Real Number Properties
In this assignment we were asked to solve three expressions using the properties of real numbers in order to do so. Each of the real number properties are essential in solving algebraic expressions. Although you may not need to use all of them in the same expression to solve you will need to use at least one. In this paper I will demonstrate the use of the properties and show the steps needed to solve each part of an expression. Understanding the properties of algebra is important because you must be able to use these properties in order to correctly put expressions and equations into their simplest form by moving terms around to solve or simplify the expression. Distribution is used to multiply across terms inside parentheses, allowing you to remove the parentheses for the problem. Moving terms to different locations is known as the commutative property. Combining like terms is referred to as the associative property.

2a(a-5)+4(a-5)
2a(a-5) + 4(a-5) This is the given expression, for problem number one. 2a^2-10a+4a-20 Using the distributive property I removed the parentheses. 2a^2-6a-20 I added the coefficients here in order to add the like terms. 2a^2-6a-20This is the simplest form of this expression.

2w-3+3(w-4)-5(w-6)
2w-3+3(w-4)-5(w-6)This is the given expression for problem number two. 2w-3+3w-12-5w-30Using the distributive property I removed the parentheses. 2w+3w-5w-3-12-30I used the commutative property to arrange the like terms. 5w-5w-15-30Two of the variable and two of constant terms are added here. 0-30The coefficients are added together.

30The expression is fully simplified.

0.05(0.3m+35n)-0.8(-0.09n-22m)
0.05(0.3m+35n)-0.8(-0.09n-22m)This is the given expression for problem number three. 0.015m+1.75n-0.72n-17.6mUsing the distribution I removed the parentheses. 0.015m-17.6m+1.75n-0.72nI used the commutative property to arrange the like terms. -17.58m+1.03nThe coefficients...

...promise, which is Ownership. Ownership of properties is not only a dream but also literally a right of passage in America that symbolizes newfound stature and success. In our society, these symbols have come under fire by those who would seek to take that away called the “Plaintiff”. This new stature comes in many forms but today we will talk about two that are in the most jeopardy and require legal protections, in the form of either RealProperty, or Intellectual Property. Realproperty (or realty) is a legal term for one of the two main classes of property in the common law, the other class being personal property (or personality). Although the precise definition of realproperty varies between jurisdictions, it usually encompasses land, rights over land and building or fixtures on land. Realproperty roughly, but not precisely, corresponds to the concept of immovable property in Civil law systems.
Second is Intellectual property. Intellectual property (IP) is a legal term that refers to creations of the mind such as musical, literary, and artistic works; inventions; and symbols, names, images, and designs used in commerce, including copyrights, trademarks, patents, and related rights. Under intellectual property law, the holder of one of these...

...Solution 2
General Comments
The aim of this question is to test whether students grasp the fundamental differences between real and personal
property. In their introduction, students should explain what is meant by the terms realproperty and personal
property. Students should also define what is meant by the term ‘land’ to indicate that it includes not just physical
territory. As part of their answer, students must therefore deal with corporeal and incorporeal hereditaments in realproperty. Finally, students should clearly set out the source and background of the differences between real and
personal property. Students will perform well where they offer detailed and clear explanations of all of the terms
mentioned.
Introduction
The law of realproperty or the realty of land law, in the words of Wylie is "concerned with rights and liabilities which
arise under our law with respect to land". Land, however, is not just physical territory; the term includes things
permanently attached to land, such as houses, buildings and other structures such as garden walls or fences.
Personal property or personalty covers all of the other forms of property. Realproperty is, as mentioned,
concerned with more than land, including buildings, as we understand the term....

...In mathematics, a realnumber is a value that represents a quantity along a continuous line. The realnumbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Realnumbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any realnumber can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include realnumbers as a special case.
These descriptions of the realnumbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the realnumbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently...

