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Unformatted text preview: Name MAT 117 Final Exam
December 15, 2003 Answer all questions. I A) Recall the game “What’s My Number?” The rules were that a number is picked with
three distinct digits. Your job is to guess what the correct number was. Here is a list
on the guesses and the information obtained for each guess. Give the number and
justify why the number you have chosen is the right number. Gu_ess Correct Digits Correct Places
123 1 0
234 1 l
345 2 0
456 1 0
567 1 1
678 0 0
789 0 0 B) Abigail was to plant ﬁg trees in a rectangular array. She has 36 trees. Find all
possible numbers of rows if each row (in a given arrangement) is to have the same number of trees. II A) Mackenzie was asked to write 2 x 126 + 10 x 123 + l x 120 as a base twelve
numeral. She wrote 2T1. Was she correct? If yes, why? If not, why not? Explain your reasoning am her possible reasoning. B) Consider the numeration system in use with some machines that uses the combination
of our digits and the ﬁrst six letters of our alphabet. It is assumed that the letters
represent ten, eleven, and so on in order. The digits in this system are thus {0, 1, 2, 3, 9, a, b, f}. i) What is the base of this numeration system? Why? ii) What number (in base ten) does the numeral aa represent? Why? III A) Jana was asked to subtract in base two: IIOOOOOOMO — 1000001,”.0. She showed this work: 1 1000002 1 1000022 1 1000222 1 1002222 1 1022222
1000011 1000111 1001111 1011111 1111111
11222222 13222222 2111111 12111111 Will she be successful in subtracting? Explain her possible reasoning. B) The table on the right indicates
the operation 69 on {a, b, c}. 6)
a
b
c i) 15 the set {a, b, c} closed under (9? Explain. ii) Does the operation 93 have an identity element in {a, b, c} ? Explain. iii) Is G) commutative on {a, b, c}? Explain. iv) Does c have an inverse? Explain. IV A) Let p, q, and r be prime numbers. Find the least common multiple of the two integers
psqr3 and p2q4. B) Consider the integer with prime factorization p x q x r, where p, q, and r are prime
numbers. Does this integer have more than six factors, exactly six factors, or less than
six factors? Justify your answer. True or False? Iftrue, explain why. If false, explain why OR give a counterexample. A) A divisibility test for ﬁve in base ﬁve need only consider the last digit in the numeral. B) There is a number that is both prime and composite. C) All real numbers are natural numbers, whole numbers or integers. D) A scatter plot is the best way to depict unpaired data. E) Experimental probability always gives the same results as theoretical probability. A) A survey of 100 college faculty who dine out regularly found that 32 eat pizza, 3O eat
burgers, 15 eat salads, 6 eat pizza and salad, 1 eats pizza and burgers, 5 eat salad and burgers, and l eats all three. (Hint: Draw a diagram to help you.) i) How many of the faculty members surveyed do not eat any ofthese three selections? ii) How many faculty membersjust eat salad (ofthe three choices given)? iii) What is the probability that a burgereating faculty will also eat pizza or eat
salad? B) The boxandwhisker plot and histogram below represent sample data taken from a
study with 50 elementary students. Answer the questions based on the information
given. lfthe information needed cannot be obtained from the graphs, SAY SO. 2 3 4 3 Hrlghl (ﬂ) i) What is the mean height ofthe students in the sample? ii) Find the number of students in the sample who are at least 4 ft tall. iii) How many students in the sample are female?
iv) What is the probability that a male student is over 4 ft tall? v) What percentage of sample students say their favorite lunch is pizza? VII A) Draw a graph representing the height of water in a bathtub as it is ﬁlled, used, and
emptied as follows: At the beginning, the tub is empty. The drain is plugged and the tap is opened
gradually to its fullest extent. The tap is closed after the tub is half ﬁlled. After some time has passed, someone gets into the tub. After bathing, the person gets out of the
tub, and then pulls the plug and allows the water to drain. Note: Label the axes appropriately and identify points on your graph with what
happens at different stages. B) Pappy Snappy, a math enthusiast, has determined that by iterating the expression x3
he always gets a larger number. Is this the whole story? Give the “whole story” and justify your response. VIII A) Think of a problem in a context appropriate for elementary school children that
illustrates the operation of division as repeated subtraction. i) Pose the problem as a question. ii) Solve the problem illustrating the use of repeated subtraction. B) Think of a real—life situation (choose a context different to those appearing in this
exam) where there is a functional relationship between an independent and dependent
variable. i) Describe the situation in words, graph, table OR equation. ii) Identify the independent variable and explain why the relationship is a function. ...
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 Spring '11
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