 ≤ x ≤ 1 and 0 otherwise
How many different samples of 4 objects can we draw from a lot of 50?
If a certain kind of tire has a life exceeding 40,000 miles with probability 0.90, what is the probability that a set of these tires on a car will last longer than 40,000 miles?
Will the probability in Prob. 5 increase or decrease if we draw without replacement. First guess, then calculate.Data from Prob. 5If a box contains 10 left-handed and 20 right-handed screws, what is
Let X be normal with mean 3.6 and variance 0.01. Find c such that P(X ≤ c) = 50%, P(X > c) = 10%, P(-c < X - 3.6 ≤ c) = 99.9%
Graph a sample space for the experiments:Rolling a die until the first Six appears
How do the probabilities in Example 4 change if you double the numbers: drawing 4 gaskets from 20, 6 of which are defective? First guess.
In Prob. 3 find c and c̃ such that P(-c < X < c) = 95% and P(0 < X < c̃) = 95%.Data from Prob. 3Graph f and F when the density of X is f(x) = k = const if -2 ≤ x ≤ 2 and 0
Represent the data by a stem-and-leaf plot, a histogram, and a boxplot:Iron content [%] of 15 specimens of hermatite (Fe2O3)72.8 70.4 71.2 69.2
Find the mean and variance of the random variable X with probability function or density f(x).Y = √3(X - μ)/π with X as in Prob. 3Data from Prob. 3Find the mean and variance of the random
Find the density of the marginal distribution of X in Prob. 2.Data from Prob. 2Find P(X > 4, Y > 4) and P(X ≤ 1, Y ≤ 1) if (X, Y) has the density f(x, y) = 1/32 if x ≥ 0, y ≥ 0, x + y
An urn contains 2 green, 3 yellow, and 5 red balls. We draw 1 ball at random and put it aside. Then we draw the next ball, and so on. Find the probability of drawing at first the 2 green balls, then
In Prob. 3 find the probability of E: At least 1 defective(i) Directly(ii) By using complements; in both cases (a) and (b).Data from Prob. 3Three screws are drawn at random from a lot of 100 screws,
Let X be normal with mean 105 and variance 25. Find P(X ≤ 112.5), P(x > 100), P(110.5 < X < 111.25).
Graph a sample space for the experiments:Tossing 2 coins
Represent the data by a stem-and-leaf plot, a histogram, and a boxplot:Phone calls per minute in an office between 9:00 A.M. and 9:10 A.M.6 6 4 2
Find the mean and variance of the random variable X with probability function or density f(x).X = Number a fair die turns up
The edge chromatic number Χe(G) of a graph G is the minimum number of colors needed for coloring the edges of G so that incident edges get different colors. Clearly, Χe(G) ≥ max d(u), where d(u)
Find an augmenting path, (1) (2) (3) 5 4.
The famous four-color theorem states that one can color the vertices of any planar graph (so that adjacent vertices get different colors) with at most four colors. It had been conjectured for a long
Find flow augmenting paths and the maximum flow. 5, 3 2 4, 2 10, 4 |2, 1\3, 2 s(1) 6) t 3, 1 3, 2 3. 1,0 5 6, 3
Find the maximum flow in the network in Fig. 502 with two sources (factories) and two sinks (consumers). 4 5. 81(1) 3 8) t2 82(2 3 4 LO 4. 3. 4.
Find another maximum flow f = 15 in Prob. 19.Data from Prob. 19 10, 7 8, 4 s(1 2) 5, 3 6, 2 7, 4 \8, 5 3, 1
A graph with n vertices is a tree if and only if it has n - 1 edges and has no cycles.Data from Prob. 16If a graph has no cycles, it must have at least 2 vertices of degree 1Data from Prob. 18A tree
If we switch from one computer to another that is 100 times as fast, what is our gain in problem size per hour in the use of an algorithm that is O(m), O(m2), O(m5), O(em)?
Find the maximum flow by inspection:In Prob. 12Data from Prob. 12 1,0 4 8, 1 2, 1 7, 1 2, 1 4, 2 (1) 2, 1 (3 8, 1 5. 1,0
Show that a graph G with n vertices can have at most n(n - 1)/2 edges, and G has exactly n(n - 1)/2 edges if G is complete, that is, if every pair of vertices of G is joined by an edge. (Recall that
Find the maximum flow by inspection:In Prob. 13Data from Prob. 13 10, 2 4, 1 8, 3 4, 2 14, 1 3) 12, 3 6, 2 5) t
A bipartite graph G = (S, T; E) is called complete if every vertex in S is joined to every vertex in T by an edge, and is denoted by Kn1,n2, where n1 and n2 are the numbers of vertices in S and T,
Find four different closed Euler trails in Fig. 485. 3 5 2.
(a) Distance, Eccentricity. Call the length of a shortest path u †’ v in a graph G = (V, E) the distance d(u, v) from u to v. For fixed u, call the greatest d(u, v) as v ranges over V the
If the Ford–Fulkerson algorithm stops without reaching t, show that the edges with one end labeled and the other end unlabeled form a cut set (S, T) whose capacity equals the maximum flow.
Find flow augmenting paths: 5, 2 (2 8, 5 10, 1 4, 2 7, 1 3, 1 9, 4 5 3 16, 6
Using augmenting paths, find a maximum cardinality matching:In Prob. 10Data from Prob. 10 (1) (2 (3 (6.
Find a shortest spanning tree by Prim€™s algorithm.For the graph in Prob. 2Data from Prob. 2 20 (2 3. 30 10 6. (5 12 2.
Find flow augmenting paths: 1,0 4 8, 1 2, 1 7, 1 2, 1 4, 2 (1) 2, 1 (3 8, 1 5. 1,0
Find the adjacency matrix of: (1) 2 3,
Find an augmenting path: (1) 2) (3 (4) (5 96. 7 (8
Does the graph in Prob. 4 have a Hamiltonian cycle?Data from Prob. 4 3 0, 4 3. 4 3. 3. 2. 2. 2.
Prove that, if the capacities in a network G are integers, then a maximum flow exists and is an integer.
Find a shortest spanning tree by Prim€™s algorithm.For the graph in Prob. 6.Data from Prob. 6 7) 10, 3 5. 12 (8) (6 12 (3 13 11 (2) (1 (5, 5.
Design an algorithm for obtaining longest spanning trees.
Can you obtain the answer to Prob. 3 from that to Prob. 1?Data from Prob. 3If you answer is yes, find S and T: (1) 3 4)
Find the maximum flow by Ford-Fulkerson:In Prob. 14Data from Prob. 14 5, 2 (2 (4) 10, 1 8, 5 4, 2 7, 1 3, 1 (1) 9, 4 3) 5 16, 6 t
Find a shortest spanning tree by Prim€™s algorithm. 5 8. (7 10 (1 (2 (3 3 3 2.
Find a minimum cut set and its capacity for the network:In Fig. 496. Verify that its capacity equals the maximum flow. 11, 8 13, 6 2 4, 3 20, 5 5, 2 6. s(1 10, 4 3,3 4 5. 7,4 3.
To get a minimum spanning tree, instead of adding shortest edges, one could think of deleting longest edges. For what graphs would this be feasible? Describe an algorithm for this.
For each graph find the shortest paths. (1) 10 (2) 8 3 5. 6 2.
Find the maximum flow by Ford-Fulkerson:In Prob. 12Data from Prob. 12 1, 0 (2 2, 1 8, 1 2, 1 4, 2 7, 1 (1) 2, 1 8, 1 5 (3. 1,0 LO
Find a shortest spanning tree by Prim€™s algorithm. 3 (3 14 15 10 5, 2.
For each graph find the shortest paths. 20 (5 8 (1 (3) 3 2.
If you answer is yes, find S and T: (2) (3 (1 4 5)
What is the maximum number of edges that a shortest path between any two vertices in a graph with n vertices can have? Give a reason. In a complete graph with all edges of length 1?
If for a complete graph (or one with very few edges missing), our data is an n Ã— n distance table (as in Prob. 13), show that the present algorithm [which is O(n2)] cannot easily be
What is the (simple) reason that Kirchhoff’s law is preserved in augmenting a flow by the use of a flow augmenting path?
Find T and cap (S, T ) for:Fig 498, S = {1, 3, 5} Cut ! 11, 11 13, 11 20, 8 s (1 10, 6 5, 0 (6) t 4,3 3, 3 5. 7,6
Find T and cap (S, T ) for:Fig 499, S = {1, 2} 8, 5 10, 8 (3 8, 4 4, 2 (7 t 6, 1 2, 1 7, 5 6. 4 6, 5 6, 1 4, 2
If you answer is yes, find S and T: (4 (1) (2 3 5 6.
For each graph find the shortest paths. 4 9. 10 4 (2 (3) (5 13 15 (1 9. 2.
Find a shortest path P: s†’t and its length by Moore€™s algorithm. Sketch the graph with the labels and indicate P by heavier lines as in Fig. 482. 3 0, 4 3. 4 3. 3. 2. 2. 2.
Solve Example 1 by Ford–Fulkerson with initial flow 0. Is it more work than in Example 1?
Find T and cap (S, T ) for:Fig 49.9, S = {1, 2, 3} 8, 5 10, 8 2. 8, 4 4, 2 6, 1 s (1 7, 5 2, 1 (7 4 6, 1 6, 5 4, 2 2.
