Solutions - Arizona State University
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.
|Body |Relative distance from |Relative distance from |
| |the Sun when compared to |the Sun when compared to|
| |the Earth’s distance from|Mercury’s distance from |
| |the Sun |the Sun |
|Sun |0 |0 |
|Mercury |0.38 |1 |
|Venus |0.73 |1.9 |
|Earth |1 |2.6 |
|Mars |1.5 |3.9 |
|Jupiter |5.3 |13.7 |
|Saturn |9.5 |24.6 |
|Uranus |19.1 |49.4 |
|Neptune |28.9 |77.5 |
|Pluto |39.5 |101.9 |
3.
|Body |Diameter of Body |Volume of Body Relative |
| |relative to the |to the smallest planet |
| |smallest planet | |
|Sun |283.3 |23,970,912.04 |
|Mercury |1 |1 |
|Venus |2.67 |19.0 |
|Earth |2.67 |19.0 |
|Mars |1.33 |2.35 |
|Jupiter |29.67 |26,118.8 |
|Saturn |25 |15,625 |
|Uranus |9.67 |904.2 |
|Neptune |10 |1000 |
|Pluto |1 |1 |
5. answers will vary
7. 1d, 2g, 3a, 4h, 5b, 6i, 7c, 8e, 9j, 10f
9.
| |Arithmetic |Exponential |
|100 |50 |7 |
|1,000 |500 |10 |
|1,000,000 |500,000 |20 |
|1,000,000,000 |500,000,000 |30 |
|1,000,000,000,000 |500,000,000,000 |40 |
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 who owned a cell phone.
3. This is the set of people who never purchased from 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. [pic]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. [pic] 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. [pic] 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. 2 29. 24
31. 4 33. 1
35. [pic]is the set of college students who smoke.
37. A \ C is the set of Arizona state residents that don’t smoke.
39. 1 41. 24
43. [pic]is the set of all refrigerators and microwaves on sale at Sears.
45. [pic]is the set of all appliances for sale at Sears.
47. [pic]is the set of doctors that earn $ 200,000 or less that are taking new patients.
49. 0
Counting Theory
1.
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
f) [pic]
g) c) d) b) e) and a) and f) are tied for last place
3. 4(7)(3)(2) = 168
5.
a) [pic]
b) [pic]
7. [pic]
9.
a) [pic]
b) [pic]
11.
a) 5! = 120
b) [pic]
c) [pic]
d) 6
e) 3
13.
a) [pic]
b) [pic]
c) [pic]
15.
a) [pic]
b) [pic]
c) [pic]
17.
a) [pic]
b) [pic]
c) 40
d) 40(39) = 1,560
e) 40(39) = 1,560
19.
a) [pic]
b) [pic]
21.
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
23.
a) [pic]
b) [pic]
c) [pic]
d) [pic]
e) [pic]
f) [pic]
g) [pic]
h) [pic]
25. Picking 5 correct out of 50
27. [pic]
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.
|State |Average Annual Numeric |Average Annual Numeric |
| |Growth from ’90 – ‘00 |Growth from 00 – ’03 |
|Florida |304,118.1 |345,563.3 |
|New York |98,929.4 |71,219.3 |
|California |405,505.6 |537,601.67 |
|Arizona |146,540.4 |150,059.67 |
|Your home state |Answers will vary |Answers will vary |
5.
|State |Predicted 2010 population |Predicted 2010 population |
| |based on Average Annual |based on Average Annual |
| |Numeric Growth from ’90 – ‘00 |Numeric Growth from ’00 – ‘03 |
|Florida |19,023,559 |19,438,011 |
|New York |19,965,745 |19,688,650 |
|California |37,926,704 |39,247,665 |
|Arizona |6,596,036 |6,631,229 |
|Your home state |Answers will vary |Answers will vary |
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. [pic] 3. [pic] 5. [pic]
7. [pic] 9. [pic]
11. 1 13. {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. 5/6 27. 5/18 29. 5/36
31. [pic] or 1 in every 104,932 Arizonian you encounter is a gun toting women who is over 80 years of age.
33. [pic]or roughly 4 in 5 Arizonian gun carriers are men.
35. [pic]or nearly twice as likely. (Each state’s population is irrelevant.)
