final study questions
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School
Mount Royal University *
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Course
1101
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
15
Uploaded by BrigadierCapybara7317
Homework 1
1.
The negation of a true statement is a (false) statement, and the negation of a false statement is a (true) statement.
2.
What is the negation of “some A are B”?
-
No A are B
3.
What can the statement “some A are not B be expressed equivalently as?
-
Not all A are B
4.
Statements that contain the words all, some, and no are called (quantified) statements
5.
The statement “no A are B” can be expressed equivalently as… -
All A are not B
6.
The negation of “all A are B” is
-
Some A are not B
7.
A statement is a sentence that is (true) or (false) but not both simultaneously. 8.
What can the statement “some A are B” be expressed equivalently as?
-
There exists at least one A that is a B
9.
The statement “all A are B” can be expressed equivalently as… -
There are no A that are not B
10.
The negation of statement p is expressed by writing (~p). we read this as (not p).
Homework 2
1.
Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. Use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements.
-
If I do not like the song and I change the station, then the DJ is not entertaining, or I look for a CD to play: (~p ∧
r) → (~q ∨
s)
2.
Dr. Smith does a study with three groups of ten students each. Each group consumes a different amount of caffeine (high, medium, and low amounts). Dr. Smith then measures all of the students
on how well they do on a concentration test. What is the dependent variable in this study?
-
The results of the concentration test 3.
If it rains, I get gloomy.
If I get gloomy, I go to a movie
Therefore, -
If I do not go to a movie, it did not rain 4.
Which of the below was evidence used by Alfred Wegener to construct his theory is Continental Drift?
-
Fossil record
5.
Even with the multiple pieces of evidence, why was Wegener’s continental drift idea still rejected
by scientists?
-
He did not have a mechanism for what caused the continents to move away from one another
6.
Strawberry plant clones are given different amounts of water for a 3-week period. The first strawberry plant receives 400 ml a day. The second plant receives 200 ml a day. The third strawberry plant receives 100 ml a day. the fourth strawberry plant does not receive any extra water; this plant only receives natural ways of receiving water. The height of the strawberry plants is recorded daily. Name the independent variable and one constant. -
Amount of water, type of water
7.
Write the indicated compound statement in its symbolic form
P: the outside humidity is low Q: the central humidifier is running
R: the air in the house is getting dry
It is not the case that if the air in the house is getting dry, then the central humidifier is not running
-
~ (r → ~ q)
8.
Construct a truth table for the given statement and then determine if the statement is a tautology [(p
~q) v q]
p
-
No 9.
Determine if the argument is deductive or inductive and if it is logically valid. The giants have lost their last seven games. Thus, they will probably lose their next game
-
Inductive, not logically valid 10.
Select the statement that is not equivalent to the statement below
It is not true that Ingrid and Melanie are both chefs. -
Ingrid is not a chef and Melanie is not a chef Statement An equivalent way to express the statement
All A are B
There are not A that are not B
Some A are B
There exists at least one A that is a B
No A are B
All A are not B
Some A are not B
Not all A are B
Homework 3
1.
James and Susan wish to have $10,000 available for their wedding in 4 years. How much money should they set aside now at 6% compounded monthly in order to reach their financial goal? ($7870.98)
2.
Add in the indicated base (BDDsixteen)
-
64A
sixteen
+
593
sixteen
3.
Write the number as Hindu-Arabic (136922)
4.
Perform the indicated operation
5.
Multiply in the indicated base. (2814sixteen)
E4
sixteen
× 2D
sixteen
6.
Convert the number to the indicated base (11244seven)
2874 to base seven
7.
A mother invests $9000 in a bank account at the time of her daughter’s birth. The interest is compounded quarterly at a rate of 7%. What will be the value of the daughter’s account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? ($36,057.53)
8.
Which is the better choice: $1000, deposited for a year at a rate of 4.8% compounded semi-
annually or at a rate of 4.7% compounded quarterly? (4.8% compounded semi-annually is better) 9.
Express the repeating decimal below as a quotient of integers. If possible, reduce to lowest terms. (856/999)
0.856
10.
