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

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 $\frac{\sqrt{2} b^3}{12}$.

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)?

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 $A B C D$ ?

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 $\lim _{n \rightarrow \infty} A_{n^{-}}$

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.

Using the information from previous exercises, find the earnings at the regular rate, the earnings at the overtime rate, and the gross earnings for the employee. Round to the nearest cent.

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Consider weights (lb) of the contents of cans of Diet Coke $( n = 36 , \overline { x } = 0.78479 \mathrm { lb } , s = 0.00439 \mathrm { lb } )$ and of the contents of cans of regular Coke $( n = 36 , \overline { x } = 0.81682 \mathrm { lb } , s = 0.00751 \mathrm { lb } )$.Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.

A regular triangular pyramid has a base length of 3.5 meters, a height of 1.3 meters, and a surface area of 21 square meters. What is the approximate slant height of the pyramid? Justify your answer by showing how you found it.

Here are the results of the first 10 free-throws of the 2010 regular season for Blake Griffin of the Los Angeles Clippers.

(a) Calculate Griffin'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 Griffin's overall free-throw percentage.

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.

A 7-sided shape is called a heptagon.

a) Does a regular heptagon tessellate? Explain your answer.

b) If your answer to Part A is yes, sketch the tessellation.

c) If your answer to Part A is no, sketch a heptagon that tessellates.

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