Podcast
Questions and Answers
Which choice is a variable?
Which choice is a variable?
Which choice is a variable?
Which choice is a variable?
Which choice is a quantitative variable?
Which choice is a quantitative variable?
Which choice represents a qualitative variable in this lawn-mowing business?
Which choice represents a qualitative variable in this lawn-mowing business?
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Which variable is related to the variable temperature?
Which variable is related to the variable temperature?
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The number of years someone regularly deposits money in a savings account is related to the amount of money in the account.
The number of years someone regularly deposits money in a savings account is related to the amount of money in the account.
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Which variable is the independent variable in the catering scenario?
Which variable is the independent variable in the catering scenario?
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Which variable is the independent variable in the car wash scenario?
Which variable is the independent variable in the car wash scenario?
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Which variable is the dependent variable in the app spending scenario?
Which variable is the dependent variable in the app spending scenario?
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What is the dependent variable—the number of weeks of vacation or the number of years employed?
What is the dependent variable—the number of weeks of vacation or the number of years employed?
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Which event allows you to predict the output based on an input?
Which event allows you to predict the output based on an input?
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What is the input in the cow's case?
What is the input in the cow's case?
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Which of these represents a function?
Which of these represents a function?
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What might the inverse function be useful for?
What might the inverse function be useful for?
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What does the inverse function do if the function doubles each input?
What does the inverse function do if the function doubles each input?
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What function models the amount of sales tax, T, when you spend x dollars?
What function models the amount of sales tax, T, when you spend x dollars?
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Which function below models your plan to add employees over the years?
Which function below models your plan to add employees over the years?
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Choose the function that models the temperature scenario.
Choose the function that models the temperature scenario.
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How much would it cost to mail a package that weighs 14 ounces?
How much would it cost to mail a package that weighs 14 ounces?
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What is the increase in pay if you were given a 9% raise?
What is the increase in pay if you were given a 9% raise?
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Find the value of the car after three years.
Find the value of the car after three years.
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Which of these would be a coordinate on the graph of the function C(p) = 20 - p?
Which of these would be a coordinate on the graph of the function C(p) = 20 - p?
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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.
Studying That Suits You
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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.
