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A detailed tutorial on what a composite solid is. Step by step tutorial including several examples of composite solids for reference.

A composite solid is exactly the same as a composite figure, only it is in 3D instead of in 2D. It is any kind of polyhedron (like a prism or a pyramid) that can be split into two or more of the basic types of polyhedrons in order to solve for the volume of the figure. Composite solids are very rare, and there are no regular types of solids that would be considered a composite solid.

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A detailed tutorial on how to make a histogram. Step by step tutorial including several examples on how to make a histogram for reference.

A histogram is similar to a bar chart or bar graph, only it cannot go in either direction – histograms can only have vertical bars. The main difference between them is that bar charts and bar graphs can be used to show the number of items in a category. Histograms are used between two sets of numbers, to show which numbers relate to each other. The numbers themselves each fall under their own category. This is a very common chart to see in the later levels of math, especially statistics, as they reflect statistical data.

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A detailed tutorial on zero pairs. Step by step tutorial including several examples of how to solve equations using zero pairs for reference.

Zero pairs are a method of adding and subtracting integers, and simplifying expressions with addition and subtraction in them. A zero pair is any pair of numbers that when added or subtracted, equal zero. Based on this definition, the only numbers that can form a zero pair, besides two zeros, are a negative number n and a positive number n. When in equations, zero pairs can be cancelled out, therefore simplifying the expression. This is very useful when more complicated equations are given.

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A detailed tutorial of difference in set theory. Step by step tutorial including several examples of difference in set theory for reference.

Difference is what you get after subtracting two numbers – or two sets. As with other examples of subtraction, order is very important for difference in set theory. Unless two sets are identical, you will end up with a different answer depending on the order. Difference is very often used in conjunction with union and intersection of sets or power sets.

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A detailed tutorial on the empty set. Step by step tutorial including several examples and a description of the properties of the empty set for reference.

The empty set is a unique set in set theory that means a set composed of nothing. In an empty set, there are no elements at all. The empty set has one very unique property – it is the subset of all sets. The set of all natural numbers up to infinity? It’s a subset. The set of prime numbers less than 20? It’s a subset of that, too. It is also a subset of itself – although that is not particurarly unique. The empty set is not used in equations, but can be used to define them.

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A detailed tutorial on power sets. Step by step tutorial including several examples of power sets and how to perform operations of power sets  for reference.

Power sets are defined as a set of all subsets. So for example, say you have a set A. The power set of A would be the set of all possible subsets of A. Power sets can also be used in normal operations, such as intersections and unions. All you do is find all possible subsets of both sets you are working with, and solve the problem like you would with a normal set.

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A detailed tutorial on the union and intersection of sets. Step by step tutorial including several examples of the union and intersection of sets for reference.

Set theory is a branch of mathematics that deals with sets of numbers and the way that they interact with each other. One part of set theory is union and intersection. Union is represented by the symbol U, and means to combine the numbers in a set. The union of A and B states that for all x in A and B, the union contains all x in A and all x in B. Intersection is represented by an upside-down letter U, and means to only use numbers that are found in both sets. The intersection of A and B states that for all x in A and B, the intersection contains all x found in both A and B. The definitions might seem similar, but they are different.

Union:

A = {1, 2, 3, 4}, B = {2, 3, 6, 7}. The union would be {1, 2, 3, 4, 6, 7}.

Intersection:

A = {1, 2, 3, 4}, B = {2, 3, 6, 7}. The intersection would be {2, 3}

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Description

A detailed tutorial on how to subtract decimals. Step by step tutorial including several examples of subtracting decimals for reference. It is a requirement to know how to subtract decimals for all math classes.

Overview

Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be a little tricky to figure out. The operation we will be talking about is subtraction. The most important thing to remember when doing anything with decimals is to match up the decimal points and add zeros onto the end if you need to. Then just subtract like you normally would, and remember to put your decimal point back in the right place.