The number of males M (in thousands) and the number of females F (in thousands) participating in high school athletic programs from 1995 through 2001 can be modeled by M = 463.76 t + 2866.4 0.09 t + 1.0 M = \frac { 463.76 t + 2866.4 } { 0.09 t + 1.0 } M = 0.09 t + 1.0 463.76 t + 2866.4 and F = 3183.41 t − 4762.2 t F = \frac { 3183.41 t - 4762.2 } { t } F = t 3183.41 t − 4762.2 . In these models, t represents the year, with t=5 corresponding to 1995. Find a rational model that represents the total number T of participants in high school athletic programs.A) 2719.65 t + 1895.8 0.91 t + 1.0 \frac { 2719.65 t + 1895.8 } { 0.91 t + 1.0 } 0.91 t + 1.0 2719.65 t + 1895.8 B) 750.27 t 2 + 5621.212 t − 4762.2 t ( 0.09 t + 1.0 ) \frac { 750.27 t ^ { 2 } + 5621.212 t - 4762.2 } { t ( 0.09 t + 1.0 ) } t ( 0.09 t + 1.0 ) 750.27 t 2 + 5621.212 t − 4762.2 C) 463.76 t 2 + 1895.8 t − 7628.6 t ( 0.09 t + 1.0 ) \frac { 463.76 t ^ { 2 } + 1895.8 t - 7628.6 } { t ( 0.09 t + 1.0 ) } t ( 0.09 t + 1.0 ) 463.76 t 2 + 1895.8 t − 7628.6 D) 3647.17 t − 7628.6 1.09 t + 1.0 \frac { 3647.17 t - 7628.6 } { 1.09 t + 1.0 } 1.09 t + 1.0 3647.17 t − 7628.6 E) 3183.41 t 2 + 7628.6 t − 1895.8 t ( 0.09 t + 1.0 ) \frac { 3183.41 t ^ { 2 } + 7628.6 t - 1895.8 } { t ( 0.09 t + 1.0 ) } t ( 0.09 t + 1.0 ) 3183.41 t 2 + 7628.6 t − 1895.8

Question

The number of males M (in thousands) and the number of females F (in thousands) participating in high school athletic programs from 1995 through 2001 can be modeled by   M = 463.76 t + 2866.4 0.09 t + 1.0 M = \frac { 463.76 t + 2866.4 } { 0.09 t + 1.0 } M = 0.09 t + 1.0 463.76 t + 2866.4 ​   and   F = 3183.41 t − 4762.2 t F = \frac { 3183.41 t - 4762.2 } { t } F = t 3183.41 t − 4762.2 ​  . In these models, t represents the year, with t=5 corresponding to 1995. Find a rational model that represents the total number T of participants in high school athletic programs.A)    2719.65 t + 1895.8 0.91 t + 1.0 \frac { 2719.65 t + 1895.8 } { 0.91 t + 1.0 } 0.91 t + 1.0 2719.65 t + 1895.8 ​ B)    750.27 t 2 + 5621.212 t − 4762.2 t ( 0.09 t + 1.0 )  \frac { 750.27 t ^ { 2 } + 5621.212 t - 4762.2 } { t ( 0.09 t + 1.0 )  } t ( 0.09 t + 1.0 )  750.27 t 2 + 5621.212 t − 4762.2 ​ C)    463.76 t 2 + 1895.8 t − 7628.6 t ( 0.09 t + 1.0 )  \frac { 463.76 t ^ { 2 } + 1895.8 t - 7628.6 } { t ( 0.09 t + 1.0 )  } t ( 0.09 t + 1.0 )  463.76 t 2 + 1895.8 t − 7628.6 ​ D)    3647.17 t − 7628.6 1.09 t + 1.0 \frac { 3647.17 t - 7628.6 } { 1.09 t + 1.0 } 1.09 t + 1.0 3647.17 t − 7628.6 ​ E)    3183.41 t 2 + 7628.6 t − 1895.8 t ( 0.09 t + 1.0 )  \frac { 3183.41 t ^ { 2 } + 7628.6 t - 1895.8 } { t ( 0.09 t + 1.0 )  } t ( 0.09 t + 1.0 )  3183.41 t 2 + 7628.6 t − 1895.8 ​

Jackson Keech · Accepted Answer

Final Answer : B, Explanation :   To find the total number of participants T, we add the models for M and F:   T = M + F = 463.76 t + 2866.4 0.09 t + 1.0 + 3183.41 t − 4762.2 t T = M + F = \frac { 463.76 t + 2866.4 } { 0.09 t + 1.0 } + \frac { 3183.41 t - 4762.2 } { t } T = M + F = 0.09 t + 1.0 463.76 t + 2866.4 ​ + t 3183.41 t − 4762.2 ​  . Simplifying this expression to a common denominator gives us the model in choice B.

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