9. the Size of the Sphere Does Not Matter, the Answer Never Changes

Solutions

ONE

Geology

1. A. Late afternoon on the 26th day of the month B. The evening of the 29th day of the month C. 1 second before the end of the month D. 1/5 of a second before the end of the month.

3. A. 15 years, 6 months B. 17 years, 3 months C. 3 minutes, 54 seconds before the 18th birthday D. 50 seconds before the 18th birthday

5. 37.7 inches 7. 37.7 inches

9. The size of the sphere does not matter, the answer never changes

Astronomy

1.

3.

5. answers will vary

7. 1d, 2g, 3a, 4h, 5b, 6i, 7c, 8e, 9j, 10f

9.

11. 1,000,000

13. 12,345,654,321 12 billion, 345 million, 654 thousand, three hundred twenty one.

Set Theory

1. This is the set of those purchasers from Amazon.com who owned a cell phone.

3. This is the set of people who never purchased from Amazon.com and do not own a cell phone.

5. This is the set of those original signers of the Declaration of Independence who became presidents, and that would be John Adams and Thomas Jefferson.

7. This is the set of perspective home buyers who can qualify for a $ 250,000 home as well as those prospective buyers who are ready to buy today and want to list their home,.

9. This is the set of the perspective home buyer in your city who could qualify for up to a $ 250,000 home, are ready to purchase a home today and want to list their house for sale.

11. This is the set of registered voters who are opposed to the death penalty and are opposed to legalized abortions for any reason or a registered democrat or both.

13. are the known suspected terrorists who have not resided in both Saudi Arabia and Chechnya. This would include all of the terrorists who have not resided in Saudi Arabia as well as those who have not resided in Chechnya.

15. is the set of those who believe in both Tarrot cards and crystal powers, but not channeling mediums.

17. {0, 1, 2, 3, 4, 6, 8} 19. {5, 7, 9} 21. {0, 8}

23. is the set with one element, the jack of diamonds.

25. B \ C is the set of there jacks, the jack of hearts, the jack of clubs and the jack of spades.

27. 229. 24

31. 433. 1

35. is the set of college students who smoke.

37. A \ C is the set of Arizona state residents that don’t smoke.

39. 141. 24

43. is the set of all refrigerators and microwaves on sale at Sears.

45. is the set of all appliances for sale at Sears.

47. is the set of doctors that earn $ 200,000 or less that are taking new patients.

49. 0

Counting Theory

1.

a)

b)

c)

d)

e)

f)

g)c) d) b) e) and a) and f) are tied for last place

3. 4(7)(3)(2) = 168

5.

a)

b)

7.

9.

a)

b)

11.

a) 5! = 120

b)

c)

d) 6

e) 3

13.

a)

b)

c)

15.

a)

b)

c)

17.

a)

b)

c)40

d)40(39) = 1,560

e)40(39) = 1,560

19.

a)

b)

21.

a)

b)

c)

d)

e)

23.

a)

b)

c)

d)

e)

f)

g)

h)

25. Picking 5 correct out of 50

27.

TWO

The World Around You

1. There would be 57 Asians, 21 Europeans, 14 from the western hemisphere (north and south) and 8 Africans. 51 would be female; 49 would be male, 70 would be non-white; 30 white 70 would be non-Christian; 30 Christian 59% of the entire world's wealth would be in the hands of only 6 people and all 6 would be from the United States 80 would live in substandard housing 70 would be unable to read 50 would suffer from malnutrition 1 would be near death; 1 would be near birth Only 1 would have a college education. No one would own a computer

3.

5.

7. Because the percent change has a compounding effect, the growth for each subsequent year will be based on a larger population from the prior year. This does not occur with numeric growth.

9. California because it had the largest population initially in ’90, and recently, the state has seen an influx of immigrants and migration from people from other states.

Introduction to Probability – Coincidences

1. Answers will vary. A sample of an answer may discuss since it is estimated that 1 in 5 may be elderly by 2030, we could expect our nation’s economic priorities to drastically change. Money will need to be set aside in the near future for essential resources needed to care for the elderly. Medicare, health care providers, pharmacists, doctors, insurance providers, should all expect expansion in their profession, and as an entity, may have to re-evaluate their own ethical issues too. One could speculate that investments in retirement communities and assisted living centers will become a hot commodity. Obviously, we can expect an increasing awareness in the field of gerontology, voting alignments could be expected to be altered from the alignments we see in place today and advances in technology show be expected to focus on the needs and limitations of the elderly.

