Math

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What is the origin of mathematical symbols?

Math was practiced as far back as Ancient Egypt, with numbers denoted with tally marks as opposed to the numerals that are used in modern times. Over the years, the symbols used in mathematical notation changed and varied wildly between countries and individuals, because there was no centralized system for a very long time.\nAcceptance of the mathematical symbols that people are familiar with today is thanks to the creation of a system that began hundreds of years ago. The symbols that create the formulas and equations that are taught in schools in the United States stem from ideas from Ancien..

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What does "zero-sum gain" mean?

The phrase "zero-sum" can be best understood by looking at it from a mathematical point of view. For example, two people make a bet for $5. The person that wins now has positive $5, and the person that loses has negative $5. Adding +5 and -5 gives a sum of 0.\nA win-win situation is an example that is not zero-sum. In this kind of situation, both participants gain something, so this is considered a positive-sum game.

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What is profile leveling?

Profile leveling is also defined as a surveying method carried out along a central line of a piece of land on which linear engineering work is to be conducted. The route of the profile can be a straight line such as a short sidewalk, a broken line such as a sewer or transmission line or a series of straight lines connected by curves such as a canal or railroad.

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What are examples of variables that follow a poisson distribution?

Discrete random variables are essentially counts; they are distinguished from continuous random variables because they are not measurements with expected growth. A discrete random variable is the number of the quantity in question, in a given area, within a given time. To provide an analogy in the difference between a discrete random variable and a continuous random variable, the discrete random variable is a snapshot of time, while a continuous random variable is streaming footage.\nTo further illustrate the property of discrete random variables, in a real life example, consider the number of..

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What are some examples of how to complete long division problems?

If the divisor is 32 and the dividend is 487, the first step is to divide 32 by the first digit of the dividend, which is 4. The result is 0, so we move onto the first two digits of the dividend, which is 48. The result of 48 divided by 32 is 1, and the remainder is 16. Place this remainder of 16 in front of the next digit, which is 7. Therefore, the next step is to divide 167 by 32. The result is 5, and the remainder is 7. Because there are no more additional digits in the dividend, the final solution to 487 divided by 32 is 15. This is determined by combining each result in sequential order...

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How do you write exponents in expanded form?

For example, if a number is given in exponent form as A^6, then this is expressed in expanded form as A x A x A x A x A x A. If A is replaced by the number 3, then the exponent is 3^6. To evaluate this exponent, multiply 3 by itself 6 times to find the answer as 729. This exponent is read as 3 raised to the 6 power. Evaluating exponents is simply repeated multiplication of the base as a factor the number of times given by the power. When writing exponents in expanded form, it is also important to know certain rules, especially when using negative powers. For example, A^(- B) has to be expresse..

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Do regular calculators give you percentages?

Some basic calculators have a percentage button included. There are two ways for these buttons to calculate values depending on how the calculator was programmed. The percentage button either reads the input as the percent in question i.e. 90 [+] 10 [%] = 99, or it can interpret that input to the value of the fraction, as in this example 90 [+] 10 [%] = 90.1.

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What resources are used to solve math equations?

In classes or projects involving algebra and functions, students need a tool capable of the Computer Algebra System for symbols, equations, inequalities, decimals, graphs and more. They may also need a tool for spreadsheets to be able to compute and store data to integrate into graphs and tables. While some of these functions are within the range of a graphing calculator, a spreadsheet program makes it easier to manipulate the data.\nIn geometry or trigonometry classes, it is useful to have an interactive geometry tool that lets students form shapes and manipulate them according to different a..

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What is "direct isometry"?

Opposite isometry is reflected in line reflection, dilations and glide reflection. The same properties are preserved, except distance is not preserved with dilations. Also with dilations, the letter order is the same, which ironically is a characteristic of direct isometry. With glide reflection and line reflection, there is reverse orientation, which means the letter order is changed.

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What is the natural log of e?

The natural logarithm function is the log function to the base of e, rather than to the base 10, as with the function log(x). The natural log of e can be solved using the natural log's exponential properties, where the ln(e^x) is always equal to x when x is a number greater than zero. The reverse of this rule is expressed as e^ln(x) = x.

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