39 R.3 Real Number Operations and Properties 164. Calculate the BAC to the nearest thousandth for a 135-lb woman who, in 3 hr, has consumed three 12-oz beers (36 oz), each having a 4.0% alcohol content. 165. Calculate the BAC to the nearest thousandth for a 200-lb man who, in 4 hr, has consumed three 20-oz beers, each having a 3.8% alcohol content. If the man’s weight were greater and all other variables remained the same, how would that affect his BAC? 166. Calculate the BAC to the nearest thousandth for a 150-lb woman who, in 2 hr, has consumed two 6-oz glasses of wine, each having a 14% alcohol content. If the woman drank the same two glasses of wine over a longer period of time, how would that affect her BAC? (Modeling) Passer Rating for NFL Quarterbacks The current system of rating passers in the National Football League is based on four performance components: completions, touchdowns, yards gained, and interceptions, as percentages of the number of passes attempted. It uses the following formula. Rating = a250 # C Ab + a1000 # T Ab + a12.5 # Y Ab + 6.25 - a1250 # I Ab 3 , where A = attempted passes, C = completed passes, T = touchdown passes, Y = yards gained passing, and I = interceptions. In addition to the weighting factors appearing in the formula, the four category ratios are limited to nonnegative values with the following maximums. 0.775 for C A , 0.11875 for T A , 12.5 for Y A , 0.095 for I A Regular-season statistics for the top six quarterbacks in 2018 are given in the table. Use the formula to determine the rating to the nearest tenth for each. Solve each problem using the passer rating formula above. 173. Peyton Manning, when he played for the Indianapolis Colts, set a full-season rating record in 2004 and held that record until Aaron Rodgers, of the Green Bay Packers, surpassed it in 2011. (As of 2018, Rodgers’s all-time record held.) If Rodgers had 343 completions, 45 touchdowns, 6 interceptions, and 4643 yards, for 502 attempts, what was his rating in 2011? 174. Steve Young, of the San Francisco 49ers, set a full season rating record of 112.8 in 1994 and held that record until Peyton Manning surpassed it in 2004. If Manning had 336 completions, 49 touchdowns, 10 interceptions, and 4557 yards, for 497 attempts, what was his rating in 2004? Quarterback, Team A Att C Comp T TD Y Yards I Int 167. Drew Brees, NO 489 364 32 3992 5 168. Patrick Mahomes, KC 580 383 50 5097 12 169. Russell Wilson, SEA 427 280 35 3448 7 170. Matt Ryan, ATL 608 422 35 4924 7 171. Philip Rivers, LAC 508 347 32 4308 12 172. Deshaun Waston, HOU 505 345 26 4165 9 Data from www.nfl.com Archie Manning, father of NFL quarterbacks Peyton and Eli, signed this photo for author Hornsby’s son, Jack.
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