OpenLLM-France/wikimedia huggingface dataset:
# Exponents

The GRE frequently tests exponents, which are numbers indicating how many times a value has been multiplied into a given system.

## Rule

When multiplying exponents, add the exponent numbers; when raising exponents to a power, multiply the exponent numbers.
An exponent is a statement of how many times a number has been multiplied into a given system. 25 is equal to 5$^2$ or 5(5). Multiplying 5$^2$ by 5$^2$ equals 5(5)(5)(5) or 5$^4$. Raising an exponent to a power multiplies the exponent numbers, while multiplying exponents merely adds their numbers.
    a$^3$(a$^4$) = a$^7$
    (b$^5$)$^6$ = b$^{30}$
A negative exponent equals one divided by the number raised to that exponent; a fractional exponent indicates a radical of the corresponding degree.

### Exponent of "0" is equal to 1

A number with an exponent of “0” equals 1.
x$^0$ = 1

## Practice

1. What does y$^2$(y$^5$) equal?
2. If (m$^4$)$^4$ = m$^x$ what does x equal?
3. If ${\tfrac {1}{2}}$ is equal to q$^{−2}$ then what does q equal?

## Answers to Practice Questions

1. y$^7$
When multiplying, add the exponent numbers.
2. 16
When raising exponents to a power, multiply the exponent numbers.
3. ${\sqrt {2}}$
Negative exponents indicate 1 divided by the number raised to this exponent.
q$^{−2}$ is ${\tfrac {1}{q^{2}}}$ so since q$^{−2}$ = ${\tfrac {1}{2}}$, then q$^2$ must equal 2 and q must equal ${\sqrt {2}}$.
# A Guide to the GRE/Digits of Numbers
## Digits of Numbers

If a question gives you the relationship between the various digits of a number, substitute variables for these digits and put the appropriate power of 10 in front of each one.
For example, the test might ask, “in a number, the hundreds digit is 2 greater than the tens digit, which is 2 greater than the units digit. If the number is equal to 195 multiplied by the units digit, what is the number?'
* Let u equal the units digit, t the tens, h the hundreds, and x the number.
* Restate the givens in terms of u, t, h, and x.
** t = u + 2
** h = t + 2 = u + 4
** x = 195u
** x = 100h + 10t + u
* Find the value of u.
** 195u = x = 100h + 10t + u
** 194u = 100h + 10t
** 194u = 100(u + 4) + 10(u + 2)
** 194u = 100u + 10u + 420 = 110u + 420
** 84u = 420
** u = 420/84 = 5
* Now you can find the values of the other numbers:
** t = 5 + 2 = 7
** h = 5 + 4 = 9
* Check your work:
** 975 = 195 * 5

### Practice

1. The tens digit of a 3-digit number is twice the units digit and one less than the hundreds digit. If the number is equal to two less than 136 times the tens digit, what is the number?
2. If the digits of a 2-digit number are reversed, the resulting number is 45 greater than the original number. If the initial 2-digit number is less than 20, then what is its value?

### Answers to Practice Questions

1. 542
Let t equal the tens digit.
100(t + 1) + 10t + t/2 = 136t - 2
    Take the original equation.
100t + 100 + 10t + t/2 = 136t - 2
    Expand the parentheses.
110.5t + 100 = 136t - 2
    Combine variables and constants.
100 = 25.5t - 2
    Subtract from both sides.
102 = 25.5t
    Add 2 to both sides.
4 = t
    Divide both sides by 25.5
    t is equal to 4, and the number is thus equal to 542.
2. 16
Let t equal the tens digit and u equal the units digit.
10u + t - (10t + u) = 45 Take the equation.
10u + t - 10t - u = 45 Expand the parentheses.
9u - 9t = 45 Combine the variables.
u - t = 5 Divide both sides by 9.
u is 5 greater than t; thus, u and t could be 1 and 6, 2 and 7, 3 and 8, 4 and 9. However, since the initial value is less than 20, the digits must be 1 and 6, which make 16 and 64.
# A Guide to the GRE/Buried Conclusions

The key points of the author are often hidden amidst thick text. Practice identifying them and picking them out.
Though commonly thought of as a theory on the origins of life, biological evolution in fact does not address this topic, but rather, the diversity of life. The concept of 5 the origins of life is called “abiogenesis” and was the question addressed by the famous Miller and Urey experiment. In 1952, the two namesakes of this experiment built a machine which applied 10 heat and electrical sparks to water and a plethora of gases to determine whether amino acids, a fundamental component of life on Earth, could form from these chemicals. The experiment produced over 15 twenty amino acids, but, while frequently cited as a milestone in the research of abiogenesis, the experiment is just as heavily disapproved by many for its inaccuracies. These criticisms are 20 heavily misplaced. Critics frequently point out that the gases used in the Miller and Urey experiment were probably quite different from those which made up the Earth's atmosphere 25 billions of years ago, and therefore, the experiment is inaccurate and its informative nature is limited. The point of the experiment, however, was never to attempt to simulate actual abiogenesis.
30 Miller and Urey were concerned with the question of whether or not amino acids could arise from gases, water, heat, and electricity, and in their research, they proved just what they set out to 35 determined. 1. What was the “Miller and Urey” experiment and what did it seek to accomplish?
2. How did the Miller and Urey experiment proceed? What was done in the experiment?
2. According to the passage, what is a common criticism of the Miller and Urey experiment, and how does the author feel with regard to this criticism?
3.06 Buried Conclusions
1. The Miller and Urey experiment sought to see whether amino acids - a basic component of life - could be produced from naturally occurring gases through application of heat and electricity. The experiment was a success, and produced over twenty such amino acids.
2. The Miller and Urey experiment ran a group of different gases (“plethora”) through a machine which applied heat and electrical sparks to these gases as well as water.
2. The passage explains that the Miller and Urey experiment is commonly criticized because the gases used in it were probably quite different from the early atmosphere on Earth. However, the author claims that this is not a valid criticism. As the author explains, the purpose of the experiment wasn't to simulate how life arose on Earth. Rather, the purpose was to determine whether it was possible for amino acids to form naturally under certain circumstances. The experiment showed this, and thus was a success.
# Conclusions & Premises
## Overview

Identify the conclusion of each argument
The “conclusion” is the ultimate point which the author seeks to have the reader believe. Conclusions are typically buried within very verbose language. For instance:
Thomas Hobbes wrote that life in the state of nature was “solitary, poor, nasty, brutish, and short.” However, many other writers took a more positive view of the state of nature. For instance, well known writers Henry David Thoreau and Ralph Waldo Emerson glorified nature as pure and virtuous compared to the evils of society and civilization. It is clear from this that Hobbes’s view of nature was quite cynical.
The conclusion is the last sentence - that Hobbes's view was cynical.
Conclusions can be located by looking for signal words such as “thus”, “therefore”, “it follows”, “so”, and “conclude.”
The conclusion will be the statement that the other sentences gravitate towards, and thus will often be signaled by language of this sort.

## Practice

Identify the conclusions in each of the following short passages.
1. The common carp frequently occurs in rivers and lakes, and is often caught by fisherman. Recently, a similar fish, the black carp, has spread into many of the same bodies of water from the fish farms where it is raised. Since the black carp is native to China, it lacks immunity to many local diseases, and since the black carp looks very similar to the common carp, fishermen who catch carp are currently at risk of contracting food poisoning from the fish.
2. Paying taxes to support government welfare programs tends to reduce citizens’ desire to provide assistance to others volitionally, since if people feel they are already contributing to the welfare of others through taxes which fund government welfare expenditures, they will feel that their obligation to society has been fulfilled. It follows that public welfare programs in fact have at least some detrimental impact on the public good.

## Answers to Practice Questions

1. The conclusion is that fishermen are at risk for food poisoning from catching the fish. This argument is explaining that, because fishermen can't distinguish the fish from other carp, and because the fish isn't immune to local diseases, fishermen will be at risk.
2. The conclusion of the argument is that tax-funded social welfare reduces incentive to give. The reason for this conclusion is that if people are forced to pay taxes, they will feel they have done enough, and will be less inclined to give.
# Decimals

Decimals are an extension of the base ten numeral system to fractions of ten (such as hundredths and thousandths). In this way they are a variation of fractions and percentages.

