
EBK MATHEMATICS: A PRACTICAL ODYSSEY
8th Edition
ISBN: 8220100546112
Author: MOWRY
Publisher: Cengage Learning US
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2.3, Problem 25E
In Exercises
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Client
1
Weight before
diet (pounds)
Weight after
diet (pounds)
128
120
2
131
123
3
140
141
4
178
170
5
121
118
6
136
136
7
118
121
8
136
127
a) Determine the mean change in patient weight from before to after the
diet (after – before). What is the 95% confidence interval of this mean
difference?
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
Chapter 2 Solutions
EBK MATHEMATICS: A PRACTICAL ODYSSEY
Ch. 2.1 - Prob. 1ECh. 2.1 - Suppose A={2,5,7,9,13,25,26}. a. Find n(A) b. True...Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Suppose n(U)=150, n(A)=37, and n(B)=84. a. If...Ch. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - Prove the Cardinal Number Rule for the Complement...Ch. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Answer the following questions using complete...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - The following questions are modeled after those...Ch. 2.2 - A survey of 200 people yielded the following...Ch. 2.2 - A survey of 300 workers yielded the following...Ch. 2.2 - The records of 1,492 high school graduates were...Ch. 2.2 - A department store surveyed 428 shoppers, and the...Ch. 2.2 - In a survey, 674 adults were asked what television...Ch. 2.2 - A survey asked 816 college freshmen whether they...Ch. 2.2 - A local 4-H club surveyed its members, and the...Ch. 2.2 - A local anime fan club surveyed its members...Ch. 2.2 - A recent survey of w shoppers that is, n(U)=w...Ch. 2.2 - A recent transportation survey of w urban...Ch. 2.2 - A consumer survey was conducted to examine...Ch. 2.2 - In a recent survey of monetary donations made by...Ch. 2.2 - Recently, Lady Gaga, Arcade Fire, and Skrillex had...Ch. 2.2 - Dr. Hawk works in an allergy clinic, and his...Ch. 2.2 - When the member of the Eye and I photo club...Ch. 2.2 - After leaving the polls, many people are asked how...Ch. 2.2 - In a recent survey consumer were asked where they...Ch. 2.2 - A company that specializes in language tutorial...Ch. 2.2 - In a recent survey, people were asked which radio...Ch. 2.2 - In a recent health insurance survey, employee at...Ch. 2.2 - A survey of 136 pet owners yielded the following...Ch. 2.2 - An exit poll of 300 votes yielded the following...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Using Venn diagrams, prove De Morgans law (AB)=AB.Ch. 2.2 - Prob. 34ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 40ECh. 2.2 - If a person has type B blood, what blood types may...Ch. 2.2 - Prob. 42ECh. 2.2 - If a person has type O blood, what blood types may...Ch. 2.2 - Answer the following questions using complete...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Exercises 4652 refer to the following: A nonprofit...Ch. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Jamie has decided to buy either a Mega or a Better...Ch. 2.3 - Prob. 4ECh. 2.3 - If you buy three pairs of jeans, four sweaters,...Ch. 2.3 - A certain model of automobiles is available in six...Ch. 2.3 - To fulfill certain requirements for a degree, a...Ch. 2.3 - To fulfill a requirement for a literature class, a...Ch. 2.3 - A sporting goods store has fourteen lines of snow...Ch. 2.3 - An audio equipment store has ten different...Ch. 2.3 - A cafeteria offers a complete dinner that includes...Ch. 2.3 - A sandwich shop offers a U-Chooz special...Ch. 2.3 - How many different Social Security numbers are...Ch. 2.3 - To use an automated teller machine ATM, a customer...Ch. 2.3 - Every book published has an International Standard...Ch. 2.3 - How many different Zip Codes are possible using a...Ch. 2.3 - Telephone area codes are three-digit numbers of...Ch. 2.3 - Major credit cards such as VISA and MasterCard...Ch. 2.3 - The serial number on a dollar bill consists of a...Ch. 2.3 - The serial number on a new twenty-dollar bill...Ch. 2.3 - Each student at State University has a student ID...Ch. 2.3 - Each student at State College has a student ID...Ch. 2.3 - In Exercises 2338, find the indicated value. 4!Ch. 2.3 - In Exercises 2338, find the indicated value. 5!Ch. 2.3 - In Exercises 2338, find the indicated value. 10!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!Ch. 2.3 - In Exercises 2338, find the indicated value. 20!Ch. 2.3 - In Exercises 2338, find the indicated value. 25!Ch. 2.3 - In Exercises 2338, find the indicated value. 6!4!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!6!Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - Find the value of n!(nr)!, when n=16 and r=14.Ch. 2.3 - Find the value of n!(nr)!, when n=19 and r=16.Ch. 2.3 - Find the value of n!(nr)!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!, when n=r.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=3.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=4.Ch. 2.3 - Find the value of n!(nr)!r!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!r!, when n=r.Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 51ECh. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.4 - In Exercises 112, find the indicated value: a. 7P3...Ch. 2.4 - In Exercises 112, find the indicated value: a. 8P4...Ch. 2.4 - In Exercises 112, find the indicated value: a. 5P5...Ch. 2.4 - In Exercises 112, find the indicated value: a. 9P0...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a. xP1...Ch. 2.4 - In Exercises 112, find the indicated value: a. xP2...