A baseball team roster consists of 22 players of which 12 are considered active. Answer the following questions using either the permutation or the combination notation. (a) How many ways are there for a manager to select 12 active players from the roster? (b) How many ways can a manager select a 9-player batting lineup from the active roster for opening day? (a) There are square ways to select 12 active players from the roster. (Type a whole number.)

40. If a spherical bubble has a volume of $972\pi cm^{3}$ , calculate the surface area of the bubble. $Surface\quad Area=\quad \sqrt {x}cm^{2}$

$\frac {1}{8}\times \square =1\frac {3}{8}$

You are helping with decorations for your grandparents' 50th wedding anniversary. You have to buy the streamers and balloons. The streamers cost $\$ 3$ per roll, and the balloons cost $\$ 5$ for a group of 10. You only have $\$ 66$ to spend on the decorations.How many rolls of streamers and groups of balloons can you buy? Let x represent streamers and y represent balloons. Write a linear inequality to represent this situation. $3x+5y\leqslant 66$ $3x+5y\lt 66$ $3x+5y\geqslant 66$ $3x+5y\gt 66$

Which equation has an a-value of $-2$ a b-value of 1, and ac-value of 3? $0=-2x^{2}+x+3$ $0=2x^{2}+x+3$ $0=-2x^{2}+3$ $0=2x^{2}-x+3$

Question 3 (1 point) Find the elasticity. $q=D(x)=\frac {1200}{x}$ $E(x)=\frac {1}{x}$ $E(x)=1$ $E(x)=\frac {x}{1200}$ $E(x)=\frac {1200}{x}$

Use any basic integration formula or formulas to find the indefinite integral.(Use C for the constant of integration.) $\int \frac {4}{1+e^{-4x}}dx$ $\square $

Solve the equation $6y^{3}-7y^{2}-3y=0$ $y=\square $ Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and $-\frac {2}{3}$ as your answers, then enter $4,-2/3$ in the box.

Factor: $3az-9ac+yz-3yc$ $3(3a+y)(a-c)$ $3(a-c)(z-y)$ $(z-3c)(3a-y)$ $(z-3c)(3a+y)$

(05.04 MC) The data to represent average test scores for a class of 16 students includes an outlier value of 72. If the outlier is included, then the mean is 86. Which statement is always true about the new data when the outlier is removed? The mean would increase. The mean would decrease. The median would increase. The median would decrease.

Between what two integers does $-\sqrt {21}$ lie? $-4$ and $-5$ $-9$ and $-10$ $-10$ and $-11$ $-3$ and $-4$