37. 4,136,100,000 39. 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. 2/169 3. 1/16 5. 1/25
7. ¾ 9. 0.015
11. 1/6 13. 0.1778 15. 0.332
17. 63/64 19. 0.107
21. 0.0094 23. 0.512 25. 4/663
27. 13/204 29. 1/221
31. 0.0059 33. 0.224 35. 0.293
Probability Using Counting Theory
1. 0.000968 3. 0.00000154 5. 0.0000184 7. 0.000495 9. 0.01 11. 0.00000923
13. [pic]
15. 0.10 17. 0.0021
19. 0.167 21. 0.03
23. 0.6181 25. 0.9846
27. 1 29. 0.1169
31. 0.7063 33. 1
35. 8/663 37. 1/17 39. 0.00023 41. 0.054 43. 0.423
The Binomial Probability Profile
1. b(8,2,0.26) = 0.310810
3. b(8,4,0.26) = 0.095922 5. 1-b(8,8,0.74) = 0.910081 7. b(8,8,0.26) = 0.000021
9. 1-b(8,8,0.26) = 0.999979 11. b(6,6,0.690146) = 0.108055
13. b(6,6,0.955088) = 0.759031 15. 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) = 0.089742 21. b(12, 11, 0.85) = 0.301218
23. b(12, 12, 0.15) = 0.0000000001
25. b(4,4,0.3) = 0.0081 27. 1 – b(10, 10, 0.94) = 0.461385 29. 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. 7/11 3. ½
5. 0.47 7. 0.62
9. 0.50 11. 0.56 13. 0.39 15. 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. 5/9 3. {(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. 1/13 11. 1/36
13. 5/6 15. 0
Bayes Theorem
1. 0.605 3. 0.80
5. 0.73 7. 0.80 9. 0.63
11. 0.24 13. 0.56 15. 0.82
Expected Value
1. 73.333 3. –0.86
5. - $ 51.63
7. $ 2350, $ 9400, $ 23,500, $ 47,000
9. winter
11. [pic]= 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. [pic]
17. c)
Construct and Drawer Inferences – Circle Graphs
1. [pic]
[pic]
3. [pic]
[pic]
5. [pic]
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
[pic][pic]
13. Maroon is forest cover, blue is no forest cover. [pic][pic][pic][pic][pic][pic]
[pic]
15. [pic]
17. answers will vary
Measure of Central Tendency
1. Mean 4 Median 4 Mode 4
3. Mean 4.12 Median 4 Mode 3 5. Mean 2.5 Median 1.5 Mode 1
7. 1:12
9.
|Utah |5.8 |50 |
|Alaska |6.8 |49 |
|Connecticut |7.0 |48 |
|Nevada |7.1 |47 |
|New Hampshire |7.2 |46 |
|Colorado |7.4 |43 |
|Hawaii |7.4 |43 |
|Wisconsin |7.4 |43 |
|Washington |7.5 |42 |
|Oregon |7.6 |41 |
|Indiana |7.7 |39 |
|Iowa |7.7 |39 |
|New Jersey |7.8 |38 |
|Delaware |7.9 |37 |
|Nebraska |8.0 |36 |
|California |8.1 |33 |
|Kansas |8.1 |33 |
|Ohio |8.1 |33 |
|Michigan |8.2 |31 |
|Minnesota |8.2 |31 |
|Idaho |8.3 |29 |
|Illinois |8.3 |29 |
|Arizona |8.4 |28 |
|Maryland |8.5 |26 |
|Vermont |8.5 |26 |
|Massachusetts |8.9 |24 |
|Wyoming |8.9 |24 |
|Florida |9.1 |21 |
|Montana |9.1 |21 |
|Pennsylvania |9.1 |21 |
|Virginia |9.5 |20 |
|Missouri |9.9 |19 |
|Maine |10.2 |18 |
|Rhode Island |10.6 |17 |
|North Dakota |11.1 |14 |
|Oklahoma |11.1 |14 |
|South Dakota |11.1 |14 |
|New York |11.3 |13 |
|West Virginia |11.9 |12 |
|New Mexico |12.8 |10 |
|Texas |12.8 |10 |
|North Carolina |13.2 |9 |
|Georgia |13.5 |7 |
|Tennessee |13.5 |7 |
|Arkansas |13.8 |6 |
|South Carolina |13.9 |5 |
|Kentucky |14.2 |4 |
|Alabama |15.5 |3 |
|District of |16.4 |(X) |
|Columbia | | |
|Louisiana |16.7 |2 |
|Mississippi |18.8 |1 |
|Median |8.9 | |
|Mode |8.1 | |
|Mean |10 | |
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 lbs Females: 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, Tampa Bay 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, Tampa Bay 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.
