Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305886803
Author: Brechner
Publisher: Cengage
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Chapter 9, Problem 6CR
A draw against commission is commission paid in _____ of sales and later _____ from the commission earned. (9-4)
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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.)
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.
4. [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.
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Chapter 9 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 9.I - An executive of a large manufacturing company...Ch. 9.I - Rick Morton works as a delivery truck driver for...Ch. 9.I - George Lopez works at a tire manufacturing plant....Ch. 9.I - You are the payroll manager for Trendy Toys, Inc.,...Ch. 9.I - Alexa Walsh sells for Supreme Designs, a...Ch. 9.I - Mike Lamb sells copiers for Royal Business...Ch. 9.I - Ed Diamond is a sales representative for Jersey...Ch. 9.I - Howard Lockwood sells for Catalina Designs, Inc....Ch. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Calculate the gross earnings per day period for...
Ch. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Calculate the gross earnings per day period for...Ch. 9.I - Prob. 5RECh. 9.I - Calculate the gross earnings per pay period for...Ch. 9.I - Prob. 7RECh. 9.I - Mary Jo Prenaris is an office manager with gross...Ch. 9.I - 9. Deb O’Connell is an accounting professional...Ch. 9.I - 10. Jennifer Brunner works 40 hours per week as a...Ch. 9.I - 11. Alan Kimball earns $22.34 per hour as a...Ch. 9.I - 12. Paul Curcio earns $8.25 per hour for regular...Ch. 9.I - Prob. 13RECh. 9.I - As the payroll manager for Stargate Industries,...Ch. 9.I - Prob. 15RECh. 9.I - As the payroll manager for Stargate Industries,...Ch. 9.I - Prob. 17RECh. 9.I - Calculate last week’s total gross pay for each of...Ch. 9.I - Prob. 19RECh. 9.I - Prob. 20RECh. 9.I - 21. Katrina Byrd assembles motor mounts for C-207...Ch. 9.I - 22. Bob Farrell works for a company that...Ch. 9.I - 23. What is the total gross pay for a salesperson...Ch. 9.I - Pamela Mello is paid on an incremental commission...Ch. 9.I - Dory Schrader is a buyer for Oceans of Notions....Ch. 9.I - Thomas Rendells company pays him a straight 6%...Ch. 9.I - 27. Katie Jergens works for Dynamic Designs...Ch. 9.I - 28. Jerry King is a server in a restaurant that...Ch. 9.II - What are the withholdings for social security and...Ch. 9.II - Rick Nicotera has year-to-date earnings of...Ch. 9.II - Jan McMillan is married, claims five exemptions,...Ch. 9.II - Using the combined wage bracket tables, what is...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - Solve the following problems using 6.2%, up to...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - As the payroll manager for Freeport enterprises,...Ch. 9.II - Use the percentage method of income tax...Ch. 9.II - Use the percentage method of income tax...Ch. 9.II - Prob. 11RECh. 9.II - Use the percentage method of income tax...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Use the combined wage bracket tables, Exhibits 9-3...Ch. 9.II - Marital Withholding Gross Combined Employee Status...Ch. 9.II - Prob. 17RECh. 9.II - ...Ch. 9.II - Marital Withholding Gross Combined Employee Status...Ch. 9.III - Big Pine Tree Service has 18 employees, 12 with...Ch. 9.III - Les Roberts, a self-employed commercial artist,...Ch. 9.III - Prob. 15TIECh. 9.III - Prob. 16TIECh. 9.III - Prob. 17TIECh. 9.III - Prob. 1RECh. 9.III - Prob. 2RECh. 9.III - 3. Arrow Asphalt & Paving Company has 24...Ch. 9.III - What are the social security and Medicare taxes...Ch. 9.III - 5. What are the social security and Medicare taxes...Ch. 9.III - Lee Sutherlin is a self-employed electrical...Ch. 9.III - Prob. 7RECh. 9.III - Prob. 8RECh. 9.III - Prob. 9RECh. 9.III - 10. Amazon Appliance Company has three installers....Ch. 9.III - Jiffy Janitorial Service employs 48 workers and...Ch. 9.III - North Beach Limousine Service employs 166 workers...Ch. 9.III - Marc Batchelor, a self-employed sales consultant,...Ch. 9 - Gross pay is the amount of earnings before payroll...Ch. 9 - 2. Annual salaries are commonly prorated to be...Ch. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - 6. A draw against commission is commission paid in...Ch. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - In addition to social security and Medicare tax...Ch. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - A plan whereby employees are given a menu of...Ch. 9 - Prob. 14CRCh. 9 - 1. Bill Pearson earns $2,800 semimonthly as a...Ch. 9 - 2. Barbara Sultan works 40 hours per week as a...Ch. 9 - Eric Shotwells company pays him $18.92 per hour...Ch. 9 - 4. Mitch Anderson is a security guard. He earns...Ch. 9 - 5. Fergie Nelson assembles toasters for the Gold...Ch. 9 - Prob. 6ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Prob. 8ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Prob. 10ATCh. 9 - Calculate the gross earnings for the following...Ch. 9 - Calculate the gross earnings for the following...Ch. 9 - Solve the following problems using 6.2% up to...Ch. 9 - Solve the following problems using 6.2% up to...Ch. 9 - Use the percentage method to solve the...Ch. 9 - Use the combined wage bracket tables. Exhibits 9-3...Ch. 9 - Use the combined wage bracket tables. Exhibits 9-3...Ch. 9 - Prob. 18ATCh. 9 - Prob. 19ATCh. 9 - 20. Paul Warren is a self-employed mechanic. Last...Ch. 9 - Tim Ries earns $48,320 annually as a supervisor...Ch. 9 - 22. Universal Exporting has three warehouse...Ch. 9 - Sky High Crane Company employs 150 workers and has...Ch. 9 - 24. Ransford Alda is a self-employed security...
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- 5. [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_forwardQ/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_forward
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