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Suppose that therearefour employees in the computer support group of the School of Engineering of a large university. Each employee will be assigned to support one of four different areas: hardware, software, networking, and wireless. Suppose that Ping is qualified to support hardware, networking, and wireless; Ouiggley is qualified to support software and networking; Ruiz is qualified to support networking and wireless, and Site a is qualified to support hardware and software.
a) Use a bipartite graph to model the four employees and their qualifications.
b) Use Hall's theorem to determine whether there is an assignment of employees to support areas so that each employee is assigned oneareato support.
c) If an assignment of employees to support areas so that each employee is assigned to one support area exists, find one.
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Chapter 10 Solutions
DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
- According to a survey conducted by the American Bar Association, 1 in every 410 Americans is a lawyer, but 1 in every 64 residents of Washington, D.C., is a lawyer. a If you select a random sample of 1500 Americans, what is the approximate probability that the sample contains at least one lawyer? b If the sample is selected from among the residents of Washington, D.C., what is the ap- proximate probability that the sample contains more than 30 lawyers? c If you stand on a Washington, D.C., street corner and interview the first 1000 persons who walked by and 30 say that they are lawyers, does this suggest that the density of lawyers passing the corner exceeds the density within the city? Explain.arrow_forward7.50 Shear strength measurements for spot welds have been found to have standard deviation 10 pounds per square inch (psi). If 100 test welds are to be measured, what is the approximate probability that the sample mean will be within 1 psi of the true population mean? 7.51 Refer to Exercise 7.50. If the standard deviation of shear strength measurements for spot welds is 10 psi, how many test welds should be sampled if we want the sample mean to be within 1 psi of the true mean with probability approximately 992arrow_forward8.12 The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (0, +1), where 0 is the true but unknown voltage of the circuit. Suppose that Y₁, Y2,..., Y, denote a random sample of such readings. a Show that Y is a biased estimator of and compute the bias. b Find a function of Y that is an unbiased estimator of 0. C Find MSE(Y) when Y is used as an estimator of 0.arrow_forward
- Q7. Prove that " there is no simple graph on four vertices, three of which have degree 3 and the remaining vertex has degree 1". (10M)arrow_forwardStella's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 37°, and traveled a distance of 2.1 kilometers before she fell in a straight line perpendicular to the ground. How far from the skydiving center did Stella land? Be sure to have all three parts of a CER answer: make a claim, provide evidence, and explain your reasoning for full credit. 2.1 km Landing spot 37% Skydiving centerarrow_forwardSolve please thanks!arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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