|1 |China |3117234298 |
|2 |India |1118324137 |
|8 | Bangladesh |628041082 |
|4 |Indonesia |572287085 |
|3 |US |439541357 |
|9 |Nigeria |398034086 |
|10 |Japan |305599205 |
|5 |Brazil |261423575 |
|12 |Philippines |206980073 |
|13 |Vietnam |198454843 |
|15 |Egypt |182681810 |
|11 |Mexico |167935354 |
|6 |Pakistan |167156152 |
|17 |Ethiopia |162843074 |
|19 |Thailand |155677255 |
|7 |Russia |150971455 |
|14 |Germany |79951871 |
|16 |Turkey |72293845 |
|18 |Iran |70878365 |
|20 |France |58611487 |
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. Exponential 9. 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-1 5. 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) [pic] b) [pic]
c) [pic] d) [pic]
e) [pic]
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 45.41 2050 -134.19
25. answers may vary 27. A 29. C 31. F
Exponential Models
1. 86.88 3. 75.74 5. 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.
| |Linear |Linear |Exponential |Exponential |
| |Model |Model |Model |Model |
|0 |10 |10 |10 |10 |
|1 |12 |8 |20 |5 |
|2 |14 |6 |40 |2.5 |
|3 |16 |4 |80 |1.25 |
[pic]
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. 0.0775 13. 0.14 15. –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.
[pic]
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
|year |2010 |2015 |2020 |2025 |2030 |2035 |2040 |
|change |250 |750 |2000 |3500 |5500 |8000 |11000 |
|year |88-9 |89-90 |90-1 |91-2 |92-3 |93-4 |94-5 |
|change |2500 |8000 |500 |4500 |500 |500 |500 |
5. [pic]
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.
|0 |2150 |change |
|1 |2160 |10 |
|2 |2190 |30 |
|3 |2240 |50 |
|4 |2300 |60 |
|5 |2500 |200 |
|6 |2600 |100 |
|7 |2650 |50 |
|8 |2680 |30 |
|9 |2700 |20 |
|10 |2705 |5 |
10. [pic]
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. [pic]
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. [pic]
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. [pic]
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.
3. From 0 to 8 seconds, the function’s behavior is decreasing at a decreasing rate.
4. From 0 to 8 seconds, the function’s behavior is decreasing at a increasing rate.
5. From 0 to 8 seconds , the function is decreasing at an increasing rate.
6.From 0 to say, 4 or 5 seconds the curve is increasing at an increasing rate. From 4 or 5 seconds to 8 seconds the curve is increasing at a decreasing rate.
7. From 0 to say, 4 or 5 seconds the curve is increasing at an increasing rate. From 4 or 5 seconds to 8 seconds the curve is increasing at a decreasing rate.
9.[pic]
11.[pic] Linear
13. There is no change in concavity due to each cross section of the cylinder or soda can is essentially the same; a circle.
15.[pic] Non linear
17. [pic] Linear
19. The concavity of the graph will be concave up as each cross section of the pyramid is smaller as we move from the bottom to the top.
21.[pic] Non Linear
23.[pic] Linear
25. picturing a wine glass to have a similar shape to a fish bowl, the first half of the graph will be concave down as each cross section of the wine glass increases in size as we move from the bottom to the top. The second half of the graph will be concave up as the cross sections change in size becoming smaller as we move from the midpoint to the top of the glass. Thus, the second half of the graph is concave up as the height will increase at an increasing rate.