## Rules

Decimals are fractions of 10, 100, 1000, and so on.
You will have access to a calculator on the GRE but it is nonetheless important that you understand the concept of decimals.
.1 is equal to one tenth; .01 is equal to one hundredth; .001 is equal to one thousandth. Decimals are added and subtracted in the same way ordinary numbers are.
When multiplying decimals, multiply the numbers without decimals; then, push the decimal place to the right once for each time each multiplier is pushed to the right of the decimal.
.05 multiplied by .05 equals .0025, not .25. 6 multiplied by .9 is 5.4, while .6 multiplied by .9 is .54. When in doubt, check these on the calculator.

## Practice

1. What is .04 multiplied by .08?
2. y is equal to .4(x). If x equals 20, what does y equal?
3. What is the value of .009(.008)(.007)?

## Answers to Practice Questions

1. .0032
4(8) is 32. .04 and .08 are both pushed 2 points to the right of the decimal; thus, their product is pushed 4 points to the right.
2. 8
.4(20) = (20) = 8
3. 0.000000504.
The multipliers are each pushed to the right of the decimal 3 times. Thus, we take their product without decimals, and push it to the right 9 times.
9(8)(7) is 504; which pushed to the right 9 times equals 0.000000504.
# Adventist Youth Honors Answer Book/Nature/Cats

Like many honors, the requirements for Cats differ from one division to the next. If your division is not listed below, use the General Conference version.
Cats (General Conference) Cats (North American Division)
# Adventist Youth Honors Answer Book/Nature/Cats/Benefits

Cats catch mice and provide friendship. They are used in China and Japan to protect silkworm cocoons from rats.
# Adventist Youth Honors Answer Book/Nature/Cats/Bible stories

* Samson and the lion. (Judges 14)
* David killed a lion and a bear (1 Samuel 17:36)
* Lion killed a disobedient prophet. (1 Kings 13)
* Benaiah killed a lion in a snowy pit. (1 Chronicles 11:22)
* Calf and the lion will lie down together in heaven. (Isaiah 11:6,7)
* Can a leopard change his spots? (Jeremiah 13:23)
* Daniel and the Lion's Den (Daniel 6)
* Daniel's dream of the lion with wings and leopard with four heads. (Daniel 7)
# Adventist Youth Honors Answer Book/Nature/Cats/Androcles

Androcles was a Roman slave who escaped and took refuge in a cave. One day, a lion entered the cave, limping badly. Androcles examined its paw and removed a large thorn. The lion became cured and tamed by Androcles and also lived in the cave with Androcles until Androcles was later re-captured. Androcles was tried and sentenced to be torn to pieces by a hungry lion. On the fateful day, the lion, chosen to destroy him, began to lick his face and hands with obvious affection instead of eating him. It was the same lion that Androcles befriended in the cave. The authorities were moved by this show of affection. The king pardoned and set Androcles free. They also allowed Androcles to keep the lion as a companion and he walked the streets of Rome with it.
# Adventist Youth Honors Answer Book/Nature/Birds/Wood Pigeon

Columba palumbus (Wood Pigeon) :
* Wood Pigeon
* Description |
* Bird callThe Wood Pigeon (Columba palumbus) is a member of the family Columbidae, doves and pigeons.
* In the colder northern and eastern parts of its European and western Asiatic range the Wood Pigeon is a migrant, but in southern and western Europe it is a well distributed and often abundant resident.
* The three Western European Columba pigeons, Wood Pigeon, Stock Pigeon, and Rock Pigeon, though superficially alike, have very distinctive characteristics; the Wood Pigeon may be identified at once by its larger size at 38-43 cm, and the white on its neck and wing. It is otherwise a basically grey bird, with a pinkish breast.
* Juvenile birds do not have the white patches on either side of the neck. When they are about 6 months old (about 3 months out of the nest) they gain a small white patch on both sides of the neck, which gradually enlarge until they are fully formed when the bird is about 6-8 months old (approx. ages only). Juvenile birds also have a greyer beak and an overall lighter grey appearance than adult birds.
* It breeds in trees in woods, parks and gardens, laying two white eggs in a simple stick nest which hatch after 17 to 19 days. Wood pigeons seem to have a preference for trees near roadways and rivers. The nests are vulnerable to attack, particularly by crows, the more so early in the year when the leaf cover is not fully formed. The young usually fly at 33 to 34 days; however if the nest is disturbed some young may be able to survive having left the nest as early as 20 days from hatching.
* Its flight is quick, performed by regular beats, with an occasional sharp flick of the wings, characteristic of pigeons in general. It takes off with a loud clattering. It perches well, and in its nuptial display walks along a horizontal branch with swelled neck, lowered wings, and fanned tail. During the display flight the bird climbs, the wings are smartly cracked like a whiplash, and the bird glides down on stiff wings. The noise in climbing flight is caused by the whipcracks on the downstroke rather than the wings striking together.
* The Wood Pigeon is gregarious, often forming very large flocks outside the breeding season. Most of its food is vegetable, taken from open fields or gardens and lawns; young shoots and seedlings are favored, and it will take grain.
* The call is a characteristic cooing (coo-coo-coo-cu-cu). This species can be an agricultural pest, and it is often shot, being a legal quarry species in most European countries. It is wary in rural areas, but often quite tame where it is not persecuted. |
# Rome's Geography
## The Tiber River