...The smallest integer that can be expressed as the sum of the cubes of two other integers in two different ways. 1729 = 93 + 103 = 13 + 123. (This was the subject of a very famous mathematical anecdote involving Srinivasa Ramanujan and G.H. Hardy, circa 1917. See A Mathematician's Apology by Hardy.
Rank, Prime number, Found by, Found date, Number of digits
1st, 257,885,161 − 1, GIMPS, 2013 January 25, 17,425,170 2nd, 243,112,609 − 1, GIMPS, 2008 August 23, 12,978,189
3rd, 242,643,801 − 1, GIMPS, 2009 April 12, 12,837,064 4th, 237,156,667 − 1, GIMPS, 2008 September 6, 11,185,272
5th, 232,582,657 − 1, GIMPS, 2006 September 4, 9,808,358 6th, 230,402,457 − 1, GIMPS, 2005 December 15, 9,152,052
7th, 225,964,951 − 1, GIMPS, 2005 February 18, 7,816,230 8th, 224,036,583 − 1, GIMPS, 2004 May 15, 7,235,733
9th, 220,996,011 − 1, GIMPS, 2003 November 17, 6,320,430 10th, 213,466,917 − 1, GIMPS, 2001 November 14, 4,053,946
-------------------------------------------------
History
The following table lists the progression of the largest known prime number in ascending order. Here Mn= 2n − 1 is the Mersenne number with exponent n.[4]
Number, Digits, Year found
M127, 39, 1876 180×(M127)2 + 1, 79, 1951 M521, 157, 1952 M607, 183, 1952 M1279, 386, 1952 M2203, 664, 1952 M2281, 687, 1952 M3217, 969, 1957 M4423, 1332, 1961 M9689,...

...-------------------------------------------------
Realnumber
In mathematics, a realnumber is a value that represents a quantity along a continuum, such as 5 (an integer), 3/4 (a rational number that is not an integer), 8.6 (a rational number expressed in decimal representation), and π (3.1415926535..., an irrational number). As a subset of the realnumbers, the integers, such as 5, express discrete rather than continuous quantities. Complex numbers include realnumbers as a special case. Realnumbers can be divided into rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two. A realnumber can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue indefinitely. The realnumbers are sometimes thought of as points on an infinitely long line called the number line or real line.
History
Vulgar fractions had been used by the Egyptians around 1000 BC; the Vedic "Sulba Sutras" ("The rules of chords") in, ca. 600 BC, include what may be the first 'use' of irrational numbers. The concept of irrationality was implicitly accepted by early Indian...

...
Module 5: Gulf Real Estate Properties
Many people dream of having a home with an ocean view from their home. Being able to walk onto your patio, sit, and admire a sunset sound like a scene in a Nicholas Sparks’ novel. So it should come to no surprise that homes with a scenic ocean view can demand a high price in the real estate market.
Below you will see just how different the price from a sample of Florida condominiums sold with and without views of the Gulf of Mexico can demand. The Gulf Real Estate Properties, Inc has provided data from 58 condominiums they have sold. The sample is broken up into 40 condominiums with Gulf of Mexico views, and 18 without.
Module 5: Gulf Real Estate Properties
Mean
“The mean is the average of the numbers. In other words it is the sum divided by the count,” (Math is Fun, 2014). Finding the mean of each sample of data is rather easy, you add them up and divide by the sample size. In every category the condominiums with a view out performed the other condominiums. The mean of the Gulf View Condominiums’ List Price and Sale Price are higher, and the number of days it takes to sell the home is less. To simplify the Gulf View Condominiums sell for more and quicker.
Gulf View Condominiums have a mean price of 600.73, while No Gulf View Condominiums have a mean of 204.95. The difference between these two...

...as well as the number of salaries above and below the mean.
Process
Display Program Title
Give instructions on the program
Open file for interactive input (write)
Prompt for Names and Salaries
Check for negative numbers
Check for sentinel value
Loop until sentinel value is entered
Get running total for Sum
Get running total for Count
Write input values to file
Close file after input
Determine if count is equal or greater than 1
Calculate average salary
Display average salary
Prompt for input Response
Determine if user wants to continue
Open file for batch processing (read)
Loop for processing file
Read salary field
Gather running total for both count variables
When the loop reaches EOF close file
Display count variables as output
Input
Input Name (Name: String)
Input Salary (Salary: Real)
Output
Display Average salary
Display Count_2 above average salary
Display Count_3 below average salary
Pseudocode
Main Module
Declare Name, Response As String
Declare...

...THE REALNUMBER SYSTEM
The realnumber system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers.
Natural Numbers
or “Counting Numbers”
1, 2, 3, 4, 5, . . .
* The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.
At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.
Whole Numbers
Natural Numbers together with “zero”
0, 1, 2, 3, 4, 5, . . .
About the Number ZeroWhat is zero? Is it a number? How can the number of nothing be a number? Is zero nothing, or is it something?Well, before this starts to sound like a Zen koan, let’s look at how we use the numeral “0.” Arab and Indian scholars were the first to use zero to develop the place-value number system that we use today. When we write a number, we use only...

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