27. [pic] Non Linear
29. [pic]
Answers will vary
31. Answers will vary
33. Answers will vary
35. Answers will vary
FIVE
Effective Rate, Simple Interest and Compound Interest
1. a) 1 year: 5.5 % 2 year: 5.21 % : 3 year: 4.95 % 10 year: 3.68 %
b) $ 59,800 c) $ 19,800
3. a) 1 year: 12 % 2 year: 10.71 % : 3 year: 9.68 % 10 year: 5.77 %
b) $ 520,000 c) $ 270,000
5. Same 7. 9.9 % annually
9. $ 490 compound interest at 9.95 % annual
11. a) $ 322,580.65 b) $ 135,754.56 c) 36,505.63
Compound Interest
1. $ 17,177.62 3. a) $ 5958.21 b) $ 5959.51
5. a) $ 1202.99 b) $ 1116.70
7. 3 years. 9. $ 165.31
11. 7.27 %
Annual Yield
1. $ 1784.83; 0.01375 3. $ 3,932.22; 0.03125
5. $ 138.23; 0.000127
7. 5 % compounded daily
9. 5.9 % compounded quarterly
11. Yield for 2 % 0.0202; Yield for 1.99 % 0.02008
Annuity
1. $ 600.54 3. $ 300.27
5. $ 5,829.09 7. $ 135,342.82 9. $ 88,965.47
11. $ 90,846.24 13. $ 4,869.11 15. $ 5,235.50
17. $ 5,235.50 19. a) $ 1264.14 b) $ 255,088.98 c) $ 505,088.96
d) $ 72,686.09 e) $ 104,881.26 f) $ 174,798.02
21. $ 5161.54
23. $ 495.57
25. Tiger: $ 538,239.44 Shaq: $ 107,647.89 LeBron: $ 269,119.72
Peyton: $ 73,046.78 KG: $ 53,823.94 De La Hoya: $ 15,378.27
Agassi: $ 188,383.80 Kobe: $ 92,269.62 Jeter: $ 46,134.81
Grant Hill: $ 84,580.48
Different Payment and Interest Conversion Periods
1. 0.000792; $ 10,835.85 3. 0.005012; $ 96,984.73 5. 0.002781; $ 65,195.88
The Mortgage Payment Equation
1. $ 1,807.03 3. $ 361.60 5. $ 2,530.93 7. $ 1,219.96
9. $ 930.54 11. $ 186,108.55 13. $ 488.61 15. $ 310.12
17. $ 62,024.12
19. $ 129,499.20; $ 266,427.83 21. $ 83,843.08; $ 57,522.30 23. $ 5707.66 25. $ 129,498.22 27. $ 13,472.60 29. $ 82,830.94
SIX
Basic Geometry Definitions
1. a) neither b) perpendicular c) perpendicular d) parallel
e) parallel f) parallel g) perpendicular h) parallel
i) parallel j) neither k) perpendicular
3. a) regular octagon b) rectangle c) circle, diameter
d) concentric circles e) regular hexagon f) concentric circles, congruent
g) rectangular solid h) perpendicular i) cone or right cylinder
j) collinear k) coplanar, parallel l) collinear , congruent
m) parallel, congruent n) concentric, coplanar
5. False 7. True
9. True 11. 48 in2 13. 6.3 in2
15. 16 in2 17. 68 in 240 in2
19. 583.1 mi 21. 245.0 in3
23. 266.9 in3 25. 252 ft3
27. 6.1 in3 29. 50.3 in3
31. 85,249.1 ft3
33. a) 2.8 ft b) 92 ft3 c) 98.5 ft2
More Geometry on Our Globe
1.
