MTH 231 Lecture 19: MTH 231 Lecture 19 - Division Rule Permutation

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orchidpig108

20 Jul 2018

School

Oregon State University

Department

Mathematics

Course

MTH 231

Professor

All

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Document Summary

Division rule : there are ways to do a procedure if can be carried out in (cid:1866) ways and each of the (cid:1866) ways are nedundant with exaetly (cid:1856) of those ways. Example : how many ways can you seat (cid:886) people in a row of chairs. Example : how many ways can you seat (cid:1877) people at a round table where two seati(cid:374)g(cid:859)s are considered then same if each pattern has the same let (cid:1872) and right neighbors. (cid:1853)(cid:1856) (cid:1854)(cid:1855) Fanons stuntmen (cid:858) ri(cid:374)g per(cid:373)utatio(cid:374)(cid:859) (cid:886)(cid:1840)(cid:883)(cid:1849) (cid:885)(cid:884) (cid:2872) ! (cid:2872)= (cid:1854)(cid:1853) (cid:1855)(cid:1856) Example : how many ways are there to seat (cid:886) people from a group to (cid:883)(cid:882) ground (cid:1853) circular. A permutation (cid:1853) (cid:1855) (cid:1854) (cid:1856) or (cid:1855) (cid:1853) (cid:1856) (cid:1854). A permutation of length (cid:1870) is chilled an r-permutation. Technically an r-permutation from (cid:1866) elements is (cid:1853) r-tuple with no repeats.

Related Questions

For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.

Week	Ad $, a	People, q	Week	Ad $, a	People, q	Week	Ad $, a	People, q
1	$ 50	112	19	$ -	81	37	$ 200	195
2	$ 150	182	20	$ 300	190	38	$ 300	205
3	$ 200	188	21	$ 150	176	39	$ 250	193
4	$ 200	184	22	$ 50	127	40	$ 100	147
5	$ 150	167	23	$ 200	187	41	$ 50	123
6	$ -	77	24	$ 200	189	42	$ 250	191
7	$ 150	173	25	$ 300	203	43	$ 50	120
8	$ -	71	26	$ 150	168	44	$ -	89
9	$ 100	149	27	$ 100	153	45	$ 300	198
10	$ 200	193	28	$ 200	194	46	$ 200	189
11	$ 250	191	29	$ 200	182	47	$ -	82
12	$ 100	146	30	$ 250	200	48	$ -	87
13	$ 100	155	31	$ 50	125	49	$ -	76
14	$ 150	177	32	$ 300	189	50	$ 100	159
15	$ 50	124	33	$ 150	173	51	$ 50	121
16	$ 150	177	34	$ 300	205	52	$ 50	120
17	$ 100	148	35	$ 200	182
18	$ -	76	36	$ -	80

) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.

Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).

2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers? How many customers would come if the owner spent the maximum on advertising?

orangemammoth442

ey table is seen below xeecions tor Chapter 1 12, Fori, b â¬ Î.el * b-aa (0 (D 14 ForVEQ r the operation defined in Example 1 on the wr John Sue Henry. P iDFor 15ine if is ass ociative by determining if the final six engu defined ang property (ii)of Theorem 1 . So no element i if the operntion debined in Example 1 of Emle if each element has an inverse Section 1.3 Groups iw comutatityn ild Chapter 3 where the Funda the exercises that follow etermining why they are not Write out the Cayley table for the gru(o)nud lensify thee element the 10 elements of the group Z 18 its operation uses ts in the first coordinnte and +2 in the secotu Ldessity the Zn and write out the Cayley table. Reeall th of each element does Theorem 1.14 tell us aont the entries in the Cayley table ol s xrewp that is set with exactly one element. A {n), will always form group since there 19. What nly one way to define an operation on the set. Be sure to shhow that the properi combination of the usual notice what set the rule is be of a group all hold. 21. We can create even create groupe with games! Consider four cups placed in a ssare patter table. If we have a penny in one of the cups there are four ways we can move it to t cup: Horizontally, Vertically, Diagonally, or Stay nehere it is. We will p, S. To define nn operation, consider two movements in a row, v.e.,m ove the penny as r tells us to, then after that move the penny as y instruets. the set of integers the set of real numbers n the set of positive integers. e set of positive integers. n the set of positive integers. on the set of integers e set of negative integers. we ple, HV D since if we first move it horizontally and then vertically nltogether e moved it diagonally. Create the Cayley table for this group, identify the identity and the inverse of cach element 22. Prove that the set A 0 under matrix multiplication. Is it abelian? 23. Verify that 3(R) is a group using the addition of funetions as defined in Example 13 e set of nonzero rational n he set of nonzero real num n on the set R (-1 Section 1.4 Basic Algebra in Groups 24. Prove the Cancellation Law (Theorem 1.20). Do not use any theorems that occur after it in the text ssociative, commutative, has roof or counterexample fo 25. Assume G is a group and a e G. Consider a fixed integer k and use PMI (Theorem 0.3) to prove that for all nEN, a aYou will need to consider cases here since k can be positive, negative, or o 26. Prove Theorem 1.23 (ii) for the case of n > 0 and m

MTH 231 Lecture 19: MTH 231 Lecture 19 - Division Rule Permutation

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