MATH 105- Final study guide
For set D= {5,7,9,11} determine n(D)
4
Write the following statement in symbolic form: It is time to sleep and this is an octopus, or I eat bananas (~ ↔ Λ V ) P:It is time to sleep Q: This is an octopus R: I eat bananas
(p Λ q) V r
Use inductive reasoning to predict the next three lines in the pattern 30, 22, 14, 6 ____, _____, _____
-2, -10, -18
One card is selected at random from a deck of cards. Determine the probability that the card is a 10
1/13
At a music store 60 people were asked their favorite type of music. Of these 10 chose rock, 29 chose country, 4 chose classical, and 26 chose something else. What is the probability that a customer will choose rock
1/6
One card is selected at random from a deck of cards. Determine the probability that the card is NOT a 7
12/13
The term 'prime rate' is best described by which of the following a. The interest rate leading banks charge to their best customers b. The current return rate of U.S. treasury bills c. The lowest interest rate available to the average borrower d. The interest rate charged by banks to the U.S. treasury
A
Express the set in roster form: The set of natural numbers between 10 and 15
A= {11, 12, 13, 14}
Express the following in set-builder notation: B= {11,12,13,14,15} ≤ ≥ ⍷
A= {x | x ⍷ N and 11≤ x ≤ 15}
The collection, organization, and analysis of data is called what type of statistics a. population b. descriptive c. sample d. inferential
B
Use DeMorgan's laws to write an equivalent statement to: It is false that Mexico is an island and Australia is an Island a. If Mexico is not an island, then Australia is not an island b. Mexico is not an island or Australia is not an island c. Medico is an island or Australia is not an island d. Mexico is not an island and Australia is not an island
B
Use DeMorgan's laws to write an equivalent statement to: It is false that you are in class or you are awake a. You are not in class or you are not awake b. You are not in class and you are not awake c. If you are not in class then you are not awake d. You are in class or you are not awake
B
Select any of the following that are statements a. Close the door. b. The earth is flat c. January is in summer d. Where is the box?
B, C
Find the letter that will be entry #63 in the sequence C,D,C,D,C,D,C,D
C
Making generalizations or predictions from collected data is called what type of statistics a. sample b. population c. inferential d. descriptive
C
The term 'moral hazard' refers to which of the following a. Financial institutions that are 'too big to fail' b. violation of ethical standards by lenders c. Protection of lenders from the results of bad loans d. refusal of lenders to lend to medium income people
C
Write the negation of: No Unicycles have three wheels a. Not all unicycles have three wheels b. Some unicycles do not have three wheels c. Some unicycles have three wheels d. All unicycles have three wheels
C
a group of people are classified according to income and then random samples from each group are taken. This is what type of sampling? a. cluster b. systematic c. Stratified d. random e. convenience
C
List the compound statements below that are true a. 5+3=8 and 5+3=10 b. 5+3=9 or 5+3=10 c. 5+3=8 or 5+3=10 d. 5+3=8 and 5+4=9
C, D
Use the fact that p → q and ~p V q are equivalent to write an equivalent form of: If Jane buys a new car then she sells her old car a. Jane does not buy a new car and she sells her old car b. Jane does not buy a new career she does not sell her old car c. Jane does not buy a new car and she sells her old car d. Jane does not buy a new car or she sells her old car
D
What is the meaning of 'home equity' a. The interest paid for the home b. The total amount paid for the home c. The value of the home minus the amount paid d. the value of the home minus the balance due
D
Write the negation of: All bears have claws a. Some bears have claws b. All bears do not have claws c. No bears have claws d. Some bears do not have claws
D
Express the set in roster form: E= {x |x ⍷ N and 15< x <20} GREATER THAN OR EQUAL TO 15
E= {15, 16, 17, 18, 19}
The word AND describes Intersection Union
Intersection
The word OR describes Intersection Union
Union
A belief on specific observations that has not been proven is called a conjecture or which of the following a. inductive reasoning b. the scientific method c. a hypothesis d. a counterexample
a hypothesis
Determine if the following pair of sets are equal, equivalent, both or neither A= {math, chemistry, history} B= {history, math, chemistry}
both
The type of reasoning used to prove a conjecture is called what type of reasoning a. scientific b. deductive c. hypothesis d. inductive
deductive
Determine if the following pair of sets are equal, equivalent, both or neither A= {math, chemistry, history} B= {a, b, c}
equivalent
Determine if the following is true or false:{h} ⍷ {g, h, l}
false
{2, 7, 8} ⊂ {8,2,7}
false
{2,6} ⊂ {2,7,8}
false
Ø = {0}
false
In science, any hypothesis must be which of the following? a. mathematical b. true c. simple d. falsifiable
falsifiable
Determine whether the set is infinite or finite. {32, 40, 48..., 64} a. infinite b. finite
finite
The process of reasoning to a general conclusion through observation of specific cases is called what type of reasoning a. conjecture b.deductive c. scientific d. inductive
inductive
Determine whether the set is infinite or finite. The set of all odd numbers greater than 29 a. infinite b. finite
infinite
Determine if the following pair of sets are equal, equivalent, both or neither A= {math, chemistry, history} B= {math, chemistry, history, philosophy}
neither
Determine if the set is well defined or not well defined. The set of the five worst U.S. parks a. well defined b. not well defined
not well defined
Write the following statement in symbolic form: I work hard or I do not get a raise (~ ↔ Λ V ) P: I work hard Q: I get a raise
p V ~q
Write the following statement in symbolic form: If it is time to sleep, then it is late or I am not tired (~ ↔ Λ V → ← ) P:It is time to sleep Q: it is late R: I am tired
p → (q V ~r)
5 ⍷ {4, 5, 6} A. True B. False
true
{2, 7} ⊂ {2,7,8}
true
{2, 7} ⊆ {2,7,8}
true
{2,7,8} ⊆ {8,2,7}
true
Ø ⊆ {2,7,8}
true
Determine if the set is well defined or not well defined. The set of U.S. Vice Presidents a. well defined b. not well defined
well defined
Write the following statement in symbolic form: It is not time to go to sleep but it is late (~ ↔ Λ V ) P:It is time to go to sleep Q: It is late
~ p Λ q
Write the following statement in symbolic form: It is false that the radio is loud or the clock is small (~ ↔ Λ V ) P: The radio is loud Q: The clock is small
~(p V q)
Write the following statement in symbolic form: I do not complete my homework or I get a raise (~ ↔ Λ V ) P: I complete my HW Q: I get a raise
~p V q
Write the following statement in symbolic form: I do not graduate if and only if I get an A. (~ ↔) P: I get an A Q: I graduate
~q ↔ p
