Choose the One Alternative That Best Completes the Statement or Answers

question 68

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The function $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 }$ describes the volume of a cube, $\mathrm { f } ( \mathrm { x } )$ , in cubic inches, whose length, width, and height each measure $x$ inches. Find the instantaneous rate of change of the volume with respect to $x$ when $x = 4$ inches.

• A) 12 cubic inches per inch
• B) \(49.21\) cubic inches per inch
• C) 48 cubic inches per inch
• D) 192 cubic inches per inch

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Definitions:

Probability

A measure of the likelihood that an event will occur, often expressed as a number between 0 and 1.

Poisson Random Variable

A type of discrete random variable that expresses the probability of a given number of events occurring in a fixed interval of time or space.

Poisson Probabilities

Probabilities calculated under the assumption of a Poisson distribution, typically used to model the number of times an event occurs in a fixed interval of time or space.

Calculate

To determine something mathematically, often by using a specific formula or procedure.