3. Answers will vary

5. Births, 41 cases (90% probability two presidents were born on the same day)

November 2, James K. Polk & Warren G. Harding

Deaths, 36 cases (83% probability two presidents died on the same day)

March 8, Millard Fillmore & William Howard Taft

July 4 John Adams & Thomas Jefferson & James Monroe (Both John Adams and Thomas Jefferson died in the same year, 1826, on the fiftieth anniversary of their signing the Declaration of Independence.)

7. In 1912 the Titanic, a transatlantic luxury liner widely touted as unsinkable strikes an iceberg and sinks with great loss of life on her maiden voyage. The Titanic had 2,207 passengers, compared to the 3000 on the Titan, and 20 lifeboats, compared to 24 on the Titan.

Probability

1. 3. 5.

7. 9.

11. 113. {HH, HT, TH, TT} 15. ½ 17. ¼

19. 3/8 21. 7/8

23. {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

25. 5/627. 5/1829. 5/36

31. or 1 in every 104,932 Arizonian you encounter is a gun toting women who is over 80 years of age.

33. or roughly 4 in 5 Arizonian gun carriers are men.

35. or nearly twice as likely. (Each state’s population is irrelevant.)

37. 4,136,100,00039. 27,200,000,000

41. For a politician to extol the risk of amusement park rides clearly diminished the risk of other recreational activities. Since there are only 5.6 billion people on the planet, the risk in these other activities show how un-risky visiting an amusement park truly is…

Independent Events and Dependent Events

1. 2/1693. 1/165. 1/25

7. ¾ 9. 0.015

11. 1/613. 0.177815. 0.332

17. 63/6419. 0.107

21. 0.009423. 0.51225. 4/663

27. 13/20429. 1/221

31. 0.005933. 0.22435. 0.293

Probability Using Counting Theory

1. 0.0009683. 0.000001545. 0.00001847. 0.0004959. 0.01 11. 0.00000923

13.

15. 0.1017. 0.0021

19. 0.16721. 0.03

23. 0.618125. 0.9846

27. 129. 0.1169

31. 0.706333. 1

35. 8/66337. 1/1739. 0.0002341. 0.054 43. 0.423

The Binomial Probability Profile

1. b(8,2,0.26) = 0.310810

3. b(8,4,0.26) = 0.0959225. 1-b(8,8,0.74) = 0.9100817. b(8,8,0.26) = 0.000021

9. 1-b(8,8,0.26) = 0.99997911. b(6,6,0.690146) = 0.108055

13. b(6,6,0.955088) = 0.75903115. b(6,0,0.5) + b(6,1,0.5) + b(6,2,0.5) + b(6,3,0.5) = 0.65625

17. 1- b(6,0,0.5) = 0.984375

19. b(7,5,5/12) = 0.08974221. b(12, 11, 0.85) = 0.301218

23. b(12, 12, 0.15) = 0.0000000001

25. b(4,4,0.3) = 0.008127. 1 – b(10, 10, 0.94) = 0.46138529. b(10, 6, 0.06) + b(10, 7, 0.06) + b(10, 8, 0.06) + b(10, 9, 0.06) + b(10, 10, 0.06) = 0.0000008

Conditional Probability

1. 7/113. ½

5. 0.477. 0.62

9. 0.5011. 0.5613. 0.3915. 0.05

17. 5/6

19. P(he or she speaks English| he or she is American)

21. P(humidity is high| it is raining)

23. P(vegetable is green | vegetable is broccoli)

Miscellaneous Problems Using Probability

1. 5/93. {(1,H,H), (2,H,H), (3,H,H), (4,H,H), (5,H,H), (6,H,H),

(1,T,H), (2,T,H), (3,T,H), (4,T,H), (5,T,H), (6,T,H),

(1,H,T), (2,H,T), (3,H,T), (4,H,T), (5,H,T), (6,H,T),

(1,T,T), (2,T,T), (3,T,T), (4,T,T), (5,T,T), (6,T,T)}

5. ¾ 7. 1/343

9. 1/1311. 1/36

13. 5/615. 0

Bayes Theorem

1. 0.6053. 0.80

5. 0.737. 0.809. 0.63

11. 0.2413. 0.5615. 0.82

Expected Value

1. 73.333 3. –0.86

5. - $ 51.63

7. $ 2350, $ 9400, $ 23,500, $ 47,000

9. winter

11. = 0.54

13. a) -1.166 b) -1 c) -0.75 d) - 0.333

15. 86.4

17. You should do your homework because it could alter your final letter grades by 4 letters, from A through D.

THREE

Causation and Correlation

1. negative correlation. 3. no correlation.

