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

Team	W	L
St. Louis	$-$	$-$
Pittsburgh	$94$	$68$
Cincinnati	$90$	$72$
Milwaukee	$74$	$88$
Chicago Cubs	$66$	$96$

When Connie camps, she uses a tent that is in the form of a regular pyramid with a square base. The length of an edge of the base is 9 feet and the height of the tent at its center is 8 feet. Find the volume of the space enclosed by the tent.

Show that each of the equations $(a, b, c \neq 0)$

$$\begin{array}{l}{x^{2}+y^{2}+z^{2}=a x} \\ {x^{2}+y^{2}+z^{2}=b y} \\ {x^{2}+y^{2}+z^{2}=c z}\end{array}$$

define a regular surface and that they all intersect orthogonally.

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

On the line provided in each of the following sentences, spell the word in parentheses, adding the prefix that is given.

Example: Red tape marks the $\underline{\textit{irregular}}$ spots on these sale items. (ir + regular)

The spy _______ the coded message. (un + scrambled)

Determine whether the specified value of t is a regular singular point of the given differential equation. $\left(1-t^{2}\right) y^{\prime \prime}+\frac{1}{\sin (t+1)} y^{\prime}+y=0 ; t=-1$

In the 2009-2010 regular season, the Portland Trail Blazers were 26-15 (26 wins and 15 losses) at home and 24-17 on the road.

a) How much better did the Trail BlazerS PERFORM at home in the 2009-2010 regular season? Calculate the difference in the proportion of wins at home and on the road.

b) Calculate a 95% confidence interval for the difference in the Blazers' ABILITY to win at home and their ability to win on the road.

c) Interpret the confidence interval in context.

d) Does the interval provide convincing evidence that the Blazers had a greater ability to win at home? Explain.

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 $( n = 36 , \overline { x } = 0.81682 \mathrm { lb } , s = 0.00751 \mathrm { lb } )$. Construct the confidence interval appropriate for the hypothesis: contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.

$\text{\blue{WHAT IF?}}$ Most prairies experience regular fires, typically every few years. If these disturbances were relatively modest, how would the species diversity of a prairie likely be affected if no burning occurred for 100 years? Explain.

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.

Write a regular expression that matches a string that represents a date given in the format DD/MM/YYY (where DD is a 2-digit day in the month,MMis a 2-digit representation of a month, and YYYY is a 4-digit year).

Determine the singular points of each differential equation. Classify each singular point as regular or irregular. $x^{3}\left(x^{2}-25\right)(x-2)^{2} y^{\prime \prime}+3 x(x-2) y^{\prime}+7(x+5) y=0$

Which statement about these poems is not true?
$F$ Both poems use rhyme.
$G$ Both poems follow a regular meter.
$H$ Each speaker asks a woman to read his verses.
$J$ Both poems are bitter in tone.

Predrag Stojakovic of the Sacramento Kings made 92.7% of his free throw attempts in the 2003–2004 NBA regular season. What is the probability that he will make exactly 10 of his next 15 free throw attempts?