To find the height equation for the soccer ball's trajectory, we start with the acceleration due to gravity of g=9.81 m/s². Converting this gives us approximately 32.18 ft/s², rounded to 32 ft/s². The height formula is h = -g/2 * t² + vt + h0. Setting t=0 and h=0, we deduce that h0=0. Thus h=-16t² + vt applies. Given that the ball reaches 50 ft in 2.5 s, it reaches 25 ft in 1.25 s. Now, using 25=-16(1.25)² + v(1.25), we find velocity v=50/1.25, which simplifies to 40. Therefore, the height equation is h = -16t² + 40t.
The probability that an individual does not utilize any facility is 0.0889. In a sports center housing 135 individuals, 73 use the gym, 59 use the swimming pool, and 31 use the track. The respective overlaps and total probabilities yield approximately this result.
