To calculate a quarterback's rating in NCAA football, you...

To calculate a quarterback's rating in NCAA football, you may use the formula $\frac{100 C+330 T-200 I+8.4 Y}{A}$, where $C=$ the number of completed passes, $A=$ the number of attempted passes, $T=$ the number of touchdown passes, $Y=$ the number of yards in the completed passes, and $I=$ the number of interceptions. Sam Bradford of the University of Oklahoma was selected as the 2008 winner of the Heisman Memorial Trophy as the Most Outstanding Football Player. Bradford, a sophomore quarterback with the Sooners, ended the season with 442 attempts, 302 completions, 4464 yards, 53 touchdowns, and only 6 interceptions. Calculate Bradford's quarterback rating for the 2008 season. (Source: NCAA) Round the answer to the nearest tenth.

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Key Concepts

Rounding and Approximation

Rounding is the process of adjusting a numerical result to a specified degree of precision. In applied mathematics and statistics, especially when working with measurements or calculated ratings, rounding helps to simplify numbers, making them easier to interpret and compare.

Order of Operations

The order of operations is a set of rules that dictate the sequence in which arithmetic operations should be carried out in a mathematical expression. This ensures that the evaluation of complex formulas, which may include multiplication, addition, subtraction, and division, yields the correct result.

Quarterback Rating Formula

The quarterback rating formula is a statistical tool used in sports analytics to quantify a quarterback's performance. It involves a mathematical expression that weights various performance metrics such as completions, touchdowns, interceptions, and passing yards to provide a single numerical measure of effectiveness.

Substitution in Algebra

Substitution in algebra involves replacing variables with their corresponding numerical values in a formula or equation. This fundamental technique is crucial when evaluating formulas, as it allows abstract expressions to be turned into concrete calculations using real data.

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