Qualitative data is data that can be observed but cannot be measured. This type of data is often in contrast to quantitative data, which is data that can be measured.
A:The sum of x² plus x² is 2x². The problem requires adding one x squared to one more x squared, which equals two x squared. Substituting 3 for x, 3² + 3² = 2(3²), or 9 + 9 = 18.
A:Imaginary numbers are typically simplified in the same way that expressions with the variable x are simplified, with the exception of the expression i^2, which has a value equal to -1. For example, the expression 2i + 8i can be simplified by writing it first as (2 + 8) * i, with the final expression written as 10i.
A:The man known as "the father of modern algebraic notation" was French mathematician Francois Viète, according to the math department at Rutgers University. His substitution of letters to mark unspecified or unknown number quantities is recognized as the beginning step in the creation of the algebraic system.
A:Algebra has been developed over thousands of years in several different countries. The earliest methods for solving mathematical problems with one or more unknown quantities come from ancient Egypt. The word "algebra" itself is derived from the title of Baghdad mathematician Al-Kwarizmi's 9th century book, "Hidab al-jabr wal-muqubala."
A:The word "equation" is related to the word "equals" and generally describes a state of balance or equilibrium, according to Dictionary.com. Equations are commonly used in mathematics and chemistry.
A:Quadratic equations govern many real world situations such as throwing a ball, calculating certain prices, construction, certain motions and electronics. They are most often used to describe motion of some sort.
A:Math is useful for economics, science, sports, social fields and a wide range of other areas for making decisions and analyzing information. Basic math skills are essential for many jobs. Math has been a core component of many human advances.
A:The abacus is a counting frame used since ancient times as a calculating device. The word abacus is derived from the Greek word "abax" meaning "flat surface."
A:A cool math game that is available online is "2048" and is offered as a mobile application. Cool Math 4 Kids offers math games geared toward children, including "The Timernator" and "Arithmetic Game."
A:A factor is a number or expression that divides another number or expression evenly without a remainder. For instance, two, four, five and 10 are factors of 20 because 20 can be divided by all those smaller numbers an exact number of times. Prime numbers are positive integers greater than one that have exactly two factors. A composite number has more than two factors.
A:"Digits" are the symbols or characters used to represent a number visually. A number like five contains one digit, whereas a number like 555 contains three digits. This is easily seen when they are written as numerals: 5 versus 555.
A:A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
A:The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.
A:A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
A:According to class notes from Bunker Hill Community College, calculus is often used in medicine in the field of pharmacology to determine the best dosage of a drug that is administered and its rate of dissolving. Usually, the drug is slowly dissolved in the stomach.
A:A Riemann sum is a method of approximating the area under the curve of a function. It adds together a series of values taken at different points of that function and multiplies them by the intervals between points. The midpoint Riemann sum uses the x-value in the middle of each of the intervals.
A:To calculate bulk density, simply weigh the sample and divide its mass by its volume. Bulk density is commonly used when referring to solid mixtures like soil. Just like particle density, bulk density is also measured in mass per volume.
A:Several types of graphs are used for displaying information in mathematics including the bar graph; pie chart or circle graph; histogram; stem and leaf plot; dot plot; scatter plot; and time-series graphs. The type of graph chosen depends on whether the data is quantitative, qualitative or paired.
A:To make a tally chart, single lines are drawn next to one another until reaching five, where the fifth line crosses the four other lines diagonally. This is a simple charting method that can be used quickly for surveys or other needs.
A:A line graph is a graph that charts the relationship between two variables or a progression of a single quantity through time. Without the lines connecting points of data, it would be difficult to make sense of the data being presented if there was no overall trend between the dots. A bar graph, on the other hand, is meant to compare two or more statistics, such as population figures.
A:A pie graph is an effective visual tool used for showing how something breaks into parts. A pie graph is essentially a circle sliced into 100 pieces. Each category or part represented in the pie graph is given a piece of the pie to represent the percentage that it comprises of the whole.
A:Graphs are beneficial because they summarize and display information in a manner that is easy for most people to comprehend. Graphs are used in many academic disciplines, including math, hard sciences and social sciences. They make appearances in corporate settings, serving as useful tools to convey financial information and facilitate data analysis.
A:The primary advantage of using a graph or chart in a presentation is that they help the audience to visualize the point of the presentation. Graphs emphasize the main point, make the data more convincing, provide a compact way of presenting information and help audiences stay engaged. Disadvantages of graphs include being time consuming to construct and costly to produce. They also require technology that some may lack.