An earthquake measuring 4.0 on the Richter scale releases______ times more energy than an earthquake measuring 2.0. (1000)
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Homework 4
1.
An industrial psychologist is interested in whether lowering the temperature in a packing room will increase productivity (number of products packed). Workers in two equivalent packing rooms participate in the study. One room is maintained at 65 degrees, the other room is left at the usual company temperature of 76 degrees. What is the control group?
-
Workers in the room at 76 degrees 2.
The process where one neutron hits a nucleus, which causes it to split releasing more neutrons which hit more nuclei causing more neutrons to be released which hit more nuclei and so on is called… -
A chain reaction 3.
Which of the following is false about bacteria?
-
Bacteria need to hijack a host cell to replicate 4.
An industrial psychologist is interested in whether lowering the temperature in a packing room will increase productivity (number of products packed). Workers in two equivalent packing rooms participate in the study. One room is maintained at 65 degrees, the other room is left at the usual company temperature of 76 degrees. -
temperature
5.
compute r, the correlation coefficient, rounded to the nearest thousandth, for the following data: (-
0.905)
X
9
7
2
6
5
11
4
Y
7
9
15
8
11
7
14
6.
what is a pathogen?
-
A microorganism that causes a disease 7.
A strep culture is sampled at two points in time, 1 hour and 10 minutes apart. 3.2 x 10^6 cells/ml are found in the first sample, and 1.8 x 10^7 cell/ml in the second sample. What was the doubling
time in minutes? (28.1)
8.
a research group studied the effects of a new toothpaste on the incidence of cavities in 1
st
grade children. The intervention group was given yummytooth toothpaste, while the control group was given an identical toothpaste that did not contain the secret ingredient in yummytooth. Subjects were observed brushing their teeth 3x per day with the assigned toothpaste. 6 months later, dental
appointments were scheduled, and the number of dental cavities present in each child was reported. What was the dependent variable?
-
The number of dental cavities 9.
A bacteria culture starts with 4000 bacteria. After 8 hours there are 64,000 bacteria present. What is the length of the doubling period? (2 hours)
10.
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid between $150,000 and $154,800 if the standard deviation is $1600. (49.85%)
Quiz 1
1.
Complete the truth table p
q
p ^ q
~(p^q)
T
T
T
F
T
F
F
T
F
T
F
T
F
F
F
T
2.
P: I eat bananas
Q: the taxes are high Write the symbolic statement ~p ^ ~q in words: I do not eat bananas and the taxes are not high
3.
Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning.
There are no computers that are not smart
-
All computers are smart
4.
Determine whether or not the sentence is a statement
Purple can be obtained by mixing red and blue together. Is this a statement?
-
Yes, because the sentence can be either true or false, but not both simultaneously
5.
Complete the truth table p
q
~p
~q
~p ^ ~q
T
T
F
F
F
T
F
F
T
F
F
T
T
F
F
F
F
T
T
T
6.
Write the negation of the statement: there are no computers that are not smart
-
some computers are not smart 7.
construct a truth table for (p ^ q) ^ ~q
p
q
~q
p ^q (p ^ q) ^ ~q
T
T
F
T
F
T
F
T
F
F
F
T
F
F
F
F
F
T
F
F
8.
p: you are human
q: you have feathers you have feathers if you are not human. ~p
q
9.
Form the negation Tuesday does not come before Wednesday
-
Tuesday comes before Wednesday
10.
P: the fire is not burning
Q: the key of C does not have three flats
Express the following symbolically: the fire is burning
-
~p
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Quiz 2
1.
Use the De Morgan law to write an equivalent English statement for the following
It is not the case that a pen and a banana are both writing implements
-
A pen is not a writing implement, or a banana is not a writing implement
2.
Complete a truth table p
q
~p
(
p
↔q)
(
~p ^ q)
(p
↔ q)
(~p v q)
T
T
F
T
T
T
T
F
F
F
F
T
F
T
T
F
T
T
F
F
T
T
T
T
3.
Determine if the below is true or false:
A conditional statement is false only when the consequent is true, and the antecedent is false
-
False
4.
Use a truth table to determine if the statements below are equivalent
~q ^ p and ~q
p
-
No 5.
