APPLIED ALGEBRA EXAM 5 QUESTIONS
WITH DETAILED VERIFIED ANSWERS
Equation
A mathematical statement that two things are equal; it consists of two expressions, one on each
side of an equals sign.
Data
A collection of facts, which might be numbers, words, measurements, observations or simply
descriptions.
Graph
A diagram showing the relationship between variable quantities on two axes drawn at right
angles.
Quantitative
A variable that is measured on a number scale; a variable with a numeric value.
Quantitative variables are number-related; they are things that you can count or measure.
Qualitative
A variable that is not numeric; also called a categorical variable, a qualitative variable describes
data that fits into categories.
Qualitative variables have to do with non-number characteristics; these are things that you
usually observe but do not count or measure.
Independent Variable
The independent variable is the variable that explains, influences, or affects the other variable.A
variable that, as it changes, affects another variable (called the dependent variable); for example,
as a person pumps more gas into a car's tank (the independent variable), the cost of the purchase
rises (the dependent variable).
,The independent variable is the variable that explains, influences, or affects the other variable.
The independent variable is put on the x-axis, or horizontal axis, on a graph.
Examples:
Consider any occupation where someone earns an hourly wage. At $15 per hour, the number of
hours worked influences total pay, so the number of hours worked is the independent variable.
This is because the number of hours worked explains how much the individual is paid.
In the example about children's height, the age of a child influences his or her height, so age is
the independent variable. Clearly, a child's height does not influence his or her age.
Finally, in the example about ordering computers, since the number of computers in the office
drives the cost, the number of computers is the independent variable.
Sometimes it can be hard to identify the independent variable without context. In fact, sometimes
the independent variable can change depending on context as well. It is always important to pay
attention to the context of variables in all situations.
You own a car wash that charges $10 for each car that goes through. If you wash 50 cars a day,
your revenue is $10×50=$500. If you only wash 20 cars a day, your revenue is $10×20=$200.
Which variable is the independent variable?
ince the number of cars washed affects your revenue, the number of cars is the independent
variable.
Dependent Variable
A variable that is changed by another variable (called the independent variable); for example,
when a person is purchasing gas, the cost (the dependent variable) rises as more gas is pumped
,into a car's tank (the independent variable).
The dependent variable is the variable that responds to the independent variable; that is, the
dependent variable responds to change.
On a graph, the dependent variable is usually labeled on the y-axis, which is the vertical axis.
In the example about making $20 per hour, pay is the dependent variable. Another way of saying
this is that because the pay responds to, or is affected by, the number of hours worked, pay is the
dependent variable.
In the example about children's height, height is the dependent variable.
Finally, in the example about ordering computers, cost is the dependent variable.
As with the independent variables, it can sometimes be hard to identify the dependent variable
without context. Also, remember that the independent and dependent variables sometimes switch
depending on context, so be careful when you assess every situation.
Independent VS Dependent Variables
In general, think of the independent variable as the input and the dependent variable as the
output. Stated another way, the independent variable's input influences what output, or outcome,
you get from the dependent variable.
Input
A quantitative variable that is chosen to find a solution, or output, of a function.
Output
A quantitative variable that is produced by a function when an input is chosen.
Variable
, What is a variable? Simply said, it is something that can vary.
Variables are letters that represent values that change frequently, and variables are often used in
mathematical expressions and in careers.
Function
A function is useful because it expresses the relationship between two quantities, where one
quantity, called the output, is determined by the value of another quantity, called the input.
A relation based on a set of inputs and a set of possible outputs where each input is related to
exactly one output.
Many real-world events can be modeled by functions. Functions are important building blocks
for understanding things like economic production of goods, financial analysis, population
growth, and even the spreading and curing of diseases.
In computer science, the phrase "garbage in, garbage out" expresses the idea that in
programming, incorrect data or poor quality input always produces faulty output, or "garbage."
The best part is that you can use functions to predict future and past values.
Function notation uses the input and output variables to show the relationship and is written
f(input) = output, where variables are used for each quantity.
For example, predicting revenue is important in business. Revenue is based on how many units
of a product are sold. If your company sells wireless speakers for $60 each, then the expression
R(n)=60n models the revenue, R, when n speakers are sold. The number of speakers sold is the
input, and revenue is the output.
