Math 141, Sem. I, 1998-99 (R.A. Brualdi)
FINAL EXAM, December 21, 1998 NAME:______________________________________
*******ACCURACY TO TWO DECIMAL PLACES*******
1. [15 points] Information about the stock market for one cold
winter week is contained in the following table. Note that the close
on one day equals the open on the next day.
(a) Fill in all the missing entries.
DAY % change OPEN(points) CLOSE(points)
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Mon. up 5%
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Tues. down 3%
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Wed. up 7% 9100
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Thurs. down 5%
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Fri. up 2%
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(b) What was the total percent change for the entire week?
(c) Assuming this total percent change for the week, what was the opening
(points) on Monday, if the close (points) was 10,000?
2. [10 points] The city of Reason has a sales tax rate of 6.5%. A
certain coat is available in a department store. The list price of
the coat is $90. A sale on Monday advertises "Take 20% off the
price." Because of lagging sales, on Tuesday the store in Reason
advertises "Take an additional 12% off Monday's price."
(a) What is the total price (including tax) of the coat in Reason on
Tuesday?
(b) With the same sale terms, you buy a sweater in Reason on
Tuesday whose total price (including tax) is $55. What was the list
price of the sweater?
3. [10 points] A large tank contains a certain amount of water at
1:30 pm. Water is pouring into the tank at a constant rate, with 210
gallons added each hour. Water is draining from the tank at a
constant rate, with 2 gallons removed every minute. At 3:15 pm, the
tank contains 1000 gallons of water.
How much water was in the tank at 1:30 pm?
4. [10 points] Around a lake there is a path of length 10
kilometers. You are jogging around the lake at a constant rate of 8
kilometers an hour. A roller blader going at a constant rate of 20
kilometers per hour, passes you and, having gone around the lake and
caught up with you, passes you again. How far did you jog in
between the two times that the roller blader passed you?
5. [10 points] Two towns Quant and Reason are 200 miles apart. Car A
starts at Quant with an initial speed of 10 mph accelerating at a
constant 8 mph^2. Car B starts at the same time from Reason with an
initial speed of 5 mph accelerating at a constant 12 mph^2.
(a) How far are the cars from Reason when they meet?
(b) How fast is car A going when it arrives at Reason?
6. [10 points] Tritium H^3 has a half-life of 12.6 years.
(a) If 200 grams are put in a container, how much remains after 50
years?
(b) How many years would it take for the 200 grams to decay to 35
grams?
7. [15 points] On January 1, 1998 you deposit $200 in a bank account
which at the end every month pays you 0.5% interest on the balance
in your account at the beginning of the month.
(a) What is the balance in your account on January 1, 2000?
(b) If the balance in your account on January 1, 2000 was $400, what was
the balance on January 1, 1998?
(c) What would the monthly interest rate have to be if $200 grew to $400
from January 1, 1998 to January 1, 2000?
8. [20 points] Quantitative University (QU) has 25 administrators,
100 faculty, and 875 students.
(a) How many different committees of four can there be if a
committee consists of only faculty?
(b) How many different committees of four can there be if a
committee is to have 1 administrator, 2 faculty, and 1 student?
(c1) Two different people are randomly selected in succession (one
after the other) from QU. What is the probability that at least one
is a student?
(c2) When two different people are randomly selected in succession
from QU, what is the expected number of students selected?