For the following term or person, write a sentence explaining its significance for the United States in the 1780s: checks and balances

Angela, Emery, Rico, and Taylor are working on a class project. Each student is assigned one of the following project roles at random, with no roles repeated: leader, presenter, recorder, and timekeeper. Find the probability in part b by using combinations or permutations. Compare your results to your answer in part b.

Simplify, if possible. $\frac{x^{2}+10 x+24}{2 x+4} \cdot \frac{2(8-x)}{x^{2}-4 x-32}$

Solve the equation. State any extraneous solutions.

$$\frac { 2 n } { 3 } + \frac { 1 } { 2 } = \frac { 2 n - 3 } { 6 }$$

A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people who the lie detector says are being deceptive. Find and interpret

$$\mu_x.$$

True or false: Tropical rainforests have the highest biodiversity of any terrestrial ecosystem.

How would environmental conditions have to change to give this albino lemur a chance for survival? A Volcanic ash covers the forest. B. The climate gets cold enough to snow. C. A city dump moves nearby. D. An earthquake lifts the land 2 meters.

Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

A conducting sphere (radius a) is placed at the center of a conducting spherical shell (inner radius b and outer radius c). The conductors are in electrostatic equilibrium. For the given charges: (a) Sketch a field line diagram. (b) Determine the charge on the inner and outer surfaces of the shell. (c) Sketch a graph of $E _ { \mathrm { r } }$, the radial component of the field, as a function of r. $\left( E _ { \mathrm { r } } > 0\right.$ if the field is radially outward and $E _ { \mathrm { r } } < 0$ if the field is radially inward.) The inner sphere has a net charge of +6 $\mu \mathrm { C }$ and the shell has a net charge of +6 $\mu \mathrm { C }$.

Write an equation for the second electron affinity of chlorine. Would you predict a positive or a negative energy value for this process? ls it possible to directly measure the second electron affini ty of chlorine?

Describe the transformation of the parent function f(x). g(x) = f(x) + 6

Camila y Ernesto estan de vacaciones. ¿Que hacen? Escoge la expresion apropiada. (Choose the best expression.)

The following exercise is based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

$$\begin{array} {|c | c | c | c | c | c | } \hline \text{Enrollment (thousands)}&53 & { 28 } & { 27 } & { 36 } & { 42 } \\ \hline \text{Burglaries}&86 & { 57 } & { 32 } & { 131 } & { 157 } \\ \hline \end{array}$$

True or false: If there is no linear correlation between enrollment and number of burglaries, then those two variables are not related in any way.

Find the unit tangent vector to the curve at the indicated points. $\mathbf{r}(t)=\langle 3 t, \cos 2 t, \sin 2 t\rangle, t=0, t=-\pi, t=\pi$