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.
2. A. November 9th B. December 16th C. New Year’s Eve, 13 seconds before midnight D. New Year’s Eve, 2 ½ seconds before midnight
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
4. A. 85 years, 8 ½ months B. 96 years C. 99 years, 38 minutes D. 99 years, 56 minutes
5. 37.7 inches 6. 37.7 inches 7. 37.7 inches 8. 37.7 inches
9. The size of the sphere does not matter, the answer never changes
Astronomy
1.
Body / Relative distance from the Sun when compared to the Earth’s distance from the Sun / Relative distance from the Sun when compared to Mercury’s distance from the SunSun / 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 / 49.4
Neptune / 28.9 / 77.5
Pluto / 39.2 / 101.9
2.
Body / Relative distance of the planet’s orbit when compared to the distance of the Earth’s orbit / Relative distance of the planet’s orbit when compared to Mercury’s orbitSun / 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 / 49.4
Neptune / 28.9 / 77.5
Pluto / 39.2 / 101.9
3.
Body / Diameter of Body relative to the smallest planet / Volume of Body Relative to the smallest planetSun / 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
4.
Body / Diameter of Body relative to the Earth / Volume of BodyRelative to the Earth
Sun / 108.125 / 1,264,091.064
Mercury / 0.375 / 0.05
Venus / 1 / 1
Earth / 1 / 1
Mars / 0.5 / 0.125
Jupiter / 11.125 / 1376.9
Saturn / 9.375 / 823.97
Uranus / 3.625 / 47.6
Neptune / 3.75 / 58.2
Pluto / 0.375 / 0.125
5. answers will vary
6. 1a, 2d, 3h, 4k, 5f, 6b, 7i, 8g, 9c, 10e, 11j
7. 1d, 2g, 3a, 4h, 5b, 6i, 7c, 8e, 9j, 10f
8. 1h, 2e, 3a, 4j, 5b, 6c, 7i, 8d, 9f, 10g
9.
Arithmetic / Exponential100 / 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
10. 1000 11. 1,000,000 12. 1021
Set Theory
1. This is the set of those purchasers from Amazon.com who owned a cell phone.
2. This is the same set as above, 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.
4. There are no elements in this set because none of the original signers of the Declaration of Independence owned 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.
6. 2
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,.
8. This is the set of those perspective buyers who cannot qualify for a $ 250,00 but they are either ready to purchase a home today or 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.
10. This is the set of registered democrats who are not opposed to the death penalty.
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.
12. This is the set of registered democrats who are not opposed to both the death penalty and legalized abortions.
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.
14. are the known suspected terrorists who have not resided in either Saudi Arabia or Chechnya. This would be the overlap of those terrorists who have not resided in Saudi Arabia and 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.
16. C \ A is the set of those who believe crystal powers but not Tarrot cards.
17. {0, 1, 2, 3, 4, 6, 8} 18. {2, 3} 19. {5, 7, 9} 20. {1} 21. {0, 8}
22. is the set of black cards and also the two red jacks.
23. is the set with one element, the jack of diamonds.
24. is the set of red cards.
25. B \ C is the set of there jacks, the jack of hearts, the jack of clubs and the jack of spades.
26. 39 27. 2 28. 36 29. 24
30. 22 31. 4 32. 4 33. 1
34. is the set of Arizona residents as well as the smokers.
35. is the set of college students who smoke.
36. is the set of non Arizona residents who don’t smoke.
37. A \ C is the set of Arizona state residents that don’t smoke.
38. is the set of non Arizona state residents who don’t smoke and are not college students.
39. 1 40. 19 41. 24 42. 2
43. is the set of all refrigerators and microwaves on sale at Sears.
44. is the empty set.
45. is the set of all appliances for sale at Sears.
46. is the set of female doctors or doctors who are taking new patients.
47. is the set of doctors that earn $ 200,000 or less that are taking new patients.
48. is the set of all doctors except those male doctors who are taking new patients.
49. 0 50. 26
Counting Theory
1.
a)
b)
c)
d)
e)
f)
g) c) d) b) e) and a) and f) are tied for last place
2.
a) 28(27)(26) = 19,656
b)
c)
d)
e)
f)
g)
h)
i)
3. 4(7)(3)(2) = 168
4. 5! = 120
5.
a)
b)
6.
a)
b)
c)
d)
e)
7.
8.
9.
a)
b)
10.
a)
b)
c)
d)
e)
f)
11.
a) 5! = 120
b)
c)
d) 6
e) 3
12. (4!)(5!) = 2,880
13.
a)
b)
c)
14.
a)
b)
15.
a)
b)
c)
16.
17.
a)
b)
c) 40
d) 40(39) = 1,560
e) 40(39) = 1,560
18.
19.
a)
b)
20.
a)
b)
c) 3(3)(2)(1) = 18
21.
a)
b)
c)
d)
e)
22. 12
23.
a)
b)
c)
d)
e)
f)
g)
h)
24.
25. Picking 5 correct out of 50
26.
a)
b)
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
2.
State / Numerical Growthfrom ’90 – ‘00 / Numerical Growth
from ’00 – ‘03
Florida / 3,041,181 / 1,036,690
New York / 989,294 / 213,658
California / 4,055,056 / 1,612,805
Arizona / 1,465,404 / 450,179
Your home state / Answers will vary / Answers will vary
3.
State / Average Annual NumericGrowth from ’90 – ‘00 / Average Annual Numeric
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
4.
State / Percent Growthfrom ’90 – ‘00 / Percent Growth
from ’00 – ‘03
Florida / 1.23 / 1.06
New York / 1.06 / 1.01
California / 1.14 / 1.05
Arizona / 1.40 / 1.09
Your home state / Answers will vary / Answers will vary
5.
State / Predicted 2010 populationbased on Average Annual
Numeric Growth from ’90 – ‘00 / Predicted 2010 population
based on Average Annual
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
6.
State / Predicted 2010 populationbased on Percentage of
Growth from ’90 – ‘00 / Predicted 2010 population
based on Percentage of
Growth from ’00 – ‘03
Florida / 20,393,282 / 19,482,430
New York / 20,273,199 / 19,618,579
California / 39,374,686 / 39,959,696
Arizona / 8,030,966 / 6,895,140
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.
8. Percent Growth from ’00-’03.
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.
2. Answers will vary 3. Answers will vary 4. 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.)
6. Some answers would include: 1880-James Garfield Elected President /1881 James Garfield Shot; 1980-Ronald Reagan Elected President /1981 Ronald Reagan Shot.
Garfield was shot by a man with a history of Mental Illness; Reagan was shot by a man with a history of mental illness. An insanity defense by both assassins. (The difference was at Garfield's shooters trial it was unsuccessfully and he was hung in June of 1882. As at Reagan's shooters trial, it was successful and he was acquitted in June of 1981.) Garfield's shooters irrational obsession lead him to believe he would achieve greatness to the World and Reagan's shooters irrational obsession lead him to believe he would achieve greatness to Jody Foster. Garfield entered the Military and quickly rose through the ranks, Reagan entered the military and quickly rose through the ranks. After the War, Garfield initially returned to his Career, teaching. After the War, Reagan initially returned to his Career, acting.
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.
8. Forty years later, four men are adrift in a boat and they kill and eat the cabin boy Richard Parker to survive.
Probability
1. 2. 3. 4. 5.