Solve
-An Open-Top Rectangular Box Has a Square Base and It

question 39

Multiple Choice

Solve.
-An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc) . Each side of the base has length $x \mathrm {~cm}$ . The box's surface area $S$ is given by
$$S ( x ) = \frac { 1024 } { x } + x ^ { 2 } .$$
Estimate the minimum surface area and the value of $x$ that will yield it.

• A) \(256 \mathrm {~cm} ^ { 2 }\) when \(x = 6 \mathrm {~cm}\)
• B) \(207 \mathrm {~cm} ^ { 2 }\) when \(x = 6 \mathrm {~cm}\)
• C) \(256 \mathrm {~cm} ^ { 2 }\) when \(x = 8 \mathrm {~cm}\)
• D) \(192 \mathrm {~cm} ^ { 2 }\) when \(\mathrm { x } = 8 \mathrm {~cm}\)

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Definitions:

Coefficient Of Determination

A statistic that indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Estimated Regression Equation

A formula that represents the relationship between dependent and independent variables and is used to predict the value of the dependent variable.

Correlation Coefficient

A numerical measure of some type of correlation, meaning a statistical relationship between two variables, ranging between -1 and 1.

Standard Error

The standard deviation of the sampling distribution of a statistic, indicating the accuracy of the estimate.