From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago.
<h3>How to apply direct proportions</h3>
A <em>direct</em> proportion is a <em>direct</em> relationship between two variables, which in this case is represented between the quantity of tourists in the city of Chicago and the population of the country of origin.
Let suppose the existence of direct proportionality and world has a population of 9000 million people, the quantity of Chinese visitors in the city of Chicago is determined by the following formula:
x = (1.393 × 10⁹ / 9 × 10⁹) × 55 × 10⁶
x = 8.512 × 10⁶
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago. 
To learn more on direct proportions, we kindly invite to check this verified question: brainly.com/question/14389660
Assuming that no overtime was factored into his wages, Alex would have gotten a gross pay of $359.60. This was done by multiplying $7.86 x 45.75 hours.
Assuming that overtime was factored into his wages, Alex would have gotten a gross pay of $382.19. This was done by figuring out how much "time and a half" is for over time. "time" = 7.86; "and a half"= 7.86/2= 3.93
Time AND a half would equal 7.86 + 3.93= 11.79.
So, Alex would get an additional $11.79 for the hours OVER 40 hours which was 5 hours and 75 minutes..
11.79 x 5.75 = 67.79
Total hours for a 40 hour work week for Alex with 7.86 would equal a gross pay of 314.40. Plus 67.79. = 382.19
3741.43 is your answer. Just do $3850 x 0.9718 and you'll get your answer. I hope this helps :)
