Leipzig is the most populous city in the federal state of Saxony, Germany. With a population of 582,277 inhabitants (1.1 million residents in the larger urban zone) it is Germany's tenth most populous city. Leipzig is located about southwest of Berlin at the confluence of the White Elster, Pleisse, and Parthe rivers at the southern end of the North German Plain.

Leipzig has been a trade city since at least the time of the Holy Roman Empire. The city sits at the intersection of the Via Regia and Via Imperii, two important medieval trade routes. Leipzig was once one of the major European centers of learning and culture in fields such as music and publishing. Leipzig became a major urban center within the German Democratic Republic (East Germany) after the Second World War, but its cultural and economic importance declined.

Leipzig later played a significant role in instigating the fall of communism in Eastern Europe, through events which took place in and around St. Nicholas Church. Since the reunification of Germany, Leipzig has undergone significant change with the restoration of some historical buildings, the demolition of others, and the development of a modern transport infrastructure. Leipzig today is an economic center, the most livable city in Germany, according to the GfK marketing research institution and has the second-best future prospects of all cities in Germany, according to HWWI and Berenberg Bank. Leipzig Zoological Garden is one of the most modern zoos in Europe and ranks first in Germany and second in Europe according to Anthony Sheridan. Since the opening of the Leipzig City Tunnel in 2013, Leipzig forms the centerpiece of the S-Bahn Mitteldeutschland public transit system. Leipzig is currently listed as Gamma World City and Germany's "Boomtown". What are the answers to this following set of questions: 1. What is the 10th populous city in Germany?
2. DId this city have anything to do with communism?
3. What?
4. What federal state is in it?
5. Is it a good city for trade?
6. How long ?
7. What is Leipzig according to GfK marketing research instituation?
8. Anything else?
9. Is it important to the S-Bahn Mittledeutschland transit system?
10. Why?
11. Did something open in 2010?
Answer: 1. Leipzig
2. Yes
3. the fall of communism
4. Saxony
5. Yes
6. Holy Roman Empire
7. economic center
8. most livable city in Germany
9. Yes
10. the centerpiece
11. No

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number "x" to its square "x". The output of a function "f" corresponding to an input "x" is denoted by "f"("x") (read ""f"of"x""). In this example, if the input is 3, then the output is 9, and we may write . Likewise, if the input is 3, then the output is also 9, and we may write . (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function.

Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation. What are the answers to this following set of questions: 1. What are functions?
2. Between what?
3. What are different types of function in today's mathematics?
4. What sort of image could you use to describe them?
5. How could a function's representation be implied?
6. Any other way?
7. What way is that?
8. How could a function be directly defined?
9. Can each input give many outputs?
10. Can an output give many inputs?
Answer: 1. relations
2. inputs and outputs
3. the central objects of investigation
4. a graph
5. as the inverse to another function
6. yes
7. a solution of a differential equation
8. by a table
9. no
10. yes

When Charles Strattion was five, he stopped growing. His mother took him to see the famous showman, P. T. Barnum, and thought a small person would be the perfect addition to his show. He hired Charles' parents along with him, and they traveled around the world together. He gave the two-foot-tall Charles a new name, general Tom Thumb. He taught Tom how to sing, dance, act, and tell jokes. When he felt Tom was ready to perform on stage, he made up ads. To stir up great interest, he said that Tom was eleven years old and had come from England. Tom's act was very popular and brought in a lot of money. By the time Tom was an adult, he had grown very rich. He had become a billionaire at the age of twenty-five. Fortunately for Tom, Mr. Barnum added more little people to his show, and Tom became lucky in love as well. One of the little people was Lavinia Warren, a school teacher. Tom was able to win her love, and they married. The ceremony and reception were _ They were attended by many rich and famous people and by about two thousand guests. Crowds filled the street of New York to have a look at their tiny wedding carriage. The couple even met with President Abraham Lincoln on their honeymoon, just before going to live in Tom's house in Connecticut. Their wedding, which took place during the Civil War, provided a welcome escape from the sad problems of war. Not willing to let this bit of sunshine fade, communities throughout the country held Tom Thumb's weddings. In these weddings, small boys and girls, all dressed up, went through marriage ceremony for fun. What are the answers to this following set of questions: 1. Who stopped growing?
2. At what age?
3. What is his new name?
4. Who did his mom take him to see?
5. Was Tom shown how to sing and perform acts?
6. Who was his wife?
7. What was her profession?
8. Was his act popular?
9. Was he rich?
10. At what age did he become wealthy?
11. Who did they meet on their honeymoon?
12. Where was his house located?
13. The wedding took place during what?
14. And how many guests attended?
15. Which state did they marry in?
Answer: 1. Charles Strattion
2. five
3. General Tom Thumb
4. P. T. Barnum
5. Yes
6. Lavinia Warren
7. teacher
8. Yes
9. Yes
10. twenty-five.
11. Abraham Lincoln
12. Connecticut
13. Civil War
14. about two thousand guests.
15. New York

I'm Marie. I work in a nursing home and my job is to look after the old people. Alice is one of them. She's a very nice old woman. This year, Alice had a difficult time. She went to hospital twice. In November, I finally could get her back to her "home". Alice hoped that her daughter could come to visit her on Christmas Eve because she wanted to be with her family, like the old days. But her daughter was coming after Christmas, so she was very sad. I also felt sad because she would be alone on the holiday! On Christmas Eve, I took her to a candlelight service at church that night. I didn't take her to my church. I took her to the church in her old neighborhood. We got there early and I let her sit near the door, so people could see her when they came in. Soon some of her friends came to the church and they all talked to her and sat with her. Alice got a lot of love from her old and new friends there. She said she loved the gift like this. That night, I thought I got the best gift: the smile on Alice's face. . What are the answers to this following set of questions: 1. What is Marie's job?
2. Is there one in particular?
3. What is her name?
4. Is Alice healthy?
5. Was she home the whole time?
6. Is she home now?
7. When did she get there?
8. Why was she sad?
Answer:
1. look after old people
2. yes
3. Alice
4. no
5. no
6. yes
7. In November
8. her daughter wouldn't be there on christmas eve