. 5. positive correlation.

7. positive correlation. 9. negative correlation.

11. negative correlation. 13. negative correlation.

15.

17. c)

Construct and Drawer Inferences – Circle Graphs

1.

3.

5.

7. answers will vary

9. Though the graph appears to show a dramatic increase from x = 0 to x = 4, notice the scale on the graph. The actual increase in profit is $1,000 to $1,000.016 or not even 2 cents. The y axis is distorted because it is such a small range.

11. answers will vary

13. Maroon is forest cover, blue is no forest cover.

15.

17. answers will vary

Measure of Central Tendency

1. Mean 4 Median 4 Mode 4

3. Mean 4.12 Median 4 Mode 35. Mean 2.5 Median 1.5 Mode 1

7. 1:12

9.

The highest number is the mean, which means the middle number, the median, is below the average, so the data may be bottom heavy. Only 18 out of 51 states/districts have a percent of elderly below the poverty level that is greater than the average. Examining this a little more closely, all but three states, are within 5 percentage points from the average. These states, Wash. DC, LA and MS are more than 5 percent above the average stand out nationwide.

Standard Deviation and Normal Distribution

1.

Mr. Venette

68 percent of his students earned between a 76 and a 84.

95 percent of his students earned between a 72 and a 88.

99.7 percent of his students earned between a 68 and a 92.

Ms. Harper

68 percent of her students earned between a 79.7 and a 84.5.

95 percent of her students earned between a 77 and a 87.

99.7 percent of her students earned between a 74.5 and a 89.5.

Despite the higher average displayed by Ms. Harper’s students, her students earned very few A’s. Just 0.15 % of her students earned A’s. By the same token, Ms. Harper failed nearly none of her students. Mr. Venette, whose students had a lower average, had considerably more A’s dispersed to them than Ms. Harper’s students.

3. 16 % 5. 84 % 7. 0.l5 % 9. 40.13 % 11. Males: 2 ¼ “ Females: 1 7/8 “

13. 5’ 5 7/8”

15. 8.38 %17. Males: 11.5 lbsFemales: 12 lbs

19. 168.92 lbs

21. 87.7 % 23. 98.78 %

25.

Bridge One

68 % of the time, there will be between 320 and 520 cars on the bridge.

95 % of the time, there will be between 220 and 620 cars on the bridge.

99.7 % of the time, there will be between 120 and 720 cars on the bridge.

Bridge Two

68 % of the time, there will be between 440 and 480 cars on the bridge.

95 % of the time, there will be between 420 and 500 cars on the bridge.

99.7 % of the time, there will be between 400 and 520 cars on the bridge.

Going over Bridge Two is the safer route, but if you are in a hurry and want to gamble, the traffic will have thinned out, use Bridge One.

27. 93.32 %29. 7.68 %31. 6.68 %

Standard Deviation

1. standard deviation = 2.78, mean = 7.88

NFC East: Philadelphia Eagles 1.48, Dallas Cowboys 0.76, Washington Redskins –1.04, New York Giants –1.40

NFC North: Green Bay Packers 0.76, Minnesota Vikings 0.40, Chicago Bears –0.32,

Detroit Lions –1.04

NFC South: Carolina Panthers 1.12, New Orleans Saints 0.04, TampaBay Buccaneers –0.32, Atlanta Falcons –1.04

NFC West: St. Louis Rams 1.48 Seattle Seahawks 0.76 San Francisco -0.32 Arizona Cardinals –1.40

3. standard deviation = 3.07 mean = 8

AFC East: New England Patriots 1.96 Miami Dolphins 0.65 Buffalo Bills –0.65 New York Jets -0.65

NFC East: Philadelphia Eagles 1.31, Dallas Cowboys 0.65, Washington Redskins –0.98, New York Giants –1.30

AFC North: Baltimore Ravens 0.65 Cincinnati Bengals 0 Pittsburgh Steelers -0.65 Cleveland Browns -0.98

