Solved Examples and Worksheet for Identifying Dependent and independent Variables for the Situations

Q1Identify the independent and dependent quantity for the situation:
Charles's score on the test is a function of the number of hours he studies.

A. Independent quantity: Score in the tests and Number of hours of study
Dependent quantity: Nil
B. Independent quantity: Score in the tests
Dependent quantity: Number of hours of study
C. Independent quantity: Number of hours of study
Dependent quantity: Number of hours of study
D. Independent quantity: Number of hours of study
Dependent quantity: Score in the tests

Solutions
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Step: 1
Independent quantity is the input and the dependent quantity is the output of the situation.
Step: 2
Independent quantity: Number of hours of study
Dependent quantity: Score in the tests
Correct Answer is :   Independent quantity: Number of hours of study
Dependent quantity: Score in the tests
Q2The cost of shipping a package overnight from Atlanta to Dallas is a function of the weight of the package in ounces. Identify the dependent variable.

A. time taken for shipping
B. cost of shipping the package
C. distance between Atlanta and Dallas
D. weight of the package

Solutions
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Step: 1
An independent variable is one whose value does not depend on anything else (the input).
Step: 2
A dependent variable is one whose value directly results from another variable (the output).
Step: 3
Since the cost of shipping is a function of the weight of the package, the cost is dependent on the weight.
Step: 4
Therefore, the cost of shipping the package is the dependent variable, and the weight of the package is the independent variable.
Correct Answer is :   cost of shipping the package
Q3The total cost of toys is a function of the number of toys purchased. Which statement is true?
A. There in no relation between the number of toys purchased and the total cost
B. Number of toys purchased is the dependent variable
C. Total cost of toys is the independent variable
D. Total cost of toys is the dependent variable

Solutions
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Step: 1
Independent quantity is the input and the dependent quantity is the output of the situation.
Step: 2
Independent quantity: Number of toys purchased
Dependent quantity: Cost of toys
Correct Answer is :   Total cost of toys is the dependent variable
Q4The side of a square is s. If the area of the square is given as A = s2, then which of the following is true?
A. A is a dependent variable
B. A is an independent variable
C. area A and side are dependent variables
D. s is a dependent variable

Solutions
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Step: 1
Independent variable is the input and the dependent variable is the output of the situation.
Step: 2
From the given function, independent variable is s and the dependent variable is A.
  [s is the input and A is the output.]
Step: 3
Therefore, the statement 'A is a dependent variable' is true.
Correct Answer is :   A is a dependent variable
Q5The time spent by Brad on a birthday party is a function of the number of his friends whom he invited. Which of the following is a dependent variable?
A. number of members in Brad ′s family
B. Brad ′s age
C. time spent by Brad on the party
D. number of friends Brad invited

Solutions
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Step: 1
Independent variable is the input and the dependent variable is the output of the situation.
Step: 2
From the given function, independent variable is the number of friends and the dependent variable is time Brad spent.
Step: 3
Among the choices, "time spent by Brad on the party" is dependent variable.
Correct Answer is :   time spent by Brad on the party
Q6The quantity of water in a boiler is a function of the time duration to which it is filled. In this function what is the dependent variable(s)?
A. there is no dependent variable
B. quantity of water
C. quantity of water in a boiler and the time duration in which it is filled
D. time duration in which water in a boliler is filled

Solutions
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Step: 1
Independent quantity is the input and the dependent quantity is the output of the situation.
Step: 2
Independent quantity: time upto which water in a boiler is filled.
Dependent quantity: quantity of water in a boiler.
Correct Answer is :   quantity of water
Q7The weight of a 2-pound roast is a function of the temperature of the oven. In this function what is the dependent variable(s)?

A. There is no dependent variable.
B. Temperature of the oven.
C. weight of a 2-pound roast.
D. weight of a 2-pound roast and temperature of the oven.

Solutions
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Step: 1
Independent quantity is the input and the dependent quantity is the output of the situation.
Step: 2
Independent quantity: Temperature of the oven
Dependent quantity: weight for a 2-pound roast
Correct Answer is :   weight of a 2-pound roast.
Q8The table shows the length in minutes of Wilma′s afternoon nap with the hours of sleep she had in the previous night. Identify the dependent and independent variable in the situation.
Hours of sleep (x)5.56.06.57.07.58.08.59.09.510.010.511.0
Minutes of nap time (y)150140130120110100908070605040

A. wilma and sleep
B. hours of sleep and minutes of nap time
C. sleep and wilma
D. minutes of nap time and hours of sleep

Solutions
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Step: 1
Independent variable is the input and the dependent variable is the output of the situation.
Step: 2
From the given function, independent variable is hours of sleep and the dependent variable is minutes of nap time.
Step: 3
Among the choices, "minutes of nap time and hours of sleep" is the correct answer.
Correct Answer is :   minutes of nap time and hours of sleep
Q9The total cost of apples that Jack purchased is a function of number of apples. Which of the statement is true?

A. There is no relation between the number of apples and the total cost.
B. The total cost of apples is the independent variable.
C. Insufficient data
D. The total cost of apples is the dependent variable.

Solutions
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Step: 1
Independent variable is the input and the dependent variable is the output of the situation.
Step: 2
From the given function, independent variables is number of apples and the dependent variable is total cost of apples.
Step: 3
Among the choices, "total cost of apples is the dependent variable" is true for the data.
Correct Answer is :   The total cost of apples is the dependent variable.
Q10The area of a square is given by A = s2. where A is the area and S is the side of the square. Which of the following is true for the data?
A. Insufficient data.
B. A is a dependent variable.
C. s is a dependent variable.
D. A is an independent variable.

Solutions
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Step: 1
A = s2
Step: 2
Area of the square depends on the side length of the square.
Step: 3
So, independent variable is side and the dependent variable is area.
Step: 4
From the given function, A is a dependent variable and s is an independent variable.
Step: 5
Among the choices, "A is a dependent variable" is true for the data.
Correct Answer is :   A is a dependent variable.

HighSchool Math