Pathways to Math Literacy with 18 Week ALEKS Access Card
1st Edition
ISBN: 9781259278723
Author: David Sobecki Professor, Brian A. Mercer
Publisher: McGraw-Hill Education
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Chapter 3.5, Problem 3G
To determine
To calculate: The weight gain by Maria after three years of college if the linear equation represents the weight of Maria, y in terms of months after starting college, x and the weight of the Maria when she started college is
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 3 Solutions
Pathways to Math Literacy with 18 Week ALEKS Access Card
Ch. 3.1 - Prob. 0LOCh. 3.1 - Prob. 1CCh. 3.1 - Prob. 2CCh. 3.1 - Prob. 3CCh. 3.1 - Prob. 4CCh. 3.1 - Prob. 5CCh. 3.1 - Prob. 1GCh. 3.1 - Prob. 2GCh. 3.1 - Prob. 3GCh. 3.1 - Prob. 4G
Ch. 3.1 - Prob. 5GCh. 3.1 - Prob. 6GCh. 3.1 - Prob. 7GCh. 3.1 - Prob. 8GCh. 3.1 - Prob. 9GCh. 3.1 - Prob. 10GCh. 3.1 - Prob. 11GCh. 3.1 - Prob. 12GCh. 3.1 - Prob. 13GCh. 3.1 - Prob. 14GCh. 3.1 - Prob. 15GCh. 3.1 - Prob. 16GCh. 3.1 - Prob. 17GCh. 3.1 - Prob. 1TCh. 3.1 - Prob. 1RCh. 3.1 - Prob. 2RCh. 3.1 - Prob. 3RCh. 3.1 - Prob. 4RCh. 3.1 - Prob. 5RCh. 3.1 - Prob. 1ACh. 3.1 - Prob. 2ACh. 3.1 - Prob. 3ACh. 3.1 - Prob. 4ACh. 3.1 - Prob. 5ACh. 3.1 - Prob. 6ACh. 3.1 - Prob. 7ACh. 3.2 - Prob. 0LOCh. 3.2 - Prob. 1CCh. 3.2 - Prob. 2CCh. 3.2 - Prob. 3CCh. 3.2 - Prob. 4CCh. 3.2 - Prob. 5CCh. 3.2 - Prob. 6CCh. 3.2 - Prob. 7CCh. 3.2 - Prob. 8CCh. 3.2 - Prob. 9CCh. 3.2 - Prob. 10CCh. 3.2 - Prob. 1GCh. 3.2 - Prob. 2GCh. 3.2 - Prob. 3GCh. 3.2 - Prob. 4GCh. 3.2 - Prob. 5GCh. 3.2 - Prob. 6GCh. 3.2 - Prob. 7GCh. 3.2 - Prob. 8GCh. 3.2 - Prob. 9GCh. 3.2 - Prob. 10GCh. 3.2 - Prob. 11GCh. 3.2 - Prob. 12GCh. 3.2 - Prob. 13GCh. 3.2 - Complete the Applications portion of this lesson...Ch. 3.2 - Prob. 1RCh. 3.2 - Prob. 2RCh. 3.2 - Type a short answer to each question. Take another...Ch. 3.2 - Type a short answer to each question. What...Ch. 3.2 - Prob. 1ACh. 3.2 - Prob. 2ACh. 3.2 - Prob. 3ACh. 3.2 - Prob. 4ACh. 3.2 - Prob. 5ACh. 3.2 - Prob. 6ACh. 3.2 - Prob. 7ACh. 3.3 - Prob. 0LOCh. 3.3 - Prob. 1GCh. 3.3 - Prob. 2GCh. 3.3 - Prob. 3GCh. 3.3 - Prob. 4GCh. 3.3 - Prob. 5GCh. 3.3 - Prob. 6GCh. 3.3 - Prob. 7GCh. 3.3 - Prob. 8GCh. 3.3 - Prob. 9GCh. 3.3 - Prob. 10GCh. 3.3 - Prob. 11GCh. 3.3 - Nice job so far, but did we forget to mention the...Ch. 3.3 - Prob. 13GCh. 3.3 - Prob. 1CCh. 3.3 - Prob. 2CCh. 3.3 - Prob. 3CCh. 3.3 - Prob. 2RCh. 3.3 - Type a short answer to each question. Take another...Ch. 3.3 - Prob. 4RCh. 3.3 - Prob. 1ACh. 3.3 - Prob. 2ACh. 3.3 - Prob. 3ACh. 3.3 - Prob. 4ACh. 3.3 - Prob. 5ACh. 3.3 - Prob. 6ACh. 3.3 - Prob. 7ACh. 3.4 - Prob. 