Rome sat on the eastern shore of the Tiber River, at the only easy crossing place between the river mouth and the mountains. Seven hills rose there out of low and marshy ground. By the beginning of the ninth century BCE, these seven hills were occupied by village communities who kept farms in the low-lying areas and retreated to their hilltops for defense.
The fording place on the river lay below a large island that was later dedicated to the Greek god of healing, Asclepius. Sometime in the sixth century BCE, the romans under the direction of their Etruscan kings built a wooden bridge over the Tiber at this point, facilitating communications between northern and southern Italy, and joining the Etrurian confederation to the Greek colonial cities in the district of Magna Graecia.

## The Seven Hills

Archaeology suggests that Rome began as a confederation of villages on the seven hills of Rome: the Capitoline, Palatine, Aventine, Viminal, Quirinal, Esquiline, and the Caelian. The low-lying ground between them was swampy and malarial. Yet the presence of a natural fording place gave Rome some unusual advantages. Once the seven villages united, and invested the time in constructing an early wall around their territory, they could charge a toll for the use of the ford (and later the bridge). This was to prove an early source of Rome's wealth. Graves dating from the ninth and eighth centuries BCE suggest two common forms of burial in the area: cremation graves are clustered in Rome's Forum or marketplace, with a smattering of inhumations around them; a much larger cemetery lay in the valley between the Esquiline and Viminal hills.
Tradition and myth provides a much more interesting, if less likely, story of Rome's founding. One of the Vestal Virgins of the nearby town of Alba Longa had a sexual encounter with the god Mars, and bore Romulus and Remus, twin sons who catalyzed the fortification of a small urban area in what is now Rome.

### Capitoline

Capitoline hill has deep roots in Roman history as its existence is acknowledged in the stories concerning the founding of Rome.
# Ancient History/Rome/Etruscans
## Origins

The Etruscans' origins have always been a highly debated topic. Many theories include that they migrated to the Italian peninsula from the East, or that they were the descendants of the ancient inhabitants there. Findings about their origins have been inconclusive.
# Ancient History/Rome/Early Rome (the Seven Hills)
## The Tiber River

Rome sat on the eastern shore of the Tiber River, at the only easy crossing place between the river mouth and the mountains. Seven hills rose there out of low and marshy ground. By the beginning of the ninth century BCE, these seven hills were occupied by village communities who kept farms in the low-lying areas and retreated to their hilltops for defense.
The fording place on the river lay below a large island that was later dedicated to the Greek god of healing, Asclepius. Sometime in the sixth century BCE, the Romans under the direction of their Etruscan kings built a wooden bridge over the Tiber at this point, facilitating communications between northern and southern Italy, and joining the Etrurian confederation to the Greek colonial cities in the district of Magna Graecia.

## The Seven Hills

Archaeology suggests that Rome began as a confederation of villages on the seven hills of Rome: the Capitoline, Palatine, Aventine, Viminal, Quirinal, Esquiline, and the Caelian. The low-lying ground between them was swampy and malarial. Yet the presence of a natural fording place gave Rome some unusual advantages. Once the seven villages united, and invested the time in constructing an early wall around their territory, they could charge a toll for the use of the ford (and later the bridge). This was to prove an early source of Rome's wealth. Graves dating from the ninth and eighth centuries BCE suggest two common forms of burial in the area: cremation graves are clustered in Rome's Forum or marketplace, with a smattering of inhumations around them; a much larger cemetery lay in the valley between the Esquiline and Viminal hills.
Tradition and myth provides a much more interesting, if less likely, story of Rome's founding. One of the Vestal Virgins of the nearby town of Alba Longa had a sexual encounter with the god Mars, and bore Romulus and Remus, twin sons who catalyzed the fortification of a small urban area in what is now Rome.

