Answer: D) At the next school assembly, choose one student from each of 20 randomly selected rows.
Step-by-step explanation:
A wouldnt be correct because it is all students from the spots program
B isnt correct because it is 10 girls and 10 boys from the girls' and boys' soccer teams
C wouldnt be correct because it would be the first 20 students she sees once she leaves statistics class
D is the only unbiased, completely random selection choice.
Answer:
x=3
Step-by-step explanation:
WY is an angle bisector, which makes both sides equivalent (it’s an isosceles triangle)
You need to add two mixed numerals.
One is positive and one is negative.
To add a positive number and a negative number, first take the absolute value of both, making them both positive. Then subtract the smaller absolute value from the larger absolute value. Finally, the sign of the answer is the same sign as the number that has the larger absolute value.
The numbers are -4 5/8 and 2 1/8
Take absolute values:
|-4 5/8| = 4 5/8
|2 1/8| = 2 1/8
Subtract the smaller absolute value from the larger absolute value.
4 5/8 - 2 1/8 = 2 4/8 = 2 1/2
The greater absolute value is 4 5/8.
Since the number with the larger absolute value was -4 5/8, a negative number, the answer is negative, -2 1/2
-4 5/8 + 2 1/8 = - 2 1/2
so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).
![\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7B0%7D%3D-%28x-3%29%28x%2B11%29%5Cimplies%200%3D%28x-3%29%28x%2B11%29%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%203%5C%5C%20-11%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B-11%7D%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D-4%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%5Cboxed%7B3%7D)
so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?
![\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20f%28-4%29%3D-%28-4-3%29%28-4%2B11%29%5Cimplies%20f%28-4%29%3D7%287%29%5Cimplies%20f%28-4%29%3D49%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7Bvertex%7D%7B%28-4~~%2C~~49%29%7D~%5Chfill)