Ch1n6.3 Worksheet
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Apr 3, 2024
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MGF1107 Assignment 1 Chapter 1 and Section 6.3
Name: ______________________ Due before Test 1.
Show work on a separate sheet of paper if extra space is needed. Solutions are provided in the ppt and the videos. Study the Lecture PPT and watch the Module Lecture Videos, pause the video any time when completing this worksheet. Upload your work to the Upload Work Here
tab in Canvas. Notes: Section 1.1
Premise
- an assumption, law, rule, widely held idea, or observation
. Then reason inductively or deductively from the premises
to obtain a conclusion
. Premises and conclusion make up a logical argument
.
Conjecture
- an educated guess based upon repeated observations of a particular process or pattern.
Inductive reasoning
can be analyzed only in terms of its strength. It cannot prove its conclusion true, at best, it shows that its conclusion probably is true. A conclusion is formed by generalizing from a set of more specific premises.
Deductive reasoning
can be analyzed in terms of its validity and soundness. It is valid if its conclusion follows necessarily from its premises. It is sound if it is valid and its premises are true. A specific conclusion is deduced from a set of more general (or equally general) premises. Validity concerns only logical structure - it can be valid even when its
conclusion is blatantly false. (example: All vehicles have 4 wheels. Bicycle is a vehicle, so bicycle has 4 wheels.)
Inductive
: Use specific examples to draw a generalization. Deductive:
Applying a generalization to specifics.
1.
Identify each premise and the conclusion in the following argument. Determine whether the argument is an example of inductive or deductive reasoning. Our house is made of brick. Both of my next-door neighbors have brick houses. Therefore, all houses in our neighborhood are made of brick.
Premises: 1.Our house is made of brick
2. Both of my next-door neighbors have brick houses.
Conclusion:
1.All houses in our neighborhood are made of brick.
Inductive or deductive? inductive
2.
Use the list of equations and inductive reasoning to predict the next multiplication fact in the list:
37 × 3 = 111,
37 × 6 = 222 ,
37 × 9 = 333,
37 × 12 = 444 , 37 × 15=555
Use inductive reasoning to determine the probable
next number in the list below. An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence.
5, 9, 13, 17, 21, 25, 29, 33
Section 1.2 (The following will be provided for exam1. Know how to use each formula.)
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Special Sum Formulas
Figurate Numbers-Triangular, Square, Pentagonal
Successive Differences http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/rose1.html
3.
Use the method of successive differences
to find the next number in the sequence. (a)
20, 31, 45, 62, 82,104 (Hint: Start with 31 - 20 = 11, use the subsequent term subtract the previous term)
(b)
8, 6, 3, 1, 2, 8, 21, … (Hint: start with 6 - 8= -2, use the subsequent term subtract the previous term)
4.
Find the sum using the special sum formula.
1 + 2 + 3 + … + 48
5.
Use the formula
given on the first page to find a)
the sixth pentagonal number. b)
the eighth triangular number.
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Section 1.3 6.
A vending machine accepts nickels, dimes, and quarters. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 30-cent purchase from the machine?
7.
Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12.
He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week? 20$
Example: Use inductive reasoning to determine the units digit of the number 3
55
.
The question is not about giving the exact value, but rather than applying the inductive reasoning to figure out the units digit.
The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, … repeating meaning that every power that is divisible by 4 will end in 1. 56 is divisible by 4. Using this inductive reasoning 3 to the 56th power would end in a 1, then moving backward to the 55th power would give you a units digit of 7. This is inductive reasoning because we are using the smaller sample size of 4 repeating unit digits to make broad theories about all powers of 3. Another similar approach: The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, … repeating. If the power is a multiple of four,
the units digit is 1. Power 52 is a multiple of 4 and it's close to power 55. Power 52 ends with units digit of 1, next 53 ends with 3, 54 ends with 9, and 55 ends with 7 following the pattern. So, the correct answer is 7 for power of 55.
8.
Homework (1.3.48) Use inductive reasoning to determine the units digit (or ones digit): (a)
The ones digit (also called the units digit) in 2
4000
. The question is not about giving the value to the expression, but rather than applying the inductive reasoning to figure out the units digit. The answer is just a single digit.
2^1=2 (units digit is 2)
2^2=4 (units digit is 4)
2^3=8 (units digit is 8)
2^ 4=16 (units digit is 6)
2^ 5 =32 (units digit is 2)
2^6 =64 (units digit is 4)
4000÷4=1000
2^4000 = 2^4 6
(b)
The units digit of the number 3
41
. 3
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9.
Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, and then climbed up 6. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder? 14
10.
If you ask Batman’s nemesis, Catwoman, how many cats she has, she answers with a riddle: “Five-sixth of my cats plus seven.” How many cats does Catwoman have? 42
Section 1.4
11.
A birdhouse for swallows can accommodate up to 8 nests. How many birdhouses would be necessary to accommodate 58 nests?
8
12.
Use the circle graph below to determine how many of the 140 students made an A or a B.
A: 21
B:35
13.
The bar graph shows the number of cups of coffee, in hundreds of cups, that a professor had in a given year. a) Estimate the number of cups in 2004. 650
b) What year shows the greatest decrease in cups? 2001
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14.
The line graph shows the average class size of a first grade class at a grade school for years 2001 through 2005.
a)
In which years did the average class size increase from the previous year? 02 03 04
b)
How much did the average size increase from 2001 to 2003?16-28=12
_______________________________________
Section 6.3 15.
What kind of calculator are you using? Scientific yes Graphing yes I have both(I hope it is not your cell phone)
Be sure that you know how to perform calculations with your calculator. Correctly use the () for the right order of operations. Locate the root symbol, the π
key, and round off each answer to the nearest place value (such as tenths, hundredths, thousandth…) when appropriate.
16.
Find the difference 4
9
−
2
15
=14/45
17.
Find the quotient 2
9
÷
5
6
=4/5
18.
Write each terminating decimal as a quotient of integers. (a) 0.437 54/125 (b) 8.2=41/5
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19.
Use the method below to decide whether each rational number would yield a repeating
or a terminating
decimal. (Hint: Write in lowest terms
before trying to decide.)
Terminating decimal
- if the only prime factor of the denominator is 2 or 5 or both.
Repeating decimal
- if a prime other than 2 or 5 appears in the prime factorization of the denominator.
Example
: 24
75
can be simplified to 8
25
by dividing 3 into both the numerator and the denominator. Next, factor the denominator 25 using prime factors: 25 = 5x5, the only prime factor of the denominator is 5 in this case, so the original fraction is a Terminating
decimal. (a)
8
15
Is the fraction simplified? (Yes) If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (Yes)
Is it a terminating or repeating decimal? (Repeating)
(b)
8
35
Is the fraction simplified? (Yes) If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (Yes) Is it a terminating or repeating decimal? (Repeating)
(c)
13
125
Is the fraction simplified? yes If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (No)
Is it a terminating or repeating decimal? (Terminating)
(d)
3
24
Is the fraction simplified? no If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (Yes)1/8
Is it a terminating or repeating decimal? (Terminating)
(e)
22
55
Is the fraction simplified? (Yes/No) no If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (no)2/5
Is it a terminating or repeating decimal? (Repeating)
(f)
24
75
Is the fraction simplified? (Yes/No) no If not, simplify the fraction. Does the simplified denominator contain factors other than 2 or 5? (Yes) 8/25
Is it a terminating or repeating decimal? (Terminating)