### Capitoline

Capitoline hill has deep roots in Roman history as its existence is acknowledged in the stories concerning the founding of Rome.
# Ancient History/Rome/Late Republic Economy

Roman trade was the engine that drove the economy of the late Roman Republic and the early Roman Empire. Fashions and trends in historiography and in popular culture have tended to neglect the economic basis of the empire in favour of the lingua franca of Latin and the exploits of the Roman legions. The language and the legions were supported by trade while being at the same time part of its backbone. Romans were businessmen — the longevity of their empire was due to their commercial trade. Whereas in theory members of the Roman Senate and their families were prohibited from engaging in trade, the members of the Equestrian order were involved in businesses, despite their upper class values that laid the emphasis on military pursuits and leisure activities. Plebeians and freedmen held shop or manned stalls at markets while vast quantities of slaves did most of the hard work. The slaves were themselves also the subject of commercial transactions, and given their high proportion in society (compared to that in Classical Greece), and the reality of runaways, the Roman Servile Wars and minor uprisings, they gave a distinct flavour to Roman commerce. The intricate, complex, and extensive accounting of Roman trade was conducted with counting boards and the Roman abacus. The abacus, using Roman numerals, was ideally suited to the counting of Roman currency and tallying of Roman measures.
# 99 Elm Problems/Problem 3

Problem 3: Implement the function nth to return the n-th element of a list.
Result:
Solutions
# 99 Elm Problems/Problem 3/Solutions

Solution 1: Recursive version
Solution 2: Point Free version
# 99 Elm Problems/Problem 33

Determine whether two positive integer numbers are coprime. Two numbers are coprime if their greatest common divisor equals 1.
# # # THIS IS A STUB # # #
Result:
Solutions
# 99 Elm Problems/Problem 32

Determine the greatest common divisor of two positive integer numbers. Use Euclid's algorithm.
# # # THIS IS A STUB # # #
Result:
Solutions
# 99 Elm Problems/Problem 34

Calculate Euler's totient function phi(m). Euler's so-called totient function phi(m) is defined as the number of positive integers r (1 <= r < m) that are coprime to m.
# # # THIS IS A STUB # # #
Result:
Solutions
# 99 Elm Problems/Problem 27/Solutions

Description of first solution
# 99 Elm Problems/Problem 31

Determine whether a given integer number is prime.
# # # THIS IS A STUB # # #
Result:
Solutions
# 99 Elm Problems/Problem 27

Group the elements of a set into disjoint subsets.27.a) In how many ways can a group of 9 people work in 3 disjoint subgroups of 2, 3 and 4 persons? Write a function that generates all the possibilities and returns them in a list.27.b) Generalize the function to allow group sizes to be specified.
# # # THIS IS A STUB # # #
Result:
Solutions
# 99 Elm Problems/Problem 28

Sort a list of lists.28.a) Sort a list of list according to length of sublists28.b) Sort the elements of this list according to their length frequency; i.e., lists with rare lengths are placed first, others with a more frequent length come later.
# # # THIS IS A STUB # # #
Result:
Solutions
# A Textbook of Community Medicine/Medical Epidemiology

According to John M Last, Epidemiology is the study of the distribution and determinants of health-related states and events in specified populations and application of this study to the control of those health problems.
It is a scientific, systematic and data driven study of all health related states or events, not disease alone. Distribution of health related states in terms of time, place and person are studied. In other terms when and where the health related states occur and what are the characteristics of those affected. Magnitude of those health related states or events in terms of incidence and prevalence are studied. Determinants of the health related states and events include causes and risk factors of those conditions. Findings of the study is applied in controlling those health related states or events.

## References

* ↑ Last JM, editor. Dictionary of epidemiology. 4th ed. New York: Oxford University Press; 2001. p. 61.
* ↑ Principles of Epidemiology in Public Health Practice, Third Edition. An Introduction to Applied Epidemiology and Biostatistics, Centre for Disease Control and Prevention