Consider this example: As an IT manager, you are responsible for upgrading the computer
systems for your company. A new software package might cost a flat fee of $87.50 plus $2 per
WITH DETAILED VERIFIED ANSWERS
Equation
A mathematical statement that two things are equal; it consists of two expressions, one on each
side of an equals sign.
Data
A collection of facts, which might be numbers, words, measurements, observations or simply
descriptions.
Graph
A diagram showing the relationship between variable quantities on two axes drawn at right
angles.
Quantitative
A variable that is measured on a number scale; a variable with a numeric value.
Quantitative variables are number-related; they are things that you can count or measure.
Qualitative
A variable that is not numeric; also called a categorical variable, a qualitative variable describes
data that fits into categories.
Qualitative variables have to do with non-number characteristics; these are things that you
usually observe but do not count or measure.
Independent Variable
The independent variable is the variable that explains, influences, or affects the other variable.A
variable that, as it changes, affects another variable (called the dependent variable); for example,
as a person pumps more gas into a car's tank (the independent variable), the cost of the purchase
rises (the dependent variable).
,The independent variable is the variable that explains, influences, or affects the other variable.
The independent variable is put on the x-axis, or horizontal axis, on a graph.
Examples:
Consider any occupation where someone earns an hourly wage. At $15 per hour, the number of
hours worked influences total pay, so the number of hours worked is the independent variable.
This is because the number of hours worked explains how much the individual is paid.
In the example about children's height, the age of a child influences his or her height, so age is
the independent variable. Clearly, a child's height does not influence his or her age.
Finally, in the example about ordering computers, since the number of computers in the office
drives the cost, the number of computers is the independent variable.
Sometimes it can be hard to identify the independent variable without context. In fact, sometimes
the independent variable can change depending on context as well. It is always important to pay
attention to the context of variables in all situations.
You own a car wash that charges $10 for each car that goes through. If you wash 50 cars a day,
your revenue is $10×50=$500. If you only wash 20 cars a day, your revenue is $10×20=$200.
Which variable is the independent variable?
ince the number of cars washed affects your revenue, the number of cars is the independent
variable.
Dependent Variable
A variable that is changed by another variable (called the independent variable); for example,
when a person is purchasing gas, the cost (the dependent variable) rises as more gas is pumped
,into a car's tank (the independent variable).
The dependent variable is the variable that responds to the independent variable; that is, the
dependent variable responds to change.
On a graph, the dependent variable is usually labeled on the y-axis, which is the vertical axis.
In the example about making $20 per hour, pay is the dependent variable. Another way of saying
this is that because the pay responds to, or is affected by, the number of hours worked, pay is the
dependent variable.
In the example about children's height, height is the dependent variable.
Finally, in the example about ordering computers, cost is the dependent variable.
As with the independent variables, it can sometimes be hard to identify the dependent variable
without context. Also, remember that the independent and dependent variables sometimes switch
depending on context, so be careful when you assess every situation.
Independent VS Dependent Variables
In general, think of the independent variable as the input and the dependent variable as the
output. Stated another way, the independent variable's input influences what output, or outcome,
you get from the dependent variable.
Input
A quantitative variable that is chosen to find a solution, or output, of a function.
Output
A quantitative variable that is produced by a function when an input is chosen.
Variable
, What is a variable? Simply said, it is something that can vary.
Variables are letters that represent values that change frequently, and variables are often used in
mathematical expressions and in careers.
Function
A function is useful because it expresses the relationship between two quantities, where one
quantity, called the output, is determined by the value of another quantity, called the input.
A relation based on a set of inputs and a set of possible outputs where each input is related to
exactly one output.
Many real-world events can be modeled by functions. Functions are important building blocks
for understanding things like economic production of goods, financial analysis, population
growth, and even the spreading and curing of diseases.
In computer science, the phrase "garbage in, garbage out" expresses the idea that in
programming, incorrect data or poor quality input always produces faulty output, or "garbage."
The best part is that you can use functions to predict future and past values.
Function notation uses the input and output variables to show the relationship and is written
f(input) = output, where variables are used for each quantity.
For example, predicting revenue is important in business. Revenue is based on how many units
of a product are sold. If your company sells wireless speakers for $60 each, then the expression
R(n)=60n models the revenue, R, when n speakers are sold. The number of speakers sold is the
input, and revenue is the output.
Consider this example: As an IT manager, you are responsible for upgrading the computer
systems for your company. A new software package might cost a flat fee of $87.50 plus $2 per