0LOCh. 3.4 - Prob. 1GCh. 3.4 - Prob. 2GCh. 3.4 - Prob. 3GCh. 3.4 - Prob. 4GCh. 3.4 - Prob. 5GCh. 3.4 - Use your equation to find the mass of each of the...Ch. 3.4 - What is the relationship between the slope of the...Ch. 3.4 - Prob. 8GCh. 3.4 - Prob. 9GCh. 3.4 - Prob. 10GCh. 3.4 - Prob. 11GCh. 3.4 - Prob. 12GCh. 3.4 - Divide each distance in your table by the...Ch. 3.4 - Prob. 14GCh. 3.4 - Prob. 15GCh. 3.4 - Prob. 16GCh. 3.4 - Prob. 17GCh. 3.4 - Prob. 1RCh. 3.4 - Prob. 2RCh. 3.4 - Prob. 3RCh. 3.4 - Use the Internet to find and write the current...Ch. 3.4 - Complete the table using the current exchange...Ch. 3.4 - Write an equation that will convert U.S. dollars...Ch. 3.4 - Which is the independent variable in your...Ch. 3.5 - Prob. 0LOCh. 3.5 - Prob. 1CCh. 3.5 - Prob. 2CCh. 3.5 - Prob. 3CCh. 3.5 - Prob. 4CCh. 3.5 - Prob. 5CCh. 3.5 - Prob. 6CCh. 3.5 - Prob. 7CCh. 3.5 - Prob. 8CCh. 3.5 - Prob. 9CCh. 3.5 - Prob. 10CCh. 3.5 - Prob. 11CCh. 3.5 - Prob. 12CCh. 3.5 - Prob. 13CCh. 3.5 - Prob. 14CCh. 3.5 - Prob. 15CCh. 3.5 - Prob. 1GCh. 3.5 - Prob. 2GCh. 3.5 - Prob. 3GCh. 3.5 - Prob. 4GCh. 3.5 - Prob. 5GCh. 3.5 - Prob. 6GCh. 3.5 - Prob. 7GCh. 3.5 - Prob. 8GCh. 3.5 - Prob. 9GCh. 3.5 - Prob. 10GCh. 3.5 - Prob. 11GCh. 3.5 - Prob. 12GCh. 3.5 - Prob. 13GCh. 3.5 - Prob. 14GCh. 3.5 - Prob. 15GCh. 3.5 - Prob. 16GCh. 3.5 - Prob. 17GCh. 3.5 - Prob. 18GCh. 3.5 - Prob. 1TCh. 3.5 - Prob. 1RCh. 3.5 - Prob. 2RCh. 3.5 - Prob. 3RCh. 3.5 - Prob. 4RCh. 3.5 - Prob. 5RCh. 3.5 - Prob. 1ACh. 3.5 - Explain why a linear equation seems like a...Ch. 3.5 - Prob. 3ACh. 3.5 - Prob. 4ACh. 3.5 - Prob. 5ACh. 3.5 - Prob. 6ACh. 3.5 - Prob. 7ACh. 3.5 - Prob. 8ACh. 3.6 - Prob. 0LOCh. 3.6 - Decide if you think the two quantities are likely...Ch. 3.6 - Prob. 2CCh. 3.6 - Prob. 3CCh. 3.6 - Prob. 4CCh. 3.6 - Prob. 5CCh. 3.6 - Prob. 6CCh. 3.6 - Prob. 7CCh. 3.6 - Prob. 8CCh. 3.6 - Prob. 9CCh. 3.6 - Prob. 10CCh. 3.6 - Prob. 11CCh. 3.6 - Prob. 12CCh. 3.6 - Prob. 13CCh. 3.6 - Prob. 14CCh. 3.6 - When finding the line of best fit using a graphing...Ch. 3.6 - Prob. 16CCh. 3.6 - Prob. 1GCh. 3.6 - Prob. 2GCh. 3.6 - Draw a scatter plot on graph paper with shoe size...Ch. 3.6 - Prob. 4GCh. 3.6 - Prob. 5GCh. 3.6 - Prob. 6GCh. 3.6 - Prob. 7GCh. 3.6 - Prob. 8GCh. 3.6 - Prob. 9GCh. 3.6 - Prob. 10GCh. 3.6 - Prob. 11GCh. 3.6 - Prob. 12GCh. 3.6 - Prob. 13GCh. 3.6 - Prob. 14GCh. 3.6 - Do an Internet search for 1968 mens long jump....Ch. 3.6 - Prob. 1RCh. 3.6 - Prob. 2RCh. 3.6 - Prob. 3RCh. 3.6 - Prob. 4RCh. 3.6 - Prob. 1ACh. 3.6 - Prob. 2ACh. 3.6 - Use a graphing calculator or spreadsheet to create...Ch. 3.6 - What is the slope of the line? What does it mean?Ch. 3.6 - Prob. 5ACh. 3.6 - Prob. 6ACh. 3.6 - Prob. 7ACh. 3.6 - What is the correlation coefficient for the data?...Ch. 3.7 - Prob. 0LOCh. 3.7 - Summarize Polyas problem solving strategy from...Ch. 3.7 - Prob. 2CCh. 3.7 - Prob. 3CCh. 3.7 - Prob. 4CCh. 3.7 - Prob. 5CCh. 3.7 - With only a 200 point final remaining, Se Ri has...Ch. 3.7 - Prob. 2GCh. 3.7 - Prob. 3GCh. 3.7 - Prob. 4GCh. 3.7 - Prob. 1RCh. 3.7 - Prob. 2RCh. 3.7 - Prob. 3RCh. 3.7 - Prob. 4RCh. 3.7 - Parents with young babies buy a lot of diapers (to...Ch. 3.7 - Prob. 5ACh. 3.7 - Prob. 6ACh. 3.7 - Prob. 7ACh. 3.7 - Prob. 8ACh. 3.7 - Prob. 9ACh. 3.7 - Prob. 10ACh. 3.7 - Prob. 11A
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- 6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.arrow_forward4. [10 marks] Find both a matching of maximum size and a vertex cover of minimum size in the following bipartite graph. Prove that your answer is correct. ย ພarrow_forward5. [10 marks] Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if |S||N(S)\X for every SCX, then G contains a matching M that matches every vertex of X (i.e., such that every x X is an end of an edge in M).arrow_forward
- Q/show that 2" +4 has a removable discontinuity at Z=2i Z(≥2-21)arrow_forwardRefer to page 100 for problems on graph theory and linear algebra. Instructions: • Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors. • Interpret the eigenvalues in the context of graph properties like connectivity or clustering. Discuss applications of spectral graph theory in network analysis. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 110 for problems on optimization. Instructions: Given a loss function, analyze its critical points to identify minima and maxima. • Discuss the role of gradient descent in finding the optimal solution. . Compare convex and non-convex functions and their implications for optimization. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forward
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- Only 100% sure experts solve it correct complete solutions okarrow_forwardGive an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.arrow_forward3. [10 marks] Let Go (Vo, Eo) and G₁ = (V1, E1) be two graphs that ⚫ have at least 2 vertices each, ⚫are disjoint (i.e., Von V₁ = 0), ⚫ and are both Eulerian. Consider connecting Go and G₁ by adding a set of new edges F, where each new edge has one end in Vo and the other end in V₁. (a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian? (b) If so, what is the size of the smallest possible F? Prove that your answers are correct.arrow_forward
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