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\def\header{{\hfill Exam 3
\hfill YELLOW
\hfill A. Miller
\hfill Fall 2005
\hfill Math 210\hfill}}

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    \string& \qquad \string\\ \string\hline}
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\begin{document}

\bigskip

{ \bf Show all work.

Simplify your answer.

Circle your answer. }

\bigskip

No books, no calculators, no cell phones, no pagers, no
electronic devices of any kind.


\par\vskip .25in
\begin{center}
Name\makebox[3in]{\hrulefill} \\
\end{center}

\bigskip
Circle your Discussion Section:
\begin{verbatim}

   343  T   12:05--12:55        1412 STERLING
   344  R   12:05--12:55        1327 STERLING
   345  T   13:20--14:10        1327 STERLING
   346  R   13:20--14:10        1327 STERLING 

\end{verbatim}
\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
   \input{exam.tbl}
  \hline \hline
 \end{tabular}
\end{center}

\immediate\openout\examTBLFile=exam.tbl

\bigskip

Solutions will be posted shortly after the exam:
www.math.wisc.edu/$\sim$miller/m210

\setcounter{page}{0}

\newpage

\prob{10} % 3.5
Three fair dice are thrown.  What is the probability that
at most one die comes up a six?  Circle your answer.

\answer $200/216$

\prob{10} % 4.2
A random variable $X$ has three possible outcomes, 10, 20, and 40.
The probability that $X$ is $10$ is $.2$ and the probability that
$X$ is $20$ is $.5$.  Find the 

(a) expected value of $X$, $\mu=E(X)$ and the 

(b) variation of $X$, $\nu=Var(X)$.

\noindent Circle your answer.

\answer $\mu=24$ $\;\;\;\;\;\nu=124$


\prob{10} % 5.1-15
Find the equation of the line thru the point $(-2,-1)$ and parallel
to the line thru the points $(2,3)$ and $(4,1)$.  Graph both lines.

\answer $y=-x-3$

\prob{10} % 5.2- 1
Suppose that Willie's Waterbeds makes a rectangular children's bed for
which the length is 25 percent larger than the width and the sum of
the length plus the width is 99 inches.  Find the length and width
of the bed.

\answer 44 by 55

\prob{10} % 5.3-31
The following is the augmented matrix for a
system of three linear equations in the four variables $x_1,x_2,x_3,x_4$.

$$
\left[
\begin{array}{rrrr|r}
 1  &  1  &  0  &  1 &  4\\
 0  &  1  &  1  &  0 &  1\\
 1  &  2  &  1  &  2 &  8\\
\end{array}\right]$$

If it has a unique solution
find it and state that the solution is unique.  

If it has no solution
state that and say why it has no solutions.  

If it has infinitely many solutions, state
that it does and find any two distinct solutions.  

\noindent Circle your
answer.

\answer There are infinitely many solutions.  Two are
$[1,0,1,3]$ and $[0,1,0,3]$

\prob{10} % 6.R- 7 (6.1)
Let
$$A=\left[
\begin{array}{rr}
 1  & 2   \\
-1  & 1   \\
\end{array}\right]
\;\;\;\;\;\;\;\;\;
B=\left[
\begin{array}{rrr}
-1  & -1 \\ 
 2  &  3 \\
\end{array}\right]
$$
Find $p$ and $q$ such that
$$pA+qB=
\left[
\begin{array}{rrr}
 -1  &   0  \\ 
  3   &  7  \\
\end{array}\right]
$$
Circle your answer.

\answer $p=1$, $q=2$

\prob{10} % 6.2- 13
Find the inverse (if it exists) of the matrix $A$.  Circle your answer.
$$A=\left[
\begin{array}{rrr}
0  &  1  &  1  \\
0  &  0  &  2  \\
1  &  0  &  1  \\
\end{array}\right]$$

\answer $$\left[
\begin{array}{rrr}
0  &  -1/2  &  1  \\
1  &  -1/2  &  0  \\
0  &   1/2  &  0  \\
\end{array}\right]$$


\finishtbl

\printanswers

\end{document}