NFC North: Green Bay Packers 0.65, Minnesota Vikings 0.33, Chicago Bears –0.33,

Detroit Lions –0.98

AFC South: Indianapolis Colts 1.31 Tennessee Titans 1.31 Jacksonville Jaguars -0.98 Houston Texans -0.98

NFC South: Carolina Panthers 0.98, New Orleans Saints 0, TampaBay Buccaneers –0.33, Atlanta Falcons –0.98

AFC West: Kansas City Chiefs 1.63 Denver Broncos 0.65 Oakland Raiders -1.3 San Diego Chargers –1.3

NFC West: St. Louis Rams 1.31 Seattle Seahawks 0.65 San Francisco -0.33 Arizona Cardinals –1.33

5. standard deviation = 69.53, mean = 330.10

AFC East: New England Patriots 0.26 Miami Dolphins -0.27 Buffalo Bills –1.26 New York Jets -0.68

AFC North: Baltimore Ravens 0.88 Cincinnati Bengals 0.23 Pittsburgh Steelers -0.43 Cleveland Browns -1.09

AFC South: Indianapolis Colts 1.68 Tennessee Titans 1.51 Jacksonville Jaguars -0.78 Houston Texans -1.08

AFC West: Kansas City Chiefs 1.55 Denver Broncos 0.73 Oakland Raiders -0.86 San Diego Chargers –0.25

7. standard deviation = 51.67, mean = 325.94

AFC East: New England Patriots -1.70 Miami Dolphins -1.26 Buffalo Bills –0.91 New York Jets -0.52

AFC North: Baltimore Ravens 0.87 Cincinnati Bengals 1.12 Pittsburgh Steelers 0.02 Cleveland Browns -0.08

AFC South: Indianapolis Colts 0.19 Tennessee Titans –0.04 Jacksonville Jaguars 0.10 Houston Texans 1.05

AFC West: Kansas City Chiefs 0.12 Denver Broncos -0.48 Oakland Raiders 1.03 San Diego Chargers 2.23

9. standard deviation 305,083,394.9; mean = 192,619,538.9; median = 82,689,518

11. standard deviation 6.12; mean = 97.2; median = 97; mode = 95

FOUR

8.13.25

1. A fabrication. For example: Using the data from 09/01/04 and 08/01/04, we have a base of 6,389,969,987/6,383,805,814 = 1.000965595. So, to find the 10/01/04, we would have 6,389,969,987(1.0009655951/12) = 6,390,210,915 instead of the table’s 6,395,935,316.

3. New order, with old order listed to the left.

5. answers will vary 7. answers will vary 9. 30 years, from 1930 to 1960

11. White: $ 43,519 African American: $ 28,921 Hispanic: $ 32,472 Asian:

$ 66,051

13. 2002 and 2003 data. It is more recent, the data is bound to be more exact as it is taken over a smaller interval of time.

Linear Versus Exponential Growth

1. Exponential 3. Exponential

5. Exponential

7. Exponential9. Linear

11. 20, 1024 In this problem, exponential growth is 1022 more than the linear growth, or over 51 times as large.

Linear Models

1. b)3. y = 3x-15. d)7. c)

Suggested answers below are in the form [x-min, x-max] by [y-min, y-max]

a) [0,10] by [0, 100]

b) [0,10] by [0, 1000]

c) [0,10] by [0, 10,000]

d) [0,10] by [0, 10,000,000]

e) [0,10] by [0, 10,000,000,000]

f) [0,10] by [0, - 10,000,000,000]

9.

a) b)

c) d)

e)

11. Input: Years since 1960

Output: Death rates from Heart Disease per 100,000 for 45-54 year old American men

13. In this country, from 1960 to 1970, per year, there were 4.38 less deaths per 100,000 for men between the ages of 45-54.

In this country, from 1970 to 1980, per year, there were 9.40 less deaths per 100,000 for men between the ages of 45-54.

In this country, from 1980 to 1985, per year, there were 9.14 less deaths per 100,000 for men between the ages of 45-54.

15. y = 420.4 – 7.34x

17. Yes. This model appears useful for the short term, but not for the long term. The predicted death rates for the year 2050 is not reasonable.

19. ’79-’95 - 4.6 ’95-’96 -2.8

21. –4.49 In this country, from 1979 to 1996, per year, there were 4.49 less deaths per 100,000 for people between the ages of 45-54.

