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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 1 Homework, Page 728 A red die and a green die have been rolled. What is the probability of the event? 1.The sum is nine.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 2 Homework, Page 728 A red die and a green die have been rolled. What is the probability of the event? 5.Both numbers are even.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 3 Homework, Page 728 9.Alrik’s gerbil cage has four compartments, A, B, C, and D. After careful observation, he estimates the proportion of time spent in each compartment and constructs the following table. (a) Is this a valid probability function? Explain. No, this is not a valid probability function because the proportions total more than 1. (b) Is there a problem with Alrik’s reasoning? Explain. The table has the gerbil spending 110% of its time in the compartments. This cannot be, as it only has 100% of the time to apportion to the various compartments. CompartmentABCD Proportion0.250.200.350.30

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 4 Homework, Page 728 Candy is produced in the following proportions: 13.A single candy is randomly selected from a newly-opened bag. What is the probability that the candy is red? ColorBrownRedYellowGreenOrangeTan Proportion0.30.2 0.1

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 5 Homework, Page 728 A peanut candy is produced in the following proportions: 17.A single peanut candy is randomly selected from each of two newly-opened bags. What is the probability that both are brown? ColorBrownRedYellowGreenOrange Proportion0.30.2 0.1

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 6 Homework, Page 728 A peanut candy is produced in the following proportions: 21.A single peanut candy is randomly selected from each of two newly-opened bags. What is the probability that neither is yellow? ColorBrownRedYellowGreenOrange Proportion0.30.2 0.1

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 7 Homework, Page 728 A card game uses a 24-card deck, containing 9 through ace of the usual four suits. Each hand has six cards. Find the probability. 25.A hand contains all four aces.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 8 Homework, Page 728 29.If it rains tomorrow, the probability is 0.8 that John will practice his piano lesson. If it does not rain, there is only a 0.4 chance John will practice. Suppose the chance of rain tomorrow is 60%. What is the probability that John will practice tomorrow?

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 9 Homework, Page 728 33. Floppy Jalopy Rent-a-Car has 25 cars available for rental, 20 big bombs and five midsize cars. If two cars are selected at random, what is the probability that both are big bombs?

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 10 Homework, Page 728 37. Explain why the following statement cannot be true. The probabilities that a computer salesperson will sell zero, one, two, or three computers in any one day are 0.12, 0.45, 0.38, and 0.15, respectively. This statement cannot be true because the probabilities add to more than one.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 11 Homework, Page 728 41. To complete the kinesiology requirement at Palpitation Tech, you must pass two classes chosen from aerobics, aquatics, defense arts, racket sports, recreational activities, rhythmic activities, soccer, gymnastics, and volleyball. If you decide to choose your two classes at random by drawing two class names from a box, what is the probability you will take racket sports and rhythmic activities?

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 12 Homework, Page 728 Ten dimes dated 1990 through 1999 are tossed. Find the probability. 45. Heads on all ten dimes

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 13 Homework, Page 728 Ten dimes dated 1990 through 1999 are tossed. Find the probability. 49. At least one head

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 14 Homework, Page 728 53. The probability of rolling a five on a pair of fair dice is: A. B. C. D. E.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 9.4 Sequences

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 16 What you’ll learn about Infinite Sequences Limits of Infinite Sequences Arithmetic and Geometric Sequences Sequences and Graphing Calculators … and why Infinite sequences, especially those with finite limits, are involved in some key concepts of calculus.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 17 Sequence Sequence - an ordered progression of numbers Finite sequence - a sequence with a finite number of entries Infinite sequence - a sequence that continues without bound Explicitly defined sequence - a sequence for which any entry may be written directly using the definition Recursively defined sequence - a sequence defined in such a manner that one must know the prior entry before being able to write the next entry using the definition

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 18 Example of an Explicitly Defined Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 19 Example of a Recursively Defined Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 20 Limit of a Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 21 Example Finding Limits of Sequences

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 22 Arithmetic Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 23 Example Arithmetic Sequences Find (a) the common difference, (b) the tenth term, (c) a recursive rule for the nth term, and (d) an explicit rule for the nth term. -2, 1, 4, 7, …

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 24 Geometric Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 25 Example Defining Geometric Sequences Find (a) the common ratio, (b) the tenth term, (c) a recursive rule for the nth term, and (d) an explicit rule for the nth term. 2, 6, 18,…

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 26 Sequences and Graphing Calculators One way to graph an explicitly defined sequence is as a scatter plot of the points of the form (k,a k ). A second way is to use the sequence mode on a graphing calculator.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 27 Example Graphing a Sequential Scatter Plot Use you calculator to generate the first 10 terms of the sequence explicitly defined by a n = 3n - 5 in a scatter plot.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 28 Example Calculating Sequence Values Use you calculator to generate the first 10 terms of the sequence recursively defined by a 1 = 4, a n = 3a n-1 + 5 in a scatter plot. Lower case u in calculator entry is obtained by pressing 2 nd and then 7.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 29 The Fibonacci Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 30 Homework Homework Assignment #29 Review Section 9.4 Page 739, Exercises: 1 - 37 (EOO), 43, 45, 47 Quiz next time

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 9.5 Series

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 32 Quick Review

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 33 Quick Review Solutions

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 34 What you’ll learn about Summation Notation Sums of Arithmetic and Geometric Sequences Infinite Series Convergences of Geometric Series … and why Infinite series are at the heart of integral calculus.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 35 Summation Notation

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 36 Sum of a Finite Arithmetic Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 37 Example Summing the Terms of an Arithmetic Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 38 Sum of a Finite Geometric Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 39 Example Summing the Terms of a Finite Geometric Sequence

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 40 Partial Sums Partial sums are the sums of a finite number of terms in an infinite sequence. In some instances, the partial sums approach a finite limit and the series is said to converge.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 41 Example Examining Partial Sums

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 42 Infinite Series

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 43 Sum of an Infinite Geometric Series

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 44 Example Summing Infinite Geometric Series

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Notes 9.4 – Sequences and Series. I. Sequences A.) A progression of numbers in a pattern. 1.) FINITE – A set number of terms 2.) INFINITE – Continues.

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