Select the contrapositive If I am in the city of Fligaroo, then I am on the planet Plochus
-
If I am not on the planet Plochus, then I am not in the city of Fligaroo
6.
A conditional statement is (equivalent) to its contrapositive, but not to its (inverse) or its (converse)
7.
Select the inverse and the converse of: if you are running on the beach, then you are not studying
-
Inverse: if you are not running on the beach, then you are studying
-
Converse: if you are not studying, then you are running on the beach 8.
The table below shows ice cream cone sales at an ice cream shop. P: vanilla is the best-selling flavour
Q; chocolate chip outsold strawberry by 13,000 cones
flavour
Sales in thousands of cones chocolate
33
Vanilla
31
Chocolate chip 27
Strawberry 14
coffee
8
butterscotch
5
Write the statement in words. ~q
~p
-
If chocolate chip did not outsell strawberry by 13,000 cones, then vanilla is not the best-selling flavour -
Truth value: true 9.
De Morgan’s laws state that ~ (p v q) is equivalent to ~p ^ ~q and ~ (p ^ q) is equivalent to ~p v ~q
10.
If the conditional statement is s
t What is the below called?
~s
t
-
The inverse Quiz 3 1.
In any base, the digit symbols begin at (0) and end at (one) less than the base
2.
Add in the indicated base 3.
Convert the myan numeral below to Hindu Arabic (46375)
4.
A movie theater has two screens and shows its movies continuously. A 30-minute documentary is
shown on one screen. A 90-minute feature is shown on the other. If both movies begin at noon, how many minutes will pass before both movies begin at the same time again? (90)
5.
Multiply in the indicated base (231five)
6.
Convert the hexadecimal numeral below to a numeral in base ten (47844)
7.
Convert the base ten numeral below to a numeral in the specified base (4443seven)
8.
Write the Babylonian numeral as a Hindu Arabic numeral (11523)
9.
Convert the numeral below to base ten (3247)
6257eight
10.
Subtract in the indicated base (111two)
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Quiz 4
1.
If you placed $3 into an account that paid interest at a rate of 5% and compounded the interest 3 times a year, how much would that account be worth in 280 years? (3,214,639.98)
2.
Perform the indicated operation (13 root 5)
3.
In a proof by contradiction, we use a conditional statement if p then q and examine whether q is true or false. Does that allow us to prove or disprove p?
-
Disprove p 4.
Perform the indicated operations and if possible, reduce the answer to its lowest terms (-11/4)
5.
If you invest $4107 in an account that pays 4.2% per year, compounded continuously, how much will you have after 16 years? ($7,685.89)
6.
Combustion reactions are “net energy producers” because (the amount of energy input is far less than the amount of energy output)
7.
Giuseppe deposits $12,000 in a passbook savings account that has a rate of 6.5%. find the effective annual yield if the interest is compounded quarterly? (6.6%)
8.
A bank offers a CD (certificate of deposit) that pays a simple interest rate of 8.5%. How much must you put in this CD now in order to have $19,760 to replace all the windows in your house in
9 years? (Closest answer $12000)
9.
Express the repeating decimal below as a quotient of integers. (970/999)
10.
Which of the following terms cannot be used to describe fossil fuels?
-
Renewable Test 1
1.
Which was not
evidence used by Alfred Wegener to construct his theory of continental drift?
-
Seafloor mapping
2.
Form the negation: Copenhagen is not the capital of Brazil -
It is not true that Copenhagen is not the capital of Brazil
3.
Determine if the statement is deductive or inductive reasoning and if it is logically valid or not: people who start school younger tend to struggle socially. Jenny is starting school early so it’s likely she won’t fit in easily.
-
Inductive, not logically valid
4.
A scientist hypothesizes that the temperature at which an alligator’s egg is incubated will determine whether the alligator will be male or female. The dependent variable is…
-
The sex of the baby alligator
5.
You water three sunflower plants with saltwater. Each plant receives a different concentration of salt solutions. A fourth plant receives regular water. After a two-week period, the height is measured. The independent variable is…
-
Concentration of salt solution 6.
What is meant by “the hypothesis is falsifiable”?
-
If the hypothesis is false, an experiment will show that it is false
7.
