An online shopping store charges a rate of 2.5 percent of the purchase price as a shipping and handling fee. The amount charged for shipping and handling is a function of the total price of the order. Which of the following is the independent quantity in this function?

A. the total price of the order
Correct!

B. the shipping and handling rate for the purchase
Incorrect. The rate charged for shipping and handling is a constant, not a variable.

C. the amount charged for shipping and handling
Incorrect. This variable is the dependent quantity in the relationship, since the amount charged is a function of the total price.

D. the weight of the package being shipped
Incorrect. While this can be a variable, it is not a variable in the relationship that is given.

A functional relationship is represented by the equation y = 2 3 x – 18. Which of the following statements best describes this functional relationship?

A. The dependent variable, y, is equal to 2 3 of the difference between the independent variable, x, and 18.
Incorrect. According to the order of opreations, 2 3 is only multiplied by x, not the difference between x and 18.

B. The dependent variable, x, is equal to 2 3 of the difference between the independent variable, y, and 18.
Incorrect. According to the order of operations, 2 3 is only multiplied by x, not the difference between x and 18. Also, in this relationship, x is the independent variable and y is the dependent variable, because the value of y depends on the value of x.

C. The dependent variable, x, is 18 less than product of the independent variable, y and 2 3 .
Incorrect. In this relationship, x is the independent variable and y is the dependent variable, because the value of y depends on the value of x.

D. The dependent variable, y, is 18 less than product of the independent variable, x and 2 3 .
Correct!

The wind speed in a hurricane is a function of the air pressure in the center of the hurricane. Which of the following statements best describes this functional relationship?

A. The air pressure in the center of the hurricane depends on the wind speed of a hurricane.
Incorrect. If this relationship were an equation, it could be written as f(air pressure) = wind speed.

B. The wind speed of a hurricane depends on the air pressure in the center of the hurricane.
Correct!

C. The wind speed of a hurricane and the air pressure in the center of the hurricane are independent of each other.
Incorrect. One variable is a function of the other, so that implies a dependency relationship.

D. The wind speed in a hurricane depends on the size of the center of the hurricane.
Incorrect. There may be a relationship between the size of the center of a hurricane and the air pressure in the center of a hurricane, but we are not given any information about that relationship.

The volume of certain 3-dimensional objects can be found using the formulas in the list below.

Which of the following statements is not true?

A. The volume of a cylinder is a function of the square of the radius of the cylinder, the height of the cylinder, and the value of π.
Incorrect. These 3 factors are used to determine the volume of a cylinder.

B.  The volume of a cone is a function of the radius of the cone, the height of the cone, and the value of 1 3 π.
Incorrect. These 3 factors are used to determine the volume of a cone.

C. The volume of a sphere depends only on the radius of the sphere.
Correct!

D. The volume of a cylinder depends on the radius and the height of the cylinder.
Incorrect. The radius and height of a cylinder are independent quantities that are used to determine the dependent quantity of volume.

Gulf Coast Phone Company is promoting a new cell phone service plan: a customer can make up to 700 minutes of calls each month for $29.99. If the number of minutes used in a month exceeds 700, then the function

c = 0.40(m − 700) + 29.99

describes the monthly charge, c, in dollars in terms of m, the total number of minutes used. Which of the following statements best describes the functional relationship used by the Gulf Coast Phone Company?

A. If a customer exceeds 700 minutes of calls each month, the total number of minutes used depends on the monthly charge.
Incorrect. In this function, the total number of minutes is used to determine the monthly charge.

B. If a customer exceeds 700 minutes of calls each month, the monthly charge depends on the total number of minutes used.
Correct!

C. The total number of minutes used is a function of the monthly charge.
Incorrect. In this function, the total number of minutes is used to determine the monthly charge.

D. If a customer exceeds 700 minutes of calls each month, the rate per minute depends on the number of minutes in excess of 700 minutes that the customer used.
Incorrect. Once the customer exceeds 700 minutes, then each additional minute costs $0.40. There is no change in the cost per additional minute.