Glossary

Annual percentage rate (APR)

The total interest that will be paid in the year.

Annual percentage yield (APY)

The real rate of return earned on an investment, taking into account the effect of compounding interest.

antecedent

The clause associated with the "if" statement in a compound statement.

Augmented matrix

A matrix in which we use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs.

bar chart

A visualization of categorical data that consists of a series of rectangles arranged side-by-side (but not touching).

bimodal

Describes the data when there are two modes.

binned frequency distribution

Groups the data into ranges of values called bins, then records the number of responses in each bin.

Boundary Line

The line with equation [latex]Ax+By=C[/latex] is the boundary line that separates the region where [latex]Ax+By > C[/latex] from the region where [latex]Ax+By

 

Categorical data

Classifies the unit into a group (or category).

categorical frequency distribution

A table with two columns. The first contains all the categories present in the data, each listed once. The second contains the frequencies of each category, which are just a count of how often each category appears in the data.

centrality

Describes the middle of a set of data.

cluster sample

A sample where clusters of units are chosen at random instead of choosing individual units.

Coefficient matrix

A matrix formed by extracting the coefficients from the system and writing them in a rectangular array.

Column

A set of numbers that are aligned vertically.

Column matrix

A matrix consisting of one column.

Compound inequalities

Inequalities that consist of more than one part.

compounding

Reinvestment of interest.

conclusion

The judgment made based on the premises.

conditional

Joining two logical statements with the word “implies” or using the phrase “if first statement, then second statement.”

Conditional Equations

An equation that is true for one value of the variable and false for all other values of the variable.

conditional probability

The probability of an event, given that another event has already occurred.

conjunction

The joining of two logical statements with the word "and" or "but."

consequent

The clause following the "then" statement in a compound statement.

Consistent system

A consistent system of equations has at least one solution.

contradiction

An equation that is false for all values of the variable.

contrapositive

The statement formed by interchanging and negating both the hypothesis and the conclusion of a conditional statement.

converse

The statement formed by interchanging the hypothesis and the conclusion of a conditional statement.

data 

Observations made on units.

deductive arguments

Deductive arguments attempt to draw specific conclusions from at least one or more general premises.

Dependent system

A dependent system is a consistent system whose equations have the same slope and the same y-intercepts.

Dimensions

The number of rows in a matrix by the number of columns in the matrix.

disjunction

The joining of two logical statements with the word “or.”

Entry

Each number in a matrix. An entry may also be called an element.

Equations

A mathematical relation in which two expressions are equal to each other.

Event

Any particular outcome or group of outcomes of a probability experiment.

Expected Value

The average gain or loss of an event if the procedure is repeated many times.

factorial

The product of an integer and all positive integers below it.

fallacy

A false or deceptive argument.

Gaussian elimination

Gaussian elimination method refers to a strategy used to obtain the row-echelon form of a matrix.

graph

A visual representation of all the solutions of the equation.

Hasty generalization

The name given to any fallacy that presents a weak inductive argument.

Histograms

Visualizations that can be used for any set of quantitative data, no matter how big or spread out.

Horizontal line

A horizontal line is the graph of an equation of the form [latex]y=b[/latex]. The line passes through the y-axis at latex[/latex].

hypothesis 

The clause following the "if" statement in a compound statement.

identity

An equation that is true for any value of the variable.

Identity matrix

A square matrix containing ones down the main diagonal and zeros everywhere else; the identity matrix acts as a 1 in matrix algebra.

Inconsistent system

A system of equations in which the equations represent two parallel lines; hence, there is no solution to the system.

Independent system

An independent system is a consistent system that has a single solution.

inductive arguments

Logical arguments that begin with specific premises and attempt to draw more general conclusions.

Inequality

A relation between two mathematical expressions that are not equal.

Intercepts of a Line

The points where a line crosses the x-axis and the y-axis are called the intercepts of the line.

Inverse

The multiplicative inverse of a matrix.

law of detachment

A valid form of a conditional argument that asserts that if both the conditional, [latex]p rightarrow q[/latex], and the hypothesis, [latex]p[/latex], are true, then the conclusion [latex]q[/latex] must also be true.

left-skewed

Data are bunched up at the high end or larger values and taper off toward the low end or smaller values.

Linear Equation

An equation of the form [latex]Ax+By=C[/latex] where A and B are not both zero is called a linear equation in two variables.

Linear Inequality

A linear inequality is an inequality that can be written in one of the following forms: [latex]Ax+By > C[/latex], [latex]Ax+By \geq C[/latex], [latex]Ax+By < C[/latex], or [latex]Ax+By \leq C[/latex], where A and B are not both zero.

Literal equations

A literal equation is an equation where variables represent known values.

logically equivalent

Two expressions that have the same truth value for all possible combinations of truth clauses for all variables in the expressions.

Main diagonal

The matrix entries that lie on the diagonal from the upper left corner to the lower right corner of a matrix.

