Fundamentals of Math Final
If A = {a, b, c} and B = {1, 2, 3}, then which of i or ii is correct? i) A = B ii) A is equivalent to B a. (i) only b. (ii) only c. both (i) and (ii) d. neither (i) nor (ii)
B
If p = Bill is golfing, q = Addie is sailing, and r = Flo is jogging, then, in words, the statement p ∧ (q ∨ r ) would read: a. Bill is golfing, or Addie is sailing and Flo is jogging. b. Bill is golfing, and Addie is sailing or Flo is jogging c. Bill is golfing and Addie is sailing, or Flo is jogging d. Bill is golfing or Addie is sailing, and Flo is jogging
B
Which of the laws is being used in the following argument: If I study, then I will pass math. I didn't pass math. Therefore, I didn't study. a. Law of Detachment (modus ponens) b. Law of Composition (modus tollens) c. Law of Syllogism or transitional law d. none of the above
B
Given the conditional p→ q is true, which of the following statements is true: i) p is necessary for q ii) p is sufficient for q iii) q is necessary for p a. (i) and (ii) only b. (i) and (iii) only c. (ii) and (iii) only d. none of the above
C
In the addition table below, the additive identity is + A B C D A C D A B B D A B C C A B C D D B C D A a)A b)B c)C d)D
C
The equations (14 + 3) + 6 = 23 and 3 + (14 + 6) = 23 can be justified using i) Addition of whole numbers is commutative. ii) Addition of whole numbers is associative. a)(i) only b)(ii) only c)Both (i) and (ii) d)None of a, b, or c.
C
The subtraction problem took place in base "a". What is "a"? 341a - 163a = 189a a)10 b)12 c)11 d)None of a, b, or c.
C
In the 5-clock, a + 4 = a)a x 4 b)a x 3 c)a x 2 d)Impossible to determine without knowing a.
D
In the 9-clock, the reciprocal (multiplicative inverse) of 6 is a)3 b)6 c)5 d)None of a, b, or c.
D
Suppose p is the statement "15 = 25" and q is the statement "5 + 5 = 10". Which of i or ii is correct? i) p → q is true ii) q → p is false a. (i) only b. (ii) only c. Neither (i) nor (ii) d. Not a, b, or c
D
Which numeral does not represent the number of x's below? x x x x x x x x x x x x x a)21six b)31four c)11twelve d)None of a, b, or c
D
Which of these is false? a)37eight =31 b)54six = 37nine c)100011two = 2Btwelve d)None of a, b, or c
D
Construct a circle graph to represent the following information about the percent of the 37,000 tons of molybdenum that are mined by each of the following countries. Round to the nearest degree. Country Percent Degrees United States 61% Canada 16% Russia 11% Chile 9% Others 3%
Degrees US: 220° Canada: 58° Russia: 40° Chile: 32° Others: 11°
True or False: "If I do not get sick, then I will graduate" is the converse of "If I get sick, then I will not graduate."
False
True or False: 2364 ≡ 427 mod 5.
False
True or False: 35 ∈ {2, 4, 6, . . . }
False
True or False: 44 ∉ {x | x ∈ N}
False
True or False: Drawing two cards from the same deck is an example of independent events.
False
True or False: For any event A, 0 < P(A) < 1 (read this carefully!).
False
True or False: Given p = Today is Monday and q = I am tired, then ~p ∧ q can be written as, "Today is not Monday, and I am not tired."
False
True or False: If A = {a, e, i, o}, then A has at most eight subsets
False
True or False: If A and B are disjoint sets, then A and B have only one element in common.
False
True or False: If ice cream cones come in 3 sizes and in 3 flavors, then there are 6 possible ice cream cones.
False
True or False: If p is false and ~q is false, then ~p ∧ ~q is true.
False
True or False: In base four, only the remainder is important.
False
True or False: In the 4-clock, 3 + 2 = 5.
False
True or False: In the 6-clock, 2 is the reciprocal (multiplicative inverse) of 3.
