$P$ is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither.

$$P=\begin{matrix} A \\ B \end{matrix} \overset{\text{$A$ \quad $B$ }}{\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}}$$

Determine whether a semiregular uniform tessellation can be created from the given shapes, with all sides 1 unit long. If so determine the number of each shape needed at each vertex to create the tessellation.

regular pentagons and squares

How many pounds of regular coffee (selling for $4 per pound) and how many pounds of Kona coffee (selling for$11.50 per pound) must be combined to get 20 pounds of a mixture worth $6 per pound?

Solve the given problem by using a system of equations.

During the $2013$ major league baseball regular season, the St. Louis Cardinals played $162$ games and won the Central Division of the National League. They won $32$ more games than they lost. What was their win-loss record that year?

The table below shows the $\bf 2013$ MLB Final Regular Season Standings, National League Central

An airline offers discounted "advance-purchase" fares to customers who buy tickets more than 30 days before travel and charges "regular" fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase fares. The "no-show" rate among people who paid regular fares is 30%, but only 5% of customers with advance-purchase tickets are no-shows. a) What percent of all ticket holders are no-shows? b) Is being a no-show independent of the type of ticket a passenger holds? Explain.

Here are the results of the first 10 free-throws of the 2010 regular season for Amare Stoudemire of the New York Knicks.

(a) Calculate Stoudemire's overall free-throw percentage after each shot.

(b) If you were to continue this process for all free-throws that he took during the regular season, describe what will happen to Stoudemire's overall free-throw percentage.

Gina can cook basmati rice 3 1/2 times faster in her pressure cooker than in a regular pot. If rice normally cooks in 20 minutes, what is the cooking time in the pressure cooker (to the nearest second)?

A store has ergonomic chairs on sale for 10% off of the regular price. Cayley finds a chair she wants to buy that has an original price of $325. How much will Cayley pay for the chair if she pays 8.5% tax?

The cube $A B C D E F G H$ with edges of length $s$ contains the tetrahedron $A C E G$.
(a) Explain why $A C E G$ is a regular tetrahedron with edges of length $\sqrt{2} s$.
(b) Show that the volume of tetrahedron $A C D E$ is $\frac{1}{6} s^3$.
(c) Show that the volume of $A C E G$ is $\frac{1}{3} s^3$.
(d) Use the similarity principle to explain why a regular tetrahedron with edges of length $b$ has volume $\frac{\sqrt{2} b^3}{12}$.

Complete the sentences about what students did last summer with the correct preterite endings of each -ar verb. Pay attention to the regular endings in the chart above and to the accent marks.

\lparenusar\rparen Esteban us____ la computadora.

Refer to City Data (Data Set I) on the prices of various products in different cities across the country. Select a subsample of the prices of regular unleaded gas for 40 cities. For the data in this subsample, determine the mean, median, and standard deviation.

Determine the independent and dependent variables for the study.

A study was conducted to determine if workers who had a flexible work schedule had greater job satisfaction than those workers who worked a regular nine-to-five work schedule.

Graphical Reasoning Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the polygon to the center of the circle, forming $n$ congruent triangles.
Let $A_n$ be the sum of the areas of the $n$ triangles. Find $\lim _{n \rightarrow \infty} A_{n^{-}}$

The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids. What are $\mathrm{m} \angle A, \mathrm{~m} \angle B, \mathrm{~m} \angle C$, and $\mathrm{m} \angle D$ in trapezoid $A B C D$ ?