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Mastering the Formal Geometry Proof

Suppose you need to solve a crime mystery. You survey the crime scene, gather the facts, and write them down in your memo pad. To solve the crime, you take the known facts and, step by step, show who committed [more…]

Sizing Up the Area of a Polygon

Not only can polygons be classified by the number of sides they have and by their angles, but they can also be grouped according to some of their qualities. Polygons can have three personality characteristics [more…]

Simple and Easy Geometry Tips and Tools

The first rule of life? Life (as well as geometry) can be difficult. But why make it more difficult than it has to be? Do you need help with geometry? Here are 11 tried-and-true tips to make your forays [more…]

Measuring and Making Angles

On a map, you trace your route and come to a fork in the road. Two diverging roads split from a common point and form an angle. The point at which the roads diverge is the [more…]

Classifying Three Types of Triangles

Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves. That is, a triangle has [more…]

How SPSS (Statistical Package for the Social Sciences) Works

The developers of the Statistical Package for the Social Sciences (SPSS) made every effort to make the software easy to use. This prevents you from making mistakes or even forgetting something. That's [more…]

Defining the Radian in Trigonometry

A person's introduction to angles is usually in terms of degrees. You probably have a good idea of what a 45-degree angle looks like. And even most middle-school students know that a triangle consists [more…]

Discovering Pythagorean Triples

The Pythagorean Theorem is certainly one of the most famous theorems in all of mathematics. Mathematicians and lay people alike have studied it for centuries, and people have proved it in many different [more…]

Mathematical Matryoshka: Counting Numbers, Integers, Rational Numbers, and Real Numbers

When you first start dealing with numbers, you learn about the four main sets, or groups, of numbers, which, like Russian matryoshka dolls, nest inside one another: [more…]

Figuring Out What Probability Means

Probabilities come in many different disguises. Some of the terms people use for probability are chance, likelihood, odds, percentage, and proportion. But the basic definition of [more…]

Multiplying with Scientific Notation

Multiplying numbers that are in scientific notation is fairly simple because multiplying powers of 10 is so easy. Here's how to multiply two numbers that are in scientific notation: [more…]

The Four Ways to Talk to SPSS

More than one way exists for you to command the Statistical Package for the Social Sciences (SPSS) to do your bidding. And you don't have to choose one and stick with it — you can perform tasks using whichever [more…]

Using Probability When Hitting the Slot Machines

Remember the movie National Lampoon's Vegas Vacation, when gambling fever consumes Chevy Chase's character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty [more…]

Generalizing Statistical Results to the Entire Population

Making conclusions about a much broader population than your sample actually represents is one of the biggest no-no's in statistics. This kind of problem is called [more…]

Crunching Numbers: Writing in Scientific Notation

Scientific notation is a system for writing very large and very small numbers that makes them easier to work with. Every number can be written in scientific notation as the product of two numbers: [more…]

Building Logical Arguments

When people say "Let's be logical" about a given situation or problem, they usually mean "Let's follow these steps:"

1. Figure out what we know to be true. [more…]

Statistics Conundrums: Dealing with Survey Nonresponders

Nonresponders are always a problem when you're calculating the results of a survey. Before you can crunch the numbers in all the surveys you get back, you have to decide what to do about the surveys you [more…]

How to Use the Order of Operations

Follow the order of operations with each algebra problem you solve. The order of operations in algebra is important if you want to find the correct answer. You first work through any grouping symbols, [more…]

Cramer’s Rule for Linear Algebra

Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]

Algebraic Permutations and Combinations

In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]

Eight Basic Algebraic Curves

Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs. [more…]

Algebra Equations for Multiplying Binomials

In algebra, multiplying binomials is easier if you recognize their patterns. You multiply the sum and difference of binomials and multiply by squaring and cubing to find some of the special products in [more…]

Algebra’s Quadratic Formula

You can find solutions for quadratic equations by factoring, completing the square, guessing, or everyone's favorite — using the quadratic formula. The best thing about the quadratic formula [more…]

Rules for Radicals — the Algebraic Kind

Working with radicals can be troublesome, but these equivalences keep algebraic radicals from running amok. Finding the root of product or quotient or a fractional exponent is simple with these formulas [more…]

Algebra’s Laws of Logarithms

Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1. [more…]

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