Because the teacher only picked 5 students out of all the students it was a sample.
If the teacher had asked every student, it would have been a population.
1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.
Answer:
0.08
Step-by-step explanation:
![{5}^{ - 2} \times \sqrt[3]{8} \\ \\ = {5}^{ - 2} \times \sqrt[3]{ {2}^{3} } \\ \\ = \frac{1}{ {5}^{2} } \times 2 \\ \\ = \frac{1}{25} \times 2 \\ \\ = \frac{2}{25} \\ \\ =0.08](https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B%20-%202%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B8%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%7B5%7D%5E%7B%20-%202%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B%20%7B2%7D%5E%7B3%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%7B5%7D%5E%7B2%7D%20%7D%20%20%5Ctimes%202%20%5C%5C%20%20%5C%5C%20%20%20%3D%20%5Cfrac%7B1%7D%7B25%7D%20%20%5Ctimes%202%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B2%7D%7B25%7D%20%5C%5C%20%5C%5C%20%3D0.08)