Construct a truth table: ~p < -- > ~q
p
Q
~p
~q
~p < -- > ~q
T
T
F
F
T
T
F
F
T
F
F
T
T
F
F
F
F
T
T
T
8.
Express the quantified statement in an equivalent way: some drinks are not liquids
-
Not all drinks are liquids
9.
P: the temperature is above 25 degrees
Q: we finished studying
R: we go to the beach Write this statement in word form: ~r
~p v ~q
-
If we do not go to the beach, then the temperature is not above 25 degrees, or we have not finished studying
10.
If it rains or snows, then I read. I am not reading,
Therefore, it is neither raining nor snowing
Which of the following is true?
-
The argument’s truth table is a tautology 11.
Write the statement in symbolic form: if you do your homework right after class then you will not fall behind, and if you do not do your homework right after class then you will
-
(p
~q) ^ (~p
q)
12.
Three wax palm trees are kept at different humidity levels inside of a greenhouse for 12 weeks. One tree is left outside in normal conditions. Height of the tree is measured once a week. One constant variable in the experiment would be… -
Type of tree
13.
With increasing distance from the epicentre, the difference in arrival times between the P and S waves… -
Increases
14.
Construct a truth table for the following: If you do your homework right after class then you will not fall behind, and if you do not do your homework right after class then you will
p
q
~p
~q
p
~q
~p
q
(p
~q) ^ (~p
q)
T
T
F
F
F
T
F
T
F
F
T
T
T
T
F
T
T
F
T
T
T
F
F
T
T
T
F
F
15.
Write the negation: no South American soccer teams have won a world cup
-
Some South American soccer teams have won a world cup
16.
Select the correct option: p v q
p < -- > q ^ ~p
-
[(p v q)
p] < -- > (q ^ ~p)
17.
Write the argument as a conditional statement:
p
q
~p
------------
Therefore, ~q -
[(p
q) ^ ~p]
~q
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Test 2
1.
You deposit $5000 in an account that pays 6% interest compounded monthly. What is the future
value after 5 years? ($6700) 2.
A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded daily. (Assume 360 days in a year) (5.1%)
3.
It takes 32 days for a 1024-gram sample of element A to decay to 4 grams. What is the half-life of element A? (4 days)
4.
What type of plate boundary? -
Transform
5.
Convert the numeral below to base ten. (2500000)
6.
Multiply in the indicted base. (3316eight)
7.
Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. What
percentage of the scores lie between 300 and 500? (47.5)
8.
What does the release of carbon dioxide, when fossil fuels are burned, directly increase?
-
The greenhouse effect 9.
Find the mean and standard deviation of the following: 7, 10, 15, 16, 17 (13.00, 4.30)
10.
What type of energy is stored within fossil fuels?
-
chemical
11.
An earthquake measuring 8.0 on the Richter scale releases… times more energy than an earthquake measuring 5.0 (32000)
12.
What type of radioactive decay does not involve the emission of a particle? -
Gamma
13.
Carbon 12 (c-12) is stable and the most abundant isotope of carbon. An ancient scrap of paper has 0.9 times the carbon 14 that a new piece of paper has. How many years old is the scrap of paper? (half-life of c-14 is 5370 years) (closest answer: 900 years)
14.
What is nuclear fission? -
The process of splitting a large atom into two smaller atoms
15.
Convert: 300 to a hexadecimal numeral. (12C)
16.
The owners of a sports stadium wanted to predict what additional refreshment options would sell well. They selected 80 seat numbers at random and surveyed the occupants of those seats. Identify the population and the sample.
-
Population is the occupants of all seats in the stadium; sample is the occupants of the 80 selected seats
17.
Suppose Carla has $12000 to invest. Which investment yields the greater return over 2 years: 9% compounded quarterly or 8.85% compounded monthly. (Rate of 9% compounded quarterly is better)
18.
At an earthquake measuring station the speeds of the first two waves to arrive are found to be 3.5 km/s and 2 km/s respectively. The first wave arrives at exactly 12:30 pm and the second wave arrives 31 seconds later. How far is the earthquake’s epicenter from the measuring station? (144.67 +- 1% (km))
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