Mario Banuelos, PhD
Associate Professor of Mathematics
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Co-authored Articles (34)
How to
Calculate Weighted Average
A weighted average, otherwise known as a weighted mean, is a little more complicated to figure out than a regular arithmetic mean. As the name suggests, a weighted average is one where the different numbers you’re work...
How to
Find the Inverse of a 3x3 Matrix
Struggling with a tough algebra problem? Finding the inverse of a matrix is key to solving systems of linear equations. Plus, inverse operations provide an easy way to simplify difficult problems in general. For example,...
How to
Calculate Angles
In geometry, an angle is the space between 2 rays (or line segments) with the same endpoint (or vertex). The most common way to measure angles is in degrees, with a full circle measuring 360 degrees. You can calculate th...
How to
Calculate Square Meters
Square meters are a measurement of ''area'', usually used to measure a two-dimensional space such as a field or floor. For example, you might measure the footprint of a couch in square meters, then measure your living ro...
2 Different Ways to Find a Circle’s Arc Length
Determining the arc length of a circle is easy with these simple formulas If you’re learning about arc lengths in geometry, your teacher probably just assigned you a bunch of problems for homework. You’ve got the cir...
How to
Calculate Probability
Chances are (pun intended) you've encountered probability by now, but what exactly is probability, and how do you calculate it? Probability is the likelihood of a specific event happening, like winning the lottery or rol...
How to
Algebraically Find the Intersection of Two Lines
When straight lines intersect on a two-dimensional graph, they meet at only one point, described by a single set of x- and y-coordinates. Because both lines pass through that point, you know that the x- and y- coordinate...
How to
Multiply Fractions With Whole Numbers
It's easy to multiply fractions by mixed fractions or whole numbers. Start by turning your mixed fractions or whole numbers into improper fractions. Then multiply the numerators of both improper fractions. Multiply the d...
How to
Find the Null Space of a Matrix
The null space of a matrix A is the set of vectors that satisfy the homogeneous equation A\mathbf{x} = 0. Unlike the column space \operatorname{Col}A, it is not immediately obvious what the relationship is between the co...
How to
Calculate Variance
What is variance? Variance is a measure of how spread out a data set is, and we calculate it by finding the average of each data point's squared difference from the mean. It's useful when creating statistical models sinc...
How to
Find the Inverse of a Function
A foundational part of learning algebra is learning how to find the inverse of a function, or f(x). The inverse of a function is denoted by f^-1(x), and it's visually represented as the original function reflected over t...
How to
Find the Least Common Denominator
In order to add or subtract fractions with different denominators (the bottom number of the fraction), you must first find a common denominator shared between them. In order to have the simplest fraction at the end, it i...
How to
Solve Fraction Questions in Math
Fraction questions can look tricky at first, but they become easier with practice and know-how. Start by learning the terminology and fundamentals, then pratice adding, subtracting, multiplying, and dividing fractions. O...
How to
Reduce a Matrix to Row Echelon Form
The row-echelon form of a matrix is highly useful for many applications. For example, it can be used to geometrically interpret different vectors, solve systems of linear equations, and find out properties such as the de...
How to
Divide Matrices
If you know how to multiply two matrices together, you're well on your way to "dividing" one matrix by another. That word is in quotes because matrices technically cannot be divided. Instead, we multiply one matrix by th...
How to
Calculate Z Scores
A Z score allows you to take any given sample within a set of data and to determine how many standard deviations above or below the mean it is. To find the Z score of a sample, you'll need to find the mean, variance and ...
How to
Find Scale Factor
The scale factor, or linear scale factor, is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are of different sizes. The scale factor is used to solve geometric pro...
How to Add Mixed Numbers Together
Add mixed fractions in a snap with this step-by-step guideA mixed number is a whole number next to a fraction, such as 5 ½, and can be difficult to add. If you want to learn how to add mixed numbers, read this article.
How to
Find the Area of a Regular Pentagon
A pentagon is a polygon with five straight sides. Almost all problems you'll find in math class will cover regular pentagons, with five equal sides. There are two common ways to find the area, depending on how much infor...
How to
Calculate P Value
''P value'' is a statistical measure that helps scientists determine whether or not their hypotheses are correct. P values are used to determine whether the results of their experiment are within the normal range of valu...
