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Unformatted text preview: Name: Exam I — Math 132 0 Show all of your work, and clearly indicate What your ﬁnal ansWer' is.
If there are two apparent answers for one question, you will receive no
credit for that problem. 0 Leave numbers as exact answers. % is ﬁne7 but .333 is not an acceptable
answer. 
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so — _ 1. While at home for the summer Hermione Granger happens across a
puzzle loving warlock and his house elf who are just coming back. from
their holiday in the States. As the founder of the Society for the Pro , motion of Elvish Welfare (S.P.E.W.), she feels it is her duty to try and . convince the warlock to free the house elf from his service. The war—
lock decides thathe will free the elf if Hermione can ﬁgure out how
much change he has remaining from his trip to the U.S.i “I have twice '
as many nickels as I have dimes, and I have two more dimes than I ‘ have quarters” starts the Warlock. “If I have 21 coins in alland $1.37
in coins, how many of each coin do I have?” 0 Assuming the warlock has q quarters, cl dimes, n nickels, and p
pennies; write an equation which relates the number of pennies,
number of nickels, number of dimes, and number of quarters the warlock has to the total amount of money he has in his pocket.
(4 points) " 0 Write an equation which relates the number of pennies, number
of nickels, number of dimes, and number of quarters the warlock
has to the total number of coins he has in his pocket. (4 points) o In both of the above equations, isolate the variable representing
“the number of pennies”, and then treat it as a “dummy” variable
so you can ﬁnd a new equation that no longer has that variable. 
(6 points) 0 Write an equation which relates d to n and a second equation
relating d to q; in each case write the equation so that dis isolated.
(3 points each) 0 Solve the Wizard’s riddle. (5 points) 2. Professor McGonagall gave her students an exam that had an easy question and a really hard question where it was expected (based on I  previOus years she had asked these questions) that 90% of thestudents,
would get the easy question correct and only 5% would get the hard 
question correCt. Due to all the craziness that goes on at Hogwart’s,
Minerva typically makes a mistake on grading. Since it is easier to
follow the reasoning in a correct answer than an incorrect answer she
usually marks a right answer as wrong about 5% of the time and a
wrong answer as right about 10% of the time. Fill in the following
table with the probability distribution for the easy question and the
hard question (15 points) .
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correctl ' —
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correctl
Graded 
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o What is the probability that a student that had the hard question
marked as correct actually answered it correctly? (5 points) o Hermione notices that Ron got both the hard and easy question
marked wrong and she suggests that he should contest the grading
on the easy question, but it’s probably not worth contesting the
harder question. Why would she suggest this? (5 points) ...
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 Spring '07
 BAE
 Math, Correctness, EASY question, Hermione Granger

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