23. 2010 45.412050 -134.19

25. answers may vary27. A29. C31. F

Exponential Models

1. 86.883. 75.745. None of the previous four predictions should be considered ‘the most accurate’. Given each time interval the data provided produces distinct ratios that really should not be considered to be the ‘same’. However, this data does reflect the pattern of logistical growth, which will be discussed later in the chapter. If one was forced to pick the best time interval the 1999-2000 may be the best choice.

7. 12,097,712,670

9. 1990: 87,080,892; 2000: 112,541,272; 2004: 124,700,271; 2010: 145,445,660

11. Yes, because the data is always increasing for the time interval from 1998 to 2002.

13. 51.05 million; 56.28 million

15. 3560

17.

Rates of Change

1. –0.00314; The price for a gallon of regular gas in the State of California decreased at an average rate of 0.00314 dollars per gallon per day from the 21st of June to the 12th of July.

3. –0.00157; The price for a gallon of regular gas in the State of California decreased at an average rate of 0.00157 dollars per gallon per day from the 5th of July to the 12th of July.

5. 2.182 calculated; 2.186 actual

7. a)

9. a) Between 1999 and 2001, the average rate of change in the number of HIV/AIDS related deaths dropped by 2500 per year in the United States. b) Between 1999 and 2001, the number of HIV/AIDS related deaths dropped by 5000 in the United States.

11. 0.077513. 0.1415. –2.5 %; From 1992-2003, the percent of 8th graders who smoked regularly dropped by 2 1/2 percent.

17. Drop of 1 %, In 2005, the percent of 8th graders who are predicted to smoke regularly will drop 1 % from 2003, down to 2.5 %.

19. –1.4 %; From 1992-2003, the percent of 12th graders who smoked regularly dropped by 1.4 percent.

17. Drop of 1.1 %, In 2005, the percent of 12th graders who are predicted to smoke regularly will drop 1.1 % from 2003, down to 14.7 %.

23.

25. There number of traffic fatalities decreased by 430.666 per year from 1990 to 2002.

27. There number of traffic fatalities increased b 19 ½ per year from 2000 to 2002.

29. 17,476

World Population and Sustainability

1. a possible growth pattern following a logistic model could be

2.answers will vary; some answers may include war, famine, drought, deforestation, etc..

3. answers will vary; if the world population does indeed follow a logistics growth pattern then by the year 3000 the population may have stabilized to say, 10 billion.

4.

5.

6. The graph is concave up over the interval of time pertaining to the years 1980-1988. The number of AIDS cases each year during this time period was increasing at an increasing rate.

7.The graph is concave down over the interval of time pertaining to the years 1988-1996.

The number of AIDS cases each year during this time period was increasing at a decreasing rate.

8. The point of inflection occurs near the year 1988. General public awareness with respect to AIDS may be the cause in how these numbers accumulate or increase.

9.

10.

11. The graph is concave up over the years 1999-2004. The number of sea otters is increasing at an increasing rate during this time period.

12. The graph is concave down over the years 2004-2011. The sea otter population is increasing at a decreasing rate during this time period.

13.The point of inflection appears to occur during the year 2004. This could simply be the result of mother nature.

14. The scatter plot certainly does not appear to have the shape of an elongated S. Thus, the data does not necessarily reflect what we normally associate with a logistics model.

15.

16. The graph is concave up over the years 1980-2004. The population appears to be increasing at an increasing rate; exponentially.

17. N/A

18. N/A

19.Yes, the data does represent a logistics curve.

20.

The point of inflection occurs in the year, 1990.

21. The graph is concave up over the years, 1990-2004. The population is decreasing at a decreasing rate.

22. The graph is concave down over the years, 1980-1990. The population is decreasing at an increasing rate.

23. The point of inflection occurs in the year 1990. Answers can vary for the, why.

24. Yes, the scatter plot of the data suggests a logistics curve.

25.

27. The scatter plot appears to be concave down over the years 1990-2004. Over this time period the population is increasing at a decreasing rate.

29. TRUE

31. TRUE

33. FALSE, after the inflection point the rate of decrease will slow providing for a concave up portion of the graph.

35. This is not true. At some time in the future the exponential model will catch up to and surpass the linear model. How many years will this take?

37. No; there are not enough resources or space to accommodate such a growth.

Concavity

1. From 0 to 8 seconds, the function’s behavior is increasing at a decreasing rate.

2. From 0 to 4 seconds, the function’s behavior is decreasing at a decreasing rate. From 4 to 8 seconds, the function’s behavior is increasing at a increasing rate.