|Rank |Building; Location | In feet |
|1 |Taipei 101; Taipei, Taiwan |3.34 |
|2 |Petronas Tower 1; Kuala Lumpur, Malaysia |2.97 |
|3 |Petronas Tower 2; Kuala Lumpur, Malaysia |2.97 |
|4 |Sears Tower; Chicago, USA |2.9 |
|5 |Jin Mao Building; Shanghai |2.76 |
|6 |Two International Finance Center; Hong Kong |2.72 |
|7 |CITIC Plaza; Guangzhou, China |2.57 |
|8 |Shun Hing Square; Shenzhen, China |2.52 |
|9 |Empire State Building, New York, USA |2.5 |
|10 |Central Plaza; Hong Kong |2.45 |
3. 0.69 ft or 8 ¼ in
5. 206.6 ft 7. 61,800,017 miles; nearly 2,483 times around the earth
9. a) 420 ft b) 1.33 or 33 % c) 1.33 or 33 % d) 1.66 or 66 %
11. a) 787,810.9 b) 875,143
13. 0.0017
15. Virginia
17. Arizona 19. Hawaii
Real Estate Math
1. answers will vary
Tribune Co.: 0.255 USA Today: 0.231
The Associated Press: 0.180 Hearst Corp.: 0.161
The New York Times: 0.106 The Washington Post: 0.103
Newhouse: 0.094 Reuters: 0.081
The Dallas Morning News 0.080 The Wall Street Journal 0.057
3. answers will vary 5. answers will vary
7. answers will vary
9. answers will vary
Trigonometry
1. 53.44
3. A = 15o, a = 6.7, c = 25.88 5. A = 80o, b = 35.26, c = 203.08
7. A = 1o, b = 229.16, c = 229.19
9. B = 60o, a = 1.81, c = 3.63 11. 2.236 13. not possible
15. 5 17. 5.83 19. 3.16
Right Triangle Applications
1. 150 to 180 feet 3. 464.84 ‘
5. 6”
7. a = 12’, b = 10’, c = 12’, d = 12’, e = 24’, f = 10’, g = 10’, h = 4’
i = 14’, j = 15’, k = 12’
9. 9130.9’, 9185.5’ 11. 20’
13. 1389.0’, 660’
SEVEN
Inductive Reasoning
1. 11 3. 0.3125 5. –15,000 7. 11/15 9. 122 11. 250 13. 5032.84375 15. 27 17. 250/190
Deductive Reasoning
1. Answer: valid 3. Answer: not valid
5. Answer: not valid 7. Answer: not valid 9. Answer: valid
11. Answer: not valid
13. Answer: valid 15. Answer: not valid
17. answers will vary
19. answers will vary
Symbolic Logic
1. Some drug companies do not spend more on advertising than research.
3. All of our troops do obey the cease-fire.
5. Some of this generation of youngsters do apply themselves.
7. Some presidents have written a good tell all book.
9. All politicians are honest about their tax deductions.
11. No ball players use steroids.
13. Some documentaries are fair and unbiased.
Quantifiers
1. Everyone is afraid of at least one person.
3. Someone is feared by somebody.
5. There is someone who is afraid of everyone.
7. Somebody owes someone money.
9. There is a person who is owed money by someone.
11. [pic] False. It is only true for [pic]
13. [pic] True. It is an algebraic equality.
15. [pic] False. The only solutions are imaginary, and thus are not integers.
17. Every integer is the square root of some other integer. False. The negative integers are not square roots of some other integer. Neither is 5, which is an integer but not a perfect square.
19. Every integer is greater than some integer squared. False. The negative integers are not greater than some integer squared.
21. [pic]where T(x) means the religion x is tolerated and M(y) means the man y gets to heaven his own way.
23. [pic]where I(x) means the man x is an island unto himself.
Connectives
1. p: The person is a democrat. q: The person will support the tax increase on the middle class. [pic]
3. p: Weapons of mass destruction are found. q: War was necessary. [pic]
5. p: The country resolves who killed JFK. q: We will trust the government. [pic]
7. p: Medicare is cut. q: My parents will suffer. r: Your parents will suffer. [pic]
9. p: John Wilkes Booth was a phenomenal actor. q: John Wilkes Booth was incredibly passionate. r: John Wilkes Booth was a lousy patriot. [pic]
11. P: You can hear. Q: You can listen. [pic]
13. P: It is a documentary. Q: It is completely accurate. R: It is unbiased. [pic]
15. P: You can smile. Q: You lie. R: You can cry. S: You tell the truth. [pic]
Truth Tables
1. T 3. T 5. F
7. TTFT 9. TTFT
11. FTTF 13. TTFTFTFT 15. TFFFTTFT 17. FTTTTTTT
Arguments
1. [pic] valid
3. [pic] not valid 5. [pic] valid 7. [pic] not valid 9. [pic] not valid 11. [pic] valid
13. [pic] valid 15. [pic] valid
Fallacies
1. Fallacy of the Slippery Slope 3. Fallacy of the Artificial Choices 5. Fallacy of the Opposite 7. Fallacy of the Artificial Choices 9. Fallacy of the Non-transitive
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