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What is the percent chance that a player selects exactly 3 winning numbers?

C ( 20 , 3 ) C ( 60 , 17 ) C ( 80 , 20 ) 12.49 %

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What is the percent chance that a player selects exactly 4 winning numbers?

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What is the percent chance that a player selects all 5 winning numbers?

C ( 20 , 5 ) C ( 60 , 15 ) C ( 80 , 20 ) 23.33 %

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What is the percent chance of winning?

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How much less is a player’s chance of selecting 3 winning numbers than the chance of selecting either 4 or 5 winning numbers?

20.50 + 23.33 12.49 = 31.34 %

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Real-world applications

Use this data for the exercises that follow: In 2013, there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). United States Census Bureau. http://www.census.gov

If you meet a U.S. citizen, what is the percent chance that the person is elderly? (Round to the nearest tenth of a percent.)

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If you meet five U.S. citizens, what is the percent chance that exactly one is elderly? (Round to the nearest tenth of a percent.)

C ( 40000000 , 1 ) C ( 277000000 , 4 ) C ( 317000000 , 5 ) = 36.78 %

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If you meet five U.S. citizens, what is the percent chance that three are elderly? (Round to the nearest tenth of a percent.)

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If you meet five U.S. citizens, what is the percent chance that four are elderly? (Round to the nearest thousandth of a percent.)

C ( 40000000 , 4 ) C ( 277000000 , 1 ) C ( 317000000 , 5 ) = 0.11 %

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It is predicted that by 2030, one in five U.S. citizens will be elderly. How much greater will the chances of meeting an elderly person be at that time? What policy changes do you foresee if these statistics hold true?

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Chapter review exercises

Sequences and Their Notation

Write the first four terms of the sequence defined by the recursive formula a 1 = 2 , a n = a n 1 + n .

2 , 4 , 7 , 11

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Evaluate 6 ! ( 5 3 ) ! 3 ! .

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Write the first four terms of the sequence defined by the explicit formula a n = 10 n + 3.

13 , 103 , 1003 , 10003

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Write the first four terms of the sequence defined by the explicit formula a n = n ! n ( n + 1 ) .

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Arithmetic Sequences

Is the sequence 4 7 , 47 21 , 82 21 , 39 7 , ... arithmetic? If so, find the common difference.

The sequence is arithmetic. The common difference is d = 5 3 .

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Is the sequence 2 , 4 , 8 , 16 , ... arithmetic? If so, find the common difference.

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An arithmetic sequence has the first term a 1 = 18 and common difference d = 8. What are the first five terms?

18 , 10 , 2 , 6 , 14

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An arithmetic sequence has terms a 3 = 11.7 and a 8 = 14.6. What is the first term?

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Write a recursive formula for the arithmetic sequence 20 , 10 , 0 , 10 ,…

a 1 = 20 ,   a n = a n 1 + 10

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Write a recursive formula for the arithmetic sequence 0 ,   1 2 ,   1 ,   3 2 , , and then find the 31 st term.

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Write an explicit formula for the arithmetic sequence 7 8 ,   29 24 ,   37 24 ,   15 8 ,

a n = 1 3 n + 13 24

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How many terms are in the finite arithmetic sequence 12 , 20 , 28 , , 172 ?

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Geometric Sequences

Find the common ratio for the geometric sequence 2.5 ,   5 ,   10 ,   20 ,

r = 2

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Is the sequence 4 ,   16 ,   28 ,   40 , geometric? If so find the common ratio. If not, explain why.

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A geometric sequence has terms a 7 = 16 , 384 and a 9 = 262 , 144  . What are the first five terms?

4 ,   16 ,   64 ,   256 ,   1024

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A geometric sequence has the first term a 1 = 3 and common ratio r = 1 2 . What is the 8 th term?

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Questions & Answers

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
Practice Key Terms 9

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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