Formulate a system of equations for each of the given scenarios. Solve by using the calculator. Express your answer using a complete sentence. Check your answer! 2) There is a total of 16 students traveling on a field trip, all sophomores ( \( x \) ), juniors ( \( y \) ), and seniors ( \( z \) ). The number of seniors is one more than twice the number of sophomores. There are three more juniors than sophomores. Find the number of students in each grade.

Solve using the Quadratic Formula. \( \begin{array}{l}3 x^{2}+4 x+5=0 \\ x=\frac{-2 \pm \sqrt{11}}{3} \\ x=\frac{-4 \pm 2 i \sqrt{11}}{2} \\ x=\frac{-4 \pm i \sqrt{11}}{6} \\ x=\frac{-2 \pm i \sqrt{11}}{3}\end{array} \)

A line passes through point \( (8,6) \) and has a slope of \( \frac{5}{2} \) Write an equation in \( A x+B y=C \) form for this line. Use integers for \( A, B \), and \( C \).

Una fábrica de producción de agua embotellada, cuenta con una máquina de envasado tomático, la cual vierte en cada botella una cierta cantidad de agua que sigue una distribución rmal con media de 500 mililitros y una varianza de 25 mililitros. ¿Qué porcentaje de las botellas llenan con agua entre 490 y 507 mililitros?

2. \( \left(\frac{1}{2}\right)^{2 x}=2^{3}-x \)

Which equation represents \( y=-3 x^{2}-30 x-70 \) in vertex form? \( \begin{array}{l}y=-3(x-5)^{2}+10 \\ y=-3(x+5)^{2}+5 \\ y=-3(x-5)^{2}+5 \\ y=-3(x+5)^{2}+10\end{array} \)