Matrix

A matrix is a rectangular array of numbers arranged into rows and columns.

mode

The value that appears most often.

multiplication principle

States that the number of ways you can select an item from a group of n items and another item from a group with m items is equal to the product of m and n.

Multiplicative inverse of a matrix

A matrix whose product with another matrix results in the identity matrix; also called the inverse of a matrix.

negation of a conditional

The negation of any statement has the opposite truth values of the original statement.

Ordered pair

An ordered pair latex[/latex] gives the coordinates of a point in a rectangular coordinate system. The first number is the x-coordinate. The second number is the y-coordinate.

ordinary annuities

An annuity where the payment is made at the end of the period.

Origin

The point [latex](0,0)[/latex] is called the origin. It is the point where the x-axis and y-axis intersect.

Outcome

The result of an experiment.

Parallel

Parallel lines are lines in the same plane that do not intersect.

payout annuity

With a payout annuity, you start with money in the account and pull money out of the account on a regular basis.

Perpendicular

Perpendicular lines are lines in the same plane that form a right angle.

Perpendicular lines

Lines in the same plane that form a right angle.

pie chart

Consists of a circle divided into wedges, with each wedge corresponding to a category.

premises

The logical statements made to support the argument.

Principal

The amount your account starts with, such as a starting investment or the amount of a loan.

Quadrants

The four regions formed by the intersecting x- and y-axes.

quantifier

A term that expresses a numerical relationship between two sets or categories.

Quantitative data

A numerical measure of a property of a unit.

range

The difference between the maximum and minimum values in the set.

rectangular coordinate system

A grid system used in algebra to show a relationship between two variables and formed by intersecting one horizontal line, called the x-axis, with a vertical line, called the y-axis.

right-skewed

Data are bunched up at the low end and taper off toward the high end.

Row

A set of numbers that are aligned horizontally.

Row matrix

A matrix consisting of one row.

Row operations

These are all operations that can be performed on a matrix without changing the solution to the corresponding system. These operations include addition, multiplication, and interchanging rows.

Row-echelon form

A matrix form in which there are ones down the main diagonal and zeros in every position below the main diagonal.

Row-equivalent

Matrices that can be changed from one to another by employing a sequence of row operations.

Sample space

The set of all possible simple events.

samples 

Groups of units from which we collect data.

savings annuity

Saving for the future by depositing a smaller amount of money from each paycheck into the bank.

Scalar multiple

Any entry of a matrix that results from scalar multiplication.

Scalar multiplication

Scalar multiplication involves finding the product of a constant by each entry in the matrix.

Simple event

An event that can only have a single outcome.

simple random sample

Chosen in a way that every unit in the population has an equal chance of being selected, and the chances of a unit being selected do not depend on the units already chosen.

slope

The measure of the steepness of a line.

slope–intercept form of an equation of a line

Slope m and y-intercept, latex[/latex] is [latex]y=mx+b[/latex].

Solution

A solution is a value of a variable that makes a true statement when substituted into the equation.

Solution of a Linear Equation in Two Variables

An ordered pair [latex](x,y)[/latex] is a solution of the linear equation [latex]Ax+By=C[/latex] if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.

solution set

A set of numerical values for each variable in the system that will satisfy all equations in the system at the same time.

Solution to a linear inequality

An ordered pair [latex](x,y)[/latex] is a solution to a linear inequality if the inequality is true when we substitute the values of x and y.

Solution to a system

A solution to a system is a set of numerical values for each variable in the system that will satisfy all equations in the system at the same time.

sound

A logical argument is sound if it is valid and all of its premises are true.

Square matrix

A matrix that has the same number of rows as columns.

Standard Form of Linear Equation

A linear equation is in standard form when it is written [latex]Ax+By=C[/latex].

Stem-and-leaf plots

Consists of a list of stems on the left and the corresponding leaves on the right, separated by a line.

stratified sample

Chosen so that particular groups in the population are certain to be represented.

symmetric

Data are bunched up in the middle, then taper off in the same way above and below the middle.

System of linear equations

A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously.

systematic random sample

Selected from an ordered list of the population (for example, names sorted alphabetically or students listed by student ID).

tautology

A logical statement that is always true.

uniform

Data are equally distributed across the range.

units 

Anything that can be measured or surveyed (such as people, animals, objectives, or experiments).

valid

A logical argument is valid if its conclusion follows from the premises.

Vertical line

A vertical line is the graph of an equation of the form [latex]x=a[/latex]. The line passes through the x-axis at [latex](a,0)[/latex].

x-axis

The horizontal number line that intersects with a vertical number line to form the rectangular coordinate system.

X-coordinate

The first number in an ordered pair.

Y-axis

The vertical number line that intersects with a horizontal number line to form the rectangular coordinate system.

Y-coordinate

The second number in an ordered pair.

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