False
True or False: In two collections of data, the collection with the higher standard deviation has the higher mean.
False
True or False: Subtraction of the whole numbers (0, 1, 2, 3, ...) has the closure property but not commutative property.
False
True or False: The sentence "How old are you?" is considered to be a statement in logic.
False
True or False: The truth values for the conditional p → ~q are T, F, T, F.
False
True or False: The variance of the data -2, 0, 2 is zero.
False
True or False: The z-score of the mean is always 0.
False
True or False: {a, t, c} is equal but not equivalent to {c, a, t, a}
False
Find the GCF and LCM of 52 and 442.
GCF: 26 LCM: 884
Use an appropriate method to determine the validity of the following arguments. State whether the argument is valid or invalid on the line given, and show your justification. If Paula is not polite, then Sally is quiet. Sally is not quiet. Therefore, Paula is not polite
Invalid
Use an appropriate method to determine the validity of the following arguments. State whether the argument is valid or invalid on the line given, and show your justification. All logic students are mathematics students. Some logic students are not gullible. Therefore, some gullible people are not mathematics students.
Invalid
Use an appropriate method to determine the validity of the following arguments. State whether the argument is valid or invalid on the line given, and show your justification. If Andre gets help, then Andre will pass. Andre did not get help. Therefore, Andre did not pass.
Invalid
To test the reliability of a lot (a unit of production) of automobile components produced at a certain factory, the first 30 components of a lot of 1000 are tested for defects. Describe the population, the sample, and any potential sources of bias.
Population: the lot of 1000 Sample: the 30 components actually tested (cluster sampling) Bias: Instead of taking the first 30, one should randomly select 30 components in the lot.
True or False: Commutativity does not hold for division.
True
True or False: Histograms are appropriate graphs for grouped numerical data.
True
True or False: If a ≡ b mod m, then a+c ≡ b+c mod m.
True
True or False: If two dice are tossed and one coin is flipped, there are 72 possible outcomes.
True
True or False: The Chinese numeration system used a symbol for zero.
True
True or False: The clock number is the additive identity in clock arithmetic.
True
True or False: The z-value is the number of standard deviations that a particular data value is from the mean.
True
True or False: Zero is the identity element for whole number addition.
True
Use an appropriate method to determine the validity of the following arguments. State whether the argument is valid or invalid on the line given, and show your justification. No golfers are sane. All students are sane. Therefore, no students are golfers.
Valid
A jar contains 13 marbles: 3 red, 4 white, and 6 blue. Two marbles are drawn without replacement. What is the probability that they are the same color? a. 4/13 b. 9/13 c. 10/13 d.none of these
a
In a certain two-dice game, you win $2 if the sum of the dots that appear is prime. Otherwise you lose $1. What is the expected value of the payoff? a.25 cents b.83 1/3 cents c.$1.00 d.none of these
a
Assume that the salaries of elementary school teachers are normally distributed with mean $29,835 and standard deviation $3000. a. Find the probability that a randomly selected elementary teacher earns more than $35,000. b.What percent of elementary teachers earns more than $25,000? c. If 25 elementary teachers are randomly selected, about how many of them would you expect to make between $30,000 and $38,000?
a) .043 b) 94.6% c) 11 teachers (or approximately 12)
For the sequence {1/3, -1/6, 1/12, -1/24,...} a) write the 17th term b) determine the sum of the first 17 terms
a) 1/196608 b) 43619/196608
Multiply or divide as appropriate. a) 1213six × 45six b) 102seven ÷ 6seven
a) 103513six b) (11R3)seven
Suppose the odds against an event A happening is 7:12; find a.the odds in favor of A: b. the probability of A:
a) 12:7 b) 12/19
Use a Venn diagram to answer the following questions. SHOW YOUR DIAGRAM! Seventy-five students participated in a survey at a local college and the following data were collected. There were 30 students taking accounting and 9 taking only psychology. Forty-one were taking statistics. Thirteen students were taking accounting and statistics but not psychology, and 17 were taking psychology and statistics. Five students were taking all three courses. Twelve people only took accounting. a) How many students in the group were not taking any of the three subjects? b) How many students in the group were taking psychology? c) How many students were taking accounting and psychology, but not statistics? d) How many students were taking just one of these subjects?
