Glossary

the total interest that will be paid in the year

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

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

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

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

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

describes the data when there are two modes

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

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

classifies the unit into a group (or category)

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.

describes the middle of a set of data

a sample where clusters of units are chosen at random, instead of choosing individual units

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

A set of numbers that are aligned vertically

A matrix consisting of one column

Inequalities that consist of more than one part

reinvestment of interest

the judgment made based on the premises

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

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

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

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

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

A consistent system of equations has at least one solution.

An equation that is false for all values of the variable

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

observations made on units

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

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

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

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

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

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

Any particular outcome or group of outcomes of a probability experiment

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

the product of an integer and all positive integers below it

A false or deceptive argument

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

a visual representation of all the solutions of the equation

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

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

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](0,b)[/latex].

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

An equation that is true for any value of the variable

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

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

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

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

A relation between two mathematical expressions that are not equal

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

The multiplicative inverse of a matrix

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. 

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

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.

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.

A literal equation is an equation where variables represent known values

two expressions that have the same truth value for all possible combinations of truth claues for all variables in the expressions.

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

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

the value that appears most often

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

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

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

An ordered pair, [latex](x,y)[/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.

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

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

The result of an experiment

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

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

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

lines in the same plane that form a right angle

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

the logical statements made to support the argument

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

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

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

is a numerical measure of a property of a unit

the difference between the maximum and minimum values in the set

data are bunched up at the low end, and taper off toward the high end

A set of numbers that are aligned horizontally

A matrix consisting of one row

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.

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

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

The set of all possible simple events

groups of units from which we collect data

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

Any entry of a matrix that results from scalar multiplication

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

An event that can only have a single outcome

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

the measure of the steepness of a line

slope m and y-intercept, [latex](0,b)[/latex] is [latex]y=mx+b[/latex].

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

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.

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

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.

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.

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

A matrix that has the same number of rows as columns

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

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

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

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

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.

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

A logical statement that is always true.

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.

data are equally distributed across the range

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

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

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].

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

The first number in an ordered pair.

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

The second number in an ordered pair.