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What is partitioning in mathematics?

The partition function represents the number of possible partitions of a natural number (n), or the number of distinct and order-independent ways of representing n as a sum of natural numbers. For example, the number 4 can be partitioned in five distinct ways: 1 + 3, 1 + 1 + 2, 1 + 2 + 1, 2 + 1 + 1, and 3 + 1. These partitions can be represented visually by a Young Diagram, which is a finite collection of boxes arranged in left-justified rows, with the row lengths decreasing.\nPartitioning is taught to young children in order to work with problems that involve large numbers by splitting them i..

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How do you calculate gross floor area?

Measure the floor areaMeasure the floor are by going through one room at a time. Measure both the length and width of each room. In the case of rooms that do not have a standard geometry, break the room up into smaller shapes and add the area. For example, consider a room that has a main section that is 10 feet wide and 10 feet long has a narrower section that is five feet wide and long. You would take the two areas, 100 ft^2 and 25 ft^2, and add them. Find the total area by adding all the room areas together at the end. Determine the length of the wallsUse the tape measure and measure the len..

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What is 10 to the sixth power?

Exponents are a way to quickly generate large numbers. Acceleration and compound interest are both examples of how even numbers that start small can quickly grow large if they are continually raised to the second power or higher. A number raised to a power means that the number is multiplied by itself however many times the power indicates.

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How do you add percentages?

To calculate the addition or subtraction of percentages, it is first necessary to understand the relationship between a percentage and its decimal representation.To Add a Percentage to a Given NumberMultiply the base number by 1 plus the percentage as a decimal. For example, to add 25 percent to the number 4: 4 x (1 + 0.25) = 4 x 1.25 = 5.To Add Two Percentages TogetherConvert the percentages to fractions with a common denominator and perform the simple addition operation. Then the answer may be converted back to a percentage. For example, to add 20 percent to 30 percent: 20 / 100 + 30 / 100 =..

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How do you calculate percentages of whole numbers?

"Percent" means "out of 100," and percentages are simply a quick way of writing fractions with a denominator of 100. For example, 72 percent is 72/100. To figure out what percentage one number (number A) is of another number (number B), divide number A by number B and multiply the answer by 100. For example, to determine what percentage 6 is of 24, first divide 6 by 24 to get .25. Multiply that value by 100 to get your answer: 25 percent.\nUnderstanding how to use percentages is useful for calculating discounts. When stores have sales offering a certain percentage off, figure out the final pri..

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What is a linear rule, and how does one write an equation with it?

Linear functions are written in the slope-intercept form of f(x) = mx + b, where m is the slope and b is the intercept. If the function is already in this form, substitute a value for x into the equation and solve it for y, then do the same for another value of x. Then, draw a line connecting the two points.\nIf two points are provided, determine the change in y and divide it by the change in x. For example, if the two points are (3, 2) and (5, 3), y increases by 1 and x increases by 2. This gives the resulting equation a value of 1/2 for m.\nNow, it's possible to find the value for b by ..

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How is the equivalent percentage figure for a number determined?

Percentage equivalents need not be confined to whole numbers. For example, the number .0572 can be expressed as 5.72 percent. As another example, .0001 becomes .01 percent, which is 1/100 of 1 percent.The use of percentages in computations existed prior to the invention of the decimal system and can be traced back to Ancient Rome. Taxes levied by the Roman emperor Augustus on certain goods were calculated as 1/100 of the sale amount. These tax computations were similar to the modern tax percentage calculations. The modern term "percent" is derived from the Latin phrase "per centum," which mean..

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What is an arithmetic sequence?

A mathematical sequence is a set of values in some order. In order for a sequence to be considered arithmetic, the terms of the sequence must have a common difference from one term to the next. For example, the sequence of counting numbers (1, 2, 3, 4, etc.) is arithmetic. The difference from each term to the next is 1. Each term can therefore be represented by x = a + d(n - 1), where "a" is the first term in the sequence, "d" is the difference between each term, and "n" is the number of the term in the sequence.\nThere are two types of arithmetic sequences: finite and infinite. A finite seque..

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How is the equation for a hyperbola determined?

The process of finding equations for hyperbolas begins with drawing a basic sketch of the hyperbolas. The value of the Y-term determines the shape of the hyperbola: if the term is negative and has a minus sign, the hyperbola will open to the left or right. If it is positive, however, the hyperbola opens on the vertical axis, and faces up or down. When finding the equation, it is best to begin by finding the center, as the rest of the graph builds around that value. Once the center is determined, the vertices can be determined, followed by the slopes of asymptotes. The asymptotes equate to the ..

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What is index form in mathematics?

A common question in math will be to write a number in index form using a different number as base. An example is being asked to write the number 16 in index form using base 2. Because 16 is 2x8, and 8 is 2x4, and 4 is 2x2, 16 in index form using base 2 would be written as 2^4.

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