a) 13 b) 26 c) 0 d) 32
Add or subtract as appropriate. a) 6Btwelve + A1twelve b) 11five - 4five c) Draw a picture model to check your work for both a) & b)
a) 150twelve b) 2five
What Hindu-Arabic number is represented by the following Roman Numerals? a)MCMXII b)CDXCVI
a) 1912 b) 496
For the sequence {0.6, 1.6, 2.6, 3.6, . . . } a) write the 23rd term b) determine the sum of the first 23rd terms
a) 22.6 b) 266.8
Perform the operations below and state the answer. a) 2 + 3 + 6 (8-clock) b) 5 × 3 × 2 (7-clock) c) 9 + (3 - 6) (12-clock) d) 5 ÷ 3 (7-clock)
a) 3 b) 2 c) 6 d) 4
Using the following scores, {20, 26, 31, 35, 15, 18, 26, 40, 24, 50, 21, 32, 26, 49, 31, 18, 22, 28} a) What is the 70th percentile? b) Determine all three quartiles: Q1 = ; Q2 = ; Q3 = c) Using the scale below, draw a box and whiskers plot for the data above:
a) 32 b) Q1 = 21, Q2 = 26, Q3 = 32 (49 and 50 are outliers)
Give the prime factorization of each number. a) 279 b) 186
a) 3²×31 b)2×3×31
For the set : {7, 11, 15, 19, ...} a) Write the general term. b) Verify that the set is infinite.
a) 4n+ 3 b) {7, 11, 15, 19,... 4n+3} {11, 15, 19, 23,... 4n+ 7}
A box of chocolates contains 5 nut candies and 10 creams. Leslie does not like nuts and cannot tell by looking at the chocolates which have nuts and which do not. However, she has been taught that once you touch a candy, you cannot put it back in the box. What is the probability that it will take the following number of tries to get a cream chocolate? a. 2 tries b. 4 tries c. 6 tries
a) 5/21 b) 5/273 c) 1/3003
A pass code consists of three letters from T - Z followed by two digits. If the letters may be repeated but the digits may not, a.how many different pass codes are possible? b.what is the probability that the first letter is a U or W and the last digit is even?
a) 7·7·7·10·9 = 30,870 b) 1/7
Find each of the following for the given set of data: {53, 42, 67, 53, 42} a. mode: b. median: c. mean: d. mid range: e. range: f. variance (Round to two decimal places): g. standard deviation (Round to two decimal places): h. Create a stem-and-leaf plot for the data.
a) mode: 42 and 53 b) median: 53 c) mean: 51.4 d) midrange: 54.5 e) range: 25 f) variance: 106.3 g) standard deviation: 10.31 h)4 | 2 2 5 | 3 3 6 | 7
Find the opposite (additive inverse) and reciprocal (multiplicative inverse--if it exists) for the following: a) 4 (6clock) b) 2 (5 clock)
a) opposite: 2; reciprocal: none b) opposite: 3; reciprocal 3
Given A = {x, y, z}: a) List all the subsets of A: b) Underline the proper subsets of A listed in part a).
a) {X}, {Y}, {Z}, {X,Y}, {X,Z}, {Y,Z}, {X,Y,Z}, { } b) {X}, {Y}, {Z}, {X,Y}, {X,Z}, {Y,Z}, { }
A small college had 150 tenured full professors and 125 tenured associate professors. A random sample of 10 of the full professors is selected and, separately, a simple random sample of 10 of the associate professors is selected. The two samples are combined to give an overall sample of 20 professors. The overall sample is a. random sample. b. a stratified sample. c. cluster sample d. a systematic sample.
