texelaare

2021-08-10

To find:
The approximated quarterback rating (to the nearest tenth) of Drew Brees of the New Orleans Saints during the 2013 regular season using, Rating $=\frac{\left(250\cdot \frac{C}{A}\right)+\left(1000\cdot \frac{T}{A}\right)+\left(12.5\cdot \frac{Y}{A}\right)+6.25-\left(1250\cdot \frac{I}{A}\right)}{3}$.

svartmaleJ

Concept: Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is Rating $=\frac{\left(250\cdot \frac{C}{A}\right)+\left(1000\cdot \frac{T}{A}\right)+\left(12.5\cdot \frac{Y}{A}\right)+6.25-\left(1250\cdot \frac{I}{A}\right)}{3}$.
Using this model, we can approximate the quarterback rating (to the nearest tenth) of Drew Brees of the New Orleans Saints during the 2013 regular season.
He attempted 650 passes, completed 446, had 5162 total yards, threw for 39 touchdowns, and had 12 interceptions.
Here,
$A=$ attempted passes $=650$,
$C=$ completed passes $=446$,
$T=$ touchdown passes $=39$,
$Y=$ yards gained passing $=5162$, and
$I=$ interceptions $=12$. [Weighting factors]
the four category ratios are limited to nonnegative values with the following maximums.
$\frac{C}{A}=0.775,\frac{T}{A}=0.11875,\frac{Y}{A}=12.5$ and $\frac{I}{A}=0.095$
Substituting the values in given model, we get
$=\frac{\left(250\cdot \frac{C}{A}\right)+\left(1000\cdot \frac{T}{A}\right)+\left(12.5\cdot \frac{Y}{A}\right)+6.25-\left(1250\cdot \frac{I}{A}\right)}{3}$
$=\frac{\left(250\cdot \frac{446}{650}\right)+\left(1000\cdot \frac{39}{650}\right)+\left(12.5\cdot \frac{5162}{650}\right)+6.25-\left(1250\cdot \frac{12}{650}\right)}{3}$
$=\frac{\left(250\cdot 0.686\right)+\left(1000\cdot 0.06\right)+\left(12.5\cdot 7.941\right)+6.25-\left(1250\cdot 0.018\right)}{3}$
$=\frac{171.5+60+99.262+6.25-22.5}{3}$
$=\frac{314.512}{3}$
$=104.83$
Final statement:
Therefore, the approximated quarterback rating (to the nearest tenth) of Drew Brees of the New Orleans Saints during the 2013 regular season is 104.83.

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