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - a. Find 3P2. b. List all of the permutations of...Ch. 2.4 - a. Find 3C2. b. List all of the combinations of...Ch. 2.4 - Prob. 15ECh. 2.4 - a. Find 4P2. b. List all of the permutations of...Ch. 2.4 - Prob. 17ECh. 2.4 - An English class consists of twenty-three students...Ch. 2.4 - In how many ways can the letters in the word...Ch. 2.4 - A committee of four is to be selected from a group...Ch. 2.4 - A softball league has thirteen teams. If every...Ch. 2.4 - In a group of eighteen people, each person shakes...Ch. 2.4 - A softball league has thirteen teams. How many...Ch. 2.4 - Three hundred people buy raffle tickets. Three...Ch. 2.4 - A group of nine women and six men must select a...Ch. 2.4 - A group of ten seniors, eight juniors, six...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - How many five-card poker hands containing two pair...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - A 5/36 lottery requires choosing five of the...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Over forty states participate in Powerball, a...Ch. 2.4 - Over forty states participate in Mega Millions, a...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - a. Find the sum of the entries in the first row of...Ch. 2.4 - a. Add adjacent entries of the sixth row of...Ch. 2.4 - Use Pascals Triangle to answer the following. a....Ch. 2.4 - Given the set S={a, b, c, d}, answer the...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutations...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Exercise 6367 refer to the following: A baseball...Ch. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.5 - Prob. 1ECh. 2.5 - In Exercises 1-10, find the cardinal numbers of...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Consider the following one-to-one correspondence...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Prob. 5CRCh. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 2.CR - Prob. 9CRCh. 2.CR - A survey of 1,000 college seniors yielded the...Ch. 2.CR - A survey of recent college graduates yielded the...Ch. 2.CR - A local anime fan club surveyed 67 of its members...Ch. 2.CR - An exit poll yielded following information...Ch. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - A certain model of pickup truck is available in...Ch. 2.CR - Each student at State University has a student ID...Ch. 2.CR - Prob. 20CRCh. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - A group of ten women and twelve men must select a...Ch. 2.CR - Prob. 24CRCh. 2.CR - Prob. 25CRCh. 2.CR - Using a standard deck of fifty-two cards no...Ch. 2.CR - Prob. 27CRCh. 2.CR - A 6/42 lottery requires choosing six of the...Ch. 2.CR - Prob. 29CRCh. 2.CR - Prob. 30CRCh. 2.CR - Prob. 31CRCh. 2.CR - Prob. 32CRCh. 2.CR - Prob. 33CRCh. 2.CR - Prob. 34CRCh. 2.CR - Prob. 35CRCh. 2.CR - Prob. 36CRCh. 2.CR - Prob. 37CRCh. 2.CR - Consider the following one to one correspondence...Ch. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Prob. 42CRCh. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Prob. 46CRCh. 2.CR - Prob. 47CRCh. 2.CR - Prob. 48CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.arrow_forward(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).arrow_forwardfind the domain of the function f(x)arrow_forward
- For each of the following functions, find the Taylor Series about the indicated center and also determine the interval of convergence for the series. 1. f(x) = ex-2, c = 2 Π == 2. f(x) = sin(x), c = 2arrow_forwardQUESTION 5. Show that if 0 ≤r≤n, then r+2 r r (c) + (+³) + (+³) +- + (*) -(+) n n+ = r (1)...using induction on n. (2) ...using a combinatorial proof.arrow_forwardUse a power series to approximate each of the following to within 3 decimal places: 1. arctan 2. In (1.01)arrow_forward
- For each of the following power series, find the interval of convergence and the radius of convergence: n² 1.0 (x + 1)" n=1 շո 3n 2. Σ n=1 (x-3)n n3arrow_forwardUse a known series to find a power series in x that has the given function as its sum: 1. xcos(x³) 2. In (1+x) xarrow_forwardif n is odd integer then 4 does not divide narrow_forward
- or W Annuities L Question 2, 5.3.7 > Find the future value for the ordinary annuity with the given payment and interest rate. PMT = $2,000; 1.65% compounded quarterly for 11 years. The future value of the ordinary annuity is $ (Do not round until the final answer. Then round to the nearest cent as needed.) example Get more help Q Search 30 Larrow_forwardFind the cdf of a random variable Y whose pdf is given by; 2, 0≤x≤1 1/3, 0≤x≤1 a) f(x)=3, 2≤x≤4 0, elsewhere 2, 1≤x≤2 b) f(x)= (3-x)2, 2≤x≤3 0, elsewherearrow_forwardFor all integers a and b, a + b is not ≡ 0(mod n) if and only if a is not ≡ 0(mod n)a or is not b ≡ 0(mod n). Is conjecture true or false?why?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning

Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell

Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL


College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning

Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
ALGEBRAIC EXPRESSIONS & EQUATIONS | GRADE 6; Author: SheenaDoria;https://www.youtube.com/watch?v=fUOdon3y1hU;License: Standard YouTube License, CC-BY
Algebraic Expression And Manipulation For O Level; Author: Maths Solution;https://www.youtube.com/watch?v=MhTyodgnzNM;License: Standard YouTube License, CC-BY
Algebra for Beginners | Basics of Algebra; Author: Geek's Lesson;https://www.youtube.com/watch?v=PVoTRu3p6ug;License: Standard YouTube License, CC-BY
Introduction to Algebra | Algebra for Beginners | Math | LetsTute; Author: Let'stute;https://www.youtube.com/watch?v=VqfeXMinM0U;License: Standard YouTube License, CC-BY