Find a shortest spanning tree by Kruskal€™s algorithm. Sketch it. 20 (1) (2 6 6, 10 (6) (5 12 2. 4.
Show that in Dijkstra’s algorithm, for Lk there is a path P: 1 → k of length Lk.
If you answer is yes, find S and T: (2 1) 4. 3.
Find a shortest path P: s†’t and its length by Moore€™s algorithm. Sketch the graph with the labels and indicate P by heavier lines as in Fig. 482. 3 0, 4 3. 4 3. 3. 2. 2. 2.
Why are slack variables always nonnegative? How many of them do we need?
Hardbrick, Inc., has two kilns. Kiln I can produce 3000 gray bricks, 2000 red bricks, and 300 glazed bricks daily. For Kiln II the corresponding figures are 2000, 5000, and 1500. Daily operating
Maximize or minimize as indicated.Maximize f = x1 + x2 subject to x1 + 2x2 ≤ 10, 2x2 + x2 ≤ 10, x2 ≤ 4.
The DC Drug Company produces two types of liquid pain killer, N (normal) and S (Super). Each bottle of N requires 2 units of drug A, 1 unit of drug B, and 1 unit of drug C. Each bottle of S requires
Maximize or minimize the given objective function f subject to the given constraints.Maximize or minimize the given objective function f subject to the given constraints.Maximize f = -10x1 + 2x2
Maximize or minimize the given objective function f subject to the given constraints.Maximize f = 5x1 + 25x2 in the region in Prob. 3.Data from Prob. 3-0.5x1 + x2 ≤ 2
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 2x1 + 3x2 subject to 5x1 + 3x2 ≤ 105, 3x1 + 6x2 ≤ 126.
Show that the gradients in Prob. 11 are orthogonal. Give a reason.Data from Prob. 11In Prob. 10, could you start from and do 5 steps?Data form Prob. 10f(x) = 9x21 + x22 + 18x1 - 4x2, 5 steps. Start
Maximize or minimize the given objective function f subject to the given constraints.Maximize f = 45.0x1 + 22.5x2 in the region in Prob. 4.Data from Prob. 4 -x1 + x2 ≤
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 2x1 + 3x2 + x3 subject to x1 + x2 + x3 ≤ 4.8, 10x1 + x3 ≤ 9.9, x2 - x3 ≤ 0.2.
Can we always expect a unique solution?
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize f = 4x1 - 10x2 - 20x3 subject to 3x1 + 4x2 + 5x3 ≤ 60, 2x1 + x2 ≤ 20, 2x1 + 3x3 ≤ 30.
Using an artificial variable, minimize f = 4x1 - x2 subject to x1 + x2 ≥ 2, -2x1 + 3x2 ≤ 1, 5x1 + 4x2 ≤ 50.
Do steepest descent steps when:f(x) = x21 - x2, x0 = (1, 1); 3 steps. Sketch your path. Predict the outcome of further steps.
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities. x1 + x2 ≥ 23x1 + 5x2 ≥ 152x1 + x2 ≥
Maximize the total output f = x1+ x2+ x3(production from three distinct processes) subject to input constraints (limitation of time available for production) 5x1 + 6х2 + 7хз 12, 7x1 + 4x2 + X3 =
Do steepest descent steps when:f(x) = x21 - x22 , x0 = (1, 2), 5 steps. First guess, then compute. Sketch the path. What if x0 = (2, 1)?
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize the daily profit in producing x1 metal frames F1 (profit $90 per frame) and x2 frames F2 (profit $50
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Prob. 19Data from Prob. 19Giant Ladders, Inc., wants to maximize its daily total output of large step ladders
Design a “method of steepest ascent” for determining maxima.
Do steepest descent steps when:f(x) = x21 + 0.5x22 - 5.0x1 - 3.0x2 + 24.95, x0 = (3, 4), 5 steps
Write in normal form and solve by the simplex method, assuming all xj to be nonnegative.Maximize the daily output in producing x1 chairs by Process P1 and x2 chairs by Process P2 subject to 3x1
Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given inequalities.2x1 - x2 ≥ 68x1 + 10x2 ≤ 80x1 - 2x2 ≥ -3
Do Prob. 1 with the last two constraints interchanged.Data from Prob. 1Maximize z = f1(x) = 7x1 + 14x2 subject to 0 ≤ x1 ≤ 6, 0 ≤ x2 ≤ 3, 7x1 + 14x2 ≤ 84.
What happens if you apply the method of steepest descent to f(x) = x21 + x22? First guess, then calculate.

Showing 2400 - 2500 of 3884

First
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Last

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App