b
What missing number will produce a mean of 11.4 for the following list of five numbers: { 7, 9, 13, 17, ?} a.10 b.11 c.12 d.none of these
b
Which of the following are necessary for n C r = n P r : i) n = 4 ii) r = 1 a.(i) only b.(ii) only c.both (i) and (ii) d.none of these
b
What is the standard deviation for these data: 2, 4, 6, 8, 10? (Be prepared to show your work on the test.) a.√8 b.√40 c.√10 d.none of these
c
Inverse: If it is raining, then the sun is not shining. conditional: converse: contrapositive:
conditional: If it is not running then the sun is not shining converse: If the sun is shining, then it is not raining contrapositive: If the sun is not shining then it is raining
Contrapositive: You will succeed if you work hard. converse: conditonal: inverse:
converse: If you don't work hard then you don't succeed conditonal: If you don't succeed then you don't work hard inverse: If you do succeed then you did work hard
What are the odds against rolling a sum greater than 10 when rolling two dice? 16 a.1:12 b.11:12 c.12:1 d.none of these
d
Find all integers n, where -15 ≤ n ≤ 18, which make 13 n mod 4 true.
{-15, -11, -7, -3, 1, 5, 9, 13, 17}
List all factors of 75.
{1, 3, 5, 15, 25, 75}
Find all integers n which make 12 ≡ 2 mod n true.
{2, 5, 10}
Write a data set that meets the following characteristics: __ n=7 x= 20 s= 0
{20, 20, 20, 20, 20, 20, 20}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: A - C
{i}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: A ∪ B
{i}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: __ A ∪ B
{k,e,l,i}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: __ __ A∩B
{k}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: ________ (A∩B)
{n,c,k,e,l}
If U = {n, i, c, k, e, l} , A = {n, i, c} , B = {i, e, l} , and C = {n, c, l} , list the elements in the following set: A ∪ (B ∩ C)
{n,i,c,e}
In a certain game, a different numbered ball from 1 to 15 is drawn by each player. If five people are playing and the value on the ball is important, how many different ways can balls be drawn?
₁₅P₅ = 360,360
How many different ways can 7 people choose a president, vice-president, and secretary for their group?
₇P₃ = 210
A 12-sided fair die, having faces numbered 1 - 12, is tossed once and the number on the top face is recorded. Let A be the event that the number is not prime, and let B be the event that the number is odd. a. Find P(A | B). b. Find P(B | A)
(a) P(A|B) = 1/3 (b) P(B|A) = 2/7
Given the following statements: p: Today is Tuesday q: The sun is not shining r: I am glad to be in class Rewrite the following sentences in symbolic form: 1) The sun is shining and I am glad to be in class, or today is Tuesday. 2) If today is Tuesday, then I am glad to be in class and the sun is shining. 3) Either today is Tuesday and I am not glad to be in class, or the sun is not shining.
1) (∼q∧r)∨p 2) p→(r∧∼q) 3) (p∧∼r)
Given the following statements: p: Today is Tuesday q: The sun is not shining r: I am glad to be in class Translate the following symbolic statements in English sentences: 1) ( q ∧ ~p) → r 2) r ∨ (q ∧ p) 3) (r ∧ ~p) ∨ (r ∧ ~q)
1) If the sun is not shining and today is not Tuesday, then I am glad to be in class. 2) I am glad to be in class, or the sun is not shining and today is Tuesday. 3) I am glad to be in class and today is not Tuesday, or I am glad to be in class and the sun is shining.
Find the probability of drawing a red ace followed by a black king in a 52 card deck, drawing without replacement.
1/663
Find all possible replacements for x to make 3x = 6 in the 9-clock.
2, 5, 8
37eight = 51b. Find b. Show your work.
6
What is the smallest counting number divisible by 2, 4, 5, 6, and 12?
60
How many distinguishable permutations can be made from the letters in the word recesses?
8!/ 3! 3! = 1120
Convert 135eight to base 10 notation.
93
Which of a, b, or c is true for the following numerals in base 11? a)10eleven + 10eleven = 20eleven b)Aeleven + 1eleven = 11eleven c)Aeleven + Aeleven = 2Aeleven d)None of a, b, or c
A
