Answer:
The total number of U.S. high school students that played on a sports team that year can be estimated to be 7,950,000.
Step-by-step explanation:
From the random sample, we can expect that 
of all students played on a sports team that year. So in the bigger sample of 15900000 high school students, we can expect 
students to have played on a sports team that year.
Answer:
y = 18
Step-by-step explanation:
Direct variation means y will change by the same factor x does. When x changes by a factor of 15/10 = 1.5, the value of y will change by that same factor
x = 10, y = 12
x= 15, y = 1.5×12 = 18
The new value of y is y = 18.
_____
Written as a proportion, you have ...
y/15 = 12/10
y = 15×12/10 = 18
__
Written as a direct variation equation, you have ...
y = kx
12 = k·10 ⇒ k = 1.2
y = 1.2·15 = 18 . . . . for x=15
now, if the denominator turns to 0, the fraction becomes undefined, and you get a "vertical asymptote" when that happens, so let's check when is that
![\bf sin\left(x-\frac{2\pi }{3} \right)=0\implies sin^{-1}\left[ sin\left(x-\frac{2\pi }{3} \right) \right]=sin^{-1}(0) \\\\\\ x-\frac{2\pi }{3}= \begin{cases} 0\\ \pi \end{cases}\implies \measuredangle x= \begin{cases} \frac{2\pi }{3}\\ \frac{5\pi }{3} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20sin%5Cleft%28x-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%20%5Cright%29%3D0%5Cimplies%20sin%5E%7B-1%7D%5Cleft%5B%20sin%5Cleft%28x-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%20%5Cright%29%20%5Cright%5D%3Dsin%5E%7B-1%7D%280%29%0A%5C%5C%5C%5C%5C%5C%0Ax-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%3D%0A%5Cbegin%7Bcases%7D%0A0%5C%5C%0A%5Cpi%20%0A%5Cend%7Bcases%7D%5Cimplies%20%5Cmeasuredangle%20x%3D%0A%5Cbegin%7Bcases%7D%0A%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%5C%5C%0A%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%0A%5Cend%7Bcases%7D)
now, at those angles, the function is asymptotic, check the picture below
Answer:
Step-by-step explanation:
