Consider n independent trials of an experiment in which each trial has two possible outcomes, success or failure. The probability of a success on each trial is p and the probability of a failure is q = 1 - p. In this context, the term $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p + q)^n$ gives the probability of k successes in the n trials of the experiment. The probability of a sales representative making a sale to any one customer is $\frac{1}{3}$. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term $_{8} C_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{4}$ in the expansion of $\left(\frac{1}{3}+\frac{2}{3}\right)^{8}$

Draw a figure that contains two triangles. Provide given information that would allow you to prove that the triangles are congruent by the ASA congruence criterion.

A farmer raises chickens and pigs. If his animals have a total of 120 heads and a total of 300 feet, how many chickens does the farmer have? F 60 G 70 H 80 J 90

Simplify each expression. (2 + i)(4 - 5i)

What is the x-coordinate of the hole in the graph of $y=\frac{x^{2}-9}{2 x^{2}-x-15} ?$

write each of the roots in standard form. Fourth roots of 256i

Use the properties and mental math to solve. Write your answer in simplest form.

$$\left( 3 \frac { 1 } { 4 } + 2 \frac { 5 } { 6 } \right) + 1 \frac { 3 } { 4 }$$

Consider the following parametric curves.

Determine $dy/dx$ in terms of t and evaluate it at the given value of t.

A spherical droplet of liquid A and radius $r_{o}$ evaporates into a stagnant layer of gas B. Derive an expression for the evaporation rate of species A in terms of the saturation pressure of species $\mathrm{A}, p_{\mathrm{A}}\left(r_{o}\right)=p_{\mathrm{A}, \mathrm{sat}}$, the partial pressure of species A at an arbitrary radius r, $p_{\mathrm{A}}(r)$, the total pressure p, and other pertinent quantities. Assume the droplet and the mixture are at a uniform pressure p and temperature T.

What is the average of 1.3, 2, and 0.81?

How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile?

How can graphing an inequality help to solve it?

Will a metal always replace another metal in a compound dissolved in water? Explain.

Which inequality has a graph with shading below a dashed boundary line?

$$F. \ 2 x + y > - 3 \\ G. \ 2 x + y \geq - 3 \\ H. \ 2 x + y \leq - 3 \\ J. \ 2 x + y < - 3$$