Applied Algebra C957 WGU - Learning Checks

Questions and Answers

Which choice is a variable?

The amount a teenager makes babysitting (correct)

Your shoe size

The cost of your daily newspaper

The number of states in the United States of America

Which choice is a variable?

The operating system on your phone

The name of the largest mountain range in the United States

The amount a babysitter charges per hour

The colors and styles of your shoes (correct)

Which choice is a quantitative variable?

M, representing the federal minimum wage

S, representing the number of regular weekly shipping deliveries your company's trucks make

P, representing the monthly profit based on the number of customers who needed plumbing services (correct)

R, representing the monthly rent for your company's office building

Which choice represents a qualitative variable in this lawn-mowing business?

H, representing the hilliness of the lawn Signup and view all the answers

Which variable is related to the variable temperature?

Hot chocolate sales Signup and view all the answers

The number of years someone regularly deposits money in a savings account is related to the amount of money in the account.

True Signup and view all the answers

Which variable is the independent variable in the catering scenario?

The number of people attending Signup and view all the answers

Which variable is the independent variable in the car wash scenario?

The number of cars washed Signup and view all the answers

Which variable is the dependent variable in the app spending scenario?

The amount of money spent Signup and view all the answers

What is the dependent variable—the number of weeks of vacation or the number of years employed?

The number of weeks of vacation Signup and view all the answers

Which event allows you to predict the output based on an input?

What comes out of a vending machine based on your selection Signup and view all the answers

What is the input in the cow's case?

The grass Signup and view all the answers

Which of these represents a function?

Input: The cost of an item; Output: The sales tax owed on the item Signup and view all the answers

What might the inverse function be useful for?

The inverse function could be used to figure out how many employees the company could employ if the budget for benefits was limited. Signup and view all the answers

What does the inverse function do if the function doubles each input?

Halves each input Signup and view all the answers

What function models the amount of sales tax, T, when you spend x dollars?

T(x) = 0.07(x) Signup and view all the answers

Which function below models your plan to add employees over the years?

N(y) = 12 + 3y Signup and view all the answers

Choose the function that models the temperature scenario.

T(h) = 50 - 2h Signup and view all the answers

How much would it cost to mail a package that weighs 14 ounces?

$3.62 Signup and view all the answers

What is the increase in pay if you were given a 9% raise?

$5,580 Signup and view all the answers

Find the value of the car after three years.

$17,800 Signup and view all the answers

Which of these would be a coordinate on the graph of the function C(p) = 20 - p?

(5, 15) Signup and view all the answers

Study Notes

Variables and Functions

Variables: Represent quantities that can change. Examples include the amount earned for babysitting or shoe sizes.
Quantitative Variables: Numerical values that can be measured, such as monthly profit from customer counts.
Qualitative Variables: Non-numerical categories that describe characteristics, like the hilliness of a lawn.

Relationships in Business

Independent Variable: Determines changes in other variables, e.g., the number of people attending an event influencing the amount of food prepared.
Dependent Variable: Responds to changes in independent variables, like the amount spent on apps based on the number of apps purchased.

Functions and Inverse Functions

Function: A relationship where each input corresponds to exactly one output. Example: The cost of an item dictates the sales tax owed.
Inverse Function: Reverses the relationship, useful for calculating necessary inputs based on desired outputs.

Mathematical Modeling

Sales Tax Function: T(x) = 0.07(x) models sales tax based on spending.
Earnings Function: B(h) = 8h expresses earnings based on hours worked.
Employee Growth Function: N(y) = 12 + 3y illustrates how employee numbers increase yearly.

Functions in Real-World Scenarios

Depreciation: V(t) = 22,000 - 1400t shows how a car's value decreases over time.
Towing Pricing Function: P(m) = 1.8m + 32 calculates the cost of towing based on miles.

Evaluating Scenarios

Temperature Decline: T(h) = 50 - 2h models how temperature decreases over time.
Pay Raise Calculation: I(r) = 62,000(r) helps determine pay increase based on percentage rates.

Inputs and Outputs

Input vs. Output: Understanding what factors influence others, such as grass being the input for the process of milk production.

Graphing and Coordinates

Graphing Functions: Identifying coordinates that satisfy given functions helps visualize relationships, such as (5, 15) for function C(p) = 20 - p.

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Description

Test your understanding of variables in this Applied Algebra C957 quiz. Each question challenges you to identify variables accurately by analyzing multiple choices. Perfect for those preparing for WGU assessments.