Respuesta :
The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .
Step-by-step explanation:
Here we have , Twenty-eight athletes participate in a 100-meter race. The time of each athlete is measured during the qualification round. The average time is 11 seconds. The 8 athletes with the fastest time qualified for the final. The average time of these 8 athletes is 10.5 seconds. Let's have equations for this:
[tex]\frac{x_1+x_2+.....+x_2_8}{28} = 11[/tex] where [tex]x_1, x_2, ....., x_2_8[/tex] are athletes
⇒ [tex]x_1 + x_2 + .. + x_2_8 = 11(28)= 308[/tex]
⇒ [tex](x_1 + x_2 + .. + x_8 )+ (x_9+x_1_0+...+x_2_8) = 308[/tex]
⇒ [tex](\frac{x_1 + x_2 + .. + x_8}{8} )(8)+ (\frac{x_9+x_1_0+...+x_2_8}{20} )(20) = 308[/tex]
⇒ [tex]10.5(8)+m(20) = 308[/tex] , where m is average time of the 20 athletes who did not qualify for the final.
⇒ [tex]84+m(20) = 308[/tex]
⇒ [tex]20m= 224[/tex]
⇒ [tex]m=11.2[/tex]
∴ The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .
