The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 8.3, Problem 17MS
Drop the needle. Try Buffon’s needle experiment by dropping a needle 50 times and recording your results. Use your numbers to give an approxim ation for it. Go to the Web and try the computer simulation. Record the results and the associated approximations of it.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They
zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity
observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy.
8 9 10
Subject
Empathy Score
Brain Activity -0.102 0.396 0.0120.38 0.035 0.406 0.102 0.517 0.14 0.744 0.246 0.575 0.216 0.719 0.368 0.775
2
3
4
6
11
12
13
14
15
16
43
47
45 55 56
61
58
54
40
52
55
60
10
67
31
100
1.2
sub ject 2 .
8,1
F20
126
-8,4
Given that the equation for the regression line is y
0.00754r – 0.04734, what is the residual for subject 2?
ANSWER:
Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy.
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Empathy Score
43
46
35
59
64
66
58
47
44
49
56
68
28
71
27
108
Brain Activity
-0.129
0.389
0.019
0.378
0.016
0.419
0.109
0.515
0.149
0.746
0.245
0.57
0.219
0.716
0.364
0.762
Given that the equation for the regression line is y^=0.00709x−0.04187y^=0.00709x−0.04187, what is the residual (or deviation), yi−y^iyi−y^i, for subject 14?ANSWER:
Speak
Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16
couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an
electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own
pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The
women also completed a psychological test that measures empathy.
Subject
Empathy Score
1
2
3
4
5
37
46 36
50 59
6 7 8
65 62 47
9
44
10 11 12 13 14 15 16
47 69 61 27 71 37 112
Brain Activity -0.104 0.386 0.009 0.374 0.027 0.417 0.1 0.512 0.155 0.748 0.257 0.573 0.21 0.729 0.352 0.78
-20
1.2
subject 13⚫
0.1
-0.4
Given that the equation for the regression line is ŷ = 0.00727x - 0.05008, what is the residual for subject 13?
ANSWER: -0.06379
120
Chapter 8 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 8.1 - Doors galore. The 21st-century version of Lets...Ch. 8.1 - Birthday surprise. How many people would you need...Ch. 8.1 - Opposite of heads. Suppose you flip a coin 100...Ch. 8.1 - Penny percent. Suppose you flip a penny 50 times,...Ch. 8.1 - Party time. At a nephews party, you decide to...Ch. 8.1 - Flipping Lincoln. Flip a penny 100 times and...Ch. 8.1 - Flashing cards. Shuffle a standard deck of 52...Ch. 8.1 - King for a day. Remove three cards from a deck of...Ch. 8.1 - A card deal stick. Remove three cards from a deck...Ch. 8.1 - A card deal switch. Remove three cards from a deck...
Ch. 8.1 - A card reunion—black first (S). Using a shuffled...Ch. 8.1 - A card reunion (H). Using a shuffled deck of...Ch. 8.1 - Prob. 14MSCh. 8.1 - Prob. 15MSCh. 8.1 - Personal perspectives. Write a short essay...Ch. 8.1 - With a group of folks. In a small group, discuss...Ch. 8.1 - One Grecian urn. A large urn in your kitchen is...Ch. 8.1 - Two Grecian urns. Your math instructor keeps two...Ch. 8.1 - Pennies from heaven (H). Residents of your...Ch. 8.1 - Dating Penny. The pennies described in the...Ch. 8.1 - Changing your pants. You have 20 coins in your...Ch. 8.2 - Black or white? Your friend chooses his sartorial...Ch. 8.2 - Eleven cents. You have a dime and a penny. Flip...Ch. 8.2 - Yummm. You have a small bag of candy-coated...Ch. 8.2 - Rubber duckies. A game at a carnival has 75 rubber...Ch. 8.2 - Legally large. What does the Law of Large Numbers...Ch. 8.2 - Lincoln takes a hit. On your wall is a poster...Ch. 8.2 - Giving orders. Order the following events in tenns...Ch. 8.2 - Two heads are better. Simultaneously flip a dime...Ch. 8.2 - Tacky probabilities. Before doing the following...Ch. 8.2 - BURGER AND STARBIRD. Suppose you randomly select a...Ch. 8.2 - Monty Hall. Read and rework the Lets Make a Deal...Ch. 8.2 - 7 or 11 (S). What is the probability of rollign a...Ch. 8.2 - D and D. You simultaneously flip a dime and roll a...Ch. 8.2 - The top 10 (ExH). Suppose you have 10 marbles....Ch. 8.2 - One five and dime (II). Someone simultaneously...Ch. 8.2 - Five flip. Someone flips five coins, but you dont...Ch. 8.2 - Flipped out. We take a coin and flip it 10,000,000...Ch. 8.2 - Spinning wheel. A roulette wheel has 36 spaces...Ch. 8.2 - December 9. Choose two people at random. What is...Ch. 8.2 - High roller (H). Using two fair dice, what is the...Ch. 8.2 - Double dice. You roll two fair dice. What is the...Ch. 8.2 - Sifly puzzle. After a professor explains the...Ch. 8.2 - Just do it. Find groups of roughly 35 people...Ch. 8.2 - No matches (S). Suppose 40 people are in a room....Ch. 8.2 - Spinner winner. If you were to spin the wheel...Ch. 8.2 - Flip side (S). Someone flips three coins behind a...Ch. 8.2 - Other flip side. Someone flips three coins behind...Ch. 8.2 - Blackjack. From a regular deck of 52 playing...Ch. 8.2 - Be rational (ExH). Suppose someone has randomly...Ch. 8.2 - Well red (H). Someone shows you three cards. One...Ch. 8.2 - Regular dice. Dungeons and Dragons players use...Ch. 8.2 - Take your seat. You decide to fly to California on...Ch. 8.2 - Eight flips. What is the probability of flipping a...Ch. 8.2 - Lottery (S). The lottery in an extremely small...Ch. 8.2 - Making the grade. What is wrong with the following...Ch. 8.2 - Dont squeeze. Five shoppers buy Charmin toilet...Ch. 8.2 - Birthday cards. Using a regular deck of 52 playing...Ch. 8.2 - Too many boys. Long, long ago and far, far away,...Ch. 8.2 - Three paradox (H). The correct probability of...Ch. 8.2 - Whats the big event? The section defines the...Ch. 8.2 - Tallying totals. For each given probability below,...Ch. 8.2 - Algebra roulette. Your math instructor has created...Ch. 8.2 - Probability beans. The jellybean jar on your math...Ch. 8.2 - Picking up the tab (H). Ed and Mike go out to...Ch. 8.3 - Daily deaths. About 58 million people die every...Ch. 8.3 - Wake-up call. Suppose you wake up each morning and...Ch. 8.3 - More than 12 monkeys. What does the Infinite...Ch. 8.3 - Get shorty. Who was Georges Louis Leclerc Comte de...Ch. 8.3 - Nothing but heads. If you flip a fair coin three...Ch. 8.3 - Pick a number. Pick a number from the following...Ch. 8.3 - Personal coincidences. List three coincidences you...Ch. 8.3 - No way. It is the last Sunday of spring break and...Ch. 8.3 - Prob. 10MSCh. 8.3 - Unlucky numbers. Suppose you randomly picked 1000...Ch. 8.3 - A bad block (S). Suppose 1054 people died in...Ch. 8.3 - Coin toss test. Ask two friends to help you repeat...Ch. 8.3 - DeceptIve dice (ExH). You asked three friends to...Ch. 8.3 - Murphys Law. If something can go wrong, it will....Ch. 8.3 - Drop the needle. Try Buffons needle experiment by...Ch. 8.3 - IBM again (H). Suppose we try the IBM...Ch. 8.3 - The dart index. Take a page of stock quotes from a...Ch. 8.3 - Random walks. Using a piece of graph paper, a...Ch. 8.3 - Random guesses (S). A multiple-choice test has 100...Ch. 8.3 - Random dates. There is a room filled with exotic...Ch. 8.3 - Random phones (H). Suppose you roll a 10-sided die...Ch. 8.3 - Fourever (ExH). Suppose you roll a die repeatedly,...Ch. 8.3 - Pick a number, revisited. In Mindscape 6, did you...Ch. 8.3 - Good start (H). Suppose the monkey is typing using...Ch. 8.3 - Even moves. Suppose you embark on a random walk on...Ch. 8.3 - Playing the numbers. Here is a numbers game. You...Ch. 8.3 - Random results. Someone looks at a list of 10,000...Ch. 8.3 - Monkey names. Suppose we have a monkey typing on a...Ch. 8.3 - The streak. Suppose you flip a fair coin 10 times...Ch. 8.3 - Girl, Girl,... (S). A couple has eight children....Ch. 8.3 - One mistake is okay. Suppose we try the IBM...Ch. 8.3 - Picking and matching. You and a friend...Ch. 8.3 - Picking and matching. You and a friend...Ch. 8.3 - Dice are different (ExH). In Mindscape 14 you...Ch. 8.3 - Death row (H). You may have noticed that two pairs...Ch. 8.3 - Striking again. Consider the striking deal game...Ch. 8.3 - Random returns. Suppose we take a random walk on...Ch. 8.3 - Random natural. Suppose you have a 10-sided die...Ch. 8.3 - Ace of spades. You randomly shuffle a deck of...Ch. 8.3 - Flipping out. You flip a coin eight times and get...Ch. 8.3 - Random reigns (H). Your (very egalitarian) school...Ch. 8.3 - Survey says... A survey in your intro psychology...Ch. 8.3 - Rock n roll. As a project in your Geology and Art...Ch. 8.3 - Random pitch. During a practice game, your...Ch. 8.4 - Have a heart. If you draw a card from a regular...Ch. 8.4 - Have a head. You ffip a coin 10 times. What is the...Ch. 8.4 - Sunny surprise. Suppose the chances are 1 in 2...Ch. 8.4 - Elephant ears. Suppose a quarter of all the...Ch. 8.4 - Little deal. In how many ways can you select three...Ch. 8.4 - The gym lock. A lock has a disk with 36 numbers...Ch. 8.4 - The dorm door. A dormitory has an electronic lock....Ch. 8.4 - 28 cents. How many different ways can you make 28...Ch. 8.4 - 82 cents. How many different ways can you make 82...Ch. 8.4 - Number please. Someone you really wanted to go out...Ch. 8.4 - Dealing with jack. Suppose you deal three cards...Ch. 8.4 - MA Lotto (H). To win the jackpot of the...Ch. 8.4 - NY Lotto (H). To win the jackpot of the New York...Ch. 8.4 - OR Lotto. To win the jackpot of the Oregon lottery...Ch. 8.4 - Burger King (S). You take a summer job making...Ch. 8.4 - More burgers. Suppose you are working at a burger...Ch. 8.4 - NetFlix. You have 65 movies on your NetFlix queue....Ch. 8.4 - Cineplex (ExH). Your local Cineplex is showing...Ch. 8.4 - One die. You roll a fair die four times. What is...Ch. 8.4 - Dressing for success. You have 5 T-shirts, 10...Ch. 8.4 - Band stand. The Drew Aderburg Band is planning a...Ch. 8.4 - Mondays undies. You are spending the weekend at a...Ch. 8.4 - Prob. 23MSCh. 8.4 - Cranking tunes. Your car stereo can be programmed...Ch. 8.4 - The Great Books. There are 20 Great Books, from...Ch. 8.4 - Morning variety (S). You wish to have a different...Ch. 8.4 - Blind mans bluff. You and a friend each pick a...Ch. 8.4 - Crime story (ExH). Suppose 20 witnesses saw...Ch. 8.4 - Theres a 4 (H). Someone you really want to go out...Ch. 8.4 - Making up the test. Your math prof says there will...Ch. 8.4 - Moving up. You have a part4ime job in a department...Ch. 8.4 - Counterfeit bills. You are given ten $100 bills...Ch. 8.4 - Car care. A burglar wishes to break into a car...Ch. 8.4 - Coins count. On your bureau you have a half...Ch. 8.4 - Math mania. There are 90 students enrolled in Math...Ch. 8.4 - Party on. You want to throw a party and can invite...Ch. 8.4 - No dice (H). You roll a pair of dice 24 times....Ch. 8.4 - Three angles. Draw 10 points on a piece of paper...Ch. 8.4 - Four parties (ExH). You want to have a party and...Ch. 8.4 - Making the cut. In 1988, the ignition keys for...Ch. 8.4 - Parental pride. The number of pictures you have of...Ch. 8.4 - Sister, Sister. The number of students in a...Ch. 8.4 - In search of a cubic. This section explains that...Ch. 8.4 - Cancellation! (H) This section explains that the...Ch. 8.4 - Keep on cancellin! Building on the previous...Ch. 8.5 - No pop quizzes. Your instructor gives mom quizzes...Ch. 8.5 - No easy quizzes (S). Your instructor starts giving...Ch. 8.5 - Silly sickness. Based on your symptoms, your...Ch. 8.5 - Making an algebra-down. Consider the equation...Ch. 8.5 - A beautiful mind. Who was John Nash? Give as many...Ch. 8.5 - Upon further study. On your instructor quizzes,...Ch. 8.5 - Power pass (ExH). The matrix below gives the yards...Ch. 8.5 - Pass with a p. Suppose the defense referred to in...Ch. 8.5 - Random run. Suppose now in Mindscape 7 the defense...Ch. 8.5 - Another random nm. Suppose now the defense...Ch. 8.5 - Lining up the defense (S). Using the payoff matrix...Ch. 8.5 - De-lines of defense. Using the payoff matrix in...Ch. 8.5 - Approximate Nash (ExH). Take the two lines from...Ch. 8.5 - Precise Nash. Use your answers to Mindscapes 8 and...Ch. 8.5 - Positive payoof (H). Below is a payoff matrix for...Ch. 8.5 - Estimating the equilibrium. Estimate the...Ch. 8.5 - Exacting the equilibrium. Find equations for the...Ch. 8.5 - Payoffs need not be positive. Heres a payoff...Ch. 8.5 - Negative equilibrium. Find equations for the two...Ch. 8.5 - Making negative sense. In what kind of game or...Ch. 8.5 - Colin and Tubbes. When first grader Cohn comes...Ch. 8.5 - Cohn and Tubbes 50—50. Suppose in Mindscape 21...Ch. 8.5 - Averaging Cohn and Tubbes. Suppose p is the...Ch. 8.5 - Colin and Tubbes line up (ExH). Referring to...Ch. 8.5 - Colin and Tubbes with a dash of Nash (S). Find the...Ch. 8.5 - Diagnosis. Based on your symptoms, your doctor...Ch. 8.5 - Sploosh test (H). Given the scenario in the...Ch. 8.5 - Diagnose the data. Using the data from the...Ch. 8.5 - My theory ... You are a paleontologist who finds...Ch. 8.5 - Going stag. Two Englishmen, Neville and Winston,...Ch. 8.5 - Selling sweets. Two snack cake companies, Snacky...Ch. 8.5 - Prisoners dilemma. Two people are suspected of...Ch. 8.5 - Match point. Find the coordinates (p,y) where the...Ch. 8.5 - Match lines. Find an equation for the line passing...Ch. 8.5 - Unmatched slopes. Two lines intersect at the point...Ch. 8.5 - Plotting percentages. Of the students in your...Ch. 8.5 - Itching for x (H). You go to the Health Center...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Assessment 71A Write each of the following as a sum in expanded place value form. a. 0.023 b. 206.06 c. 312.010...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Let 2n (equally spaced) points on a circle be chosen. Show that the number of ways to join these points in pair...
Introductory Combinatorics
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Consider the parallelepiped with edges OA,OB, and OC, where A(2,1,0),B(1,2,0), and C(0,1,). Find the real numbe...
Calculus Volume 3
Explain how to solve the next equation by reasoning about numbers , operations , and expressions rather than by...
Mathematics for Elementary Teachers with Activities (5th Edition)
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2014, Los Angeles also experienced an earthquake which measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes.arrow_forwardA driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forwardAt the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125, Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?arrow_forward
- Find the intensities of earthquakes whose magnitudes are (a) R=6.0 and (b) R=7.9.arrow_forwardEmpathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Subject 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 Empathy Score Brain Activity -0.114 0.39 0.019 0.379 0.010.4120.10.5150.153 0.746 0.250.56 0.214 0.717 0.366 0.778 37 51 44 54 56 67 68 54 48 47 68 65 28 62 26 100 1.2 sub jęct 9 10.0 -20 120 -8,4 Given that the equation for the regression line is ŷ = 0.00683x – 0.03024, what is the residual for subject 9?arrow_forwardEmpathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. 13 14 15 36 113 2 7 8 9 10 5 6 53 55 59 58 53 Brain Activity -0.1010.398 0.017 0.368 0.02 0.424 0.09 0.5160.1530.737 0.252 0.568 0.217 0.712 0.359 0.776 Subject 1 3 4 11 12 16 Empathy Score 42 55 40 48 43 68 61 18 59 1.2 sub ject 5 e 10,0 20 120 -8,4 Given that the equation for the regression line is y = 0.00635x +0.00218, what is the residual for subject 5? ANSWER:arrow_forward
- This one has been bugging me for a few days and be interested to see how you calculate it. Thanksarrow_forwardEmpathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been datin for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Subject Empathy Score Brain Activity -20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 38 46 40 59 57 60 68 54 42 50 57 67 25 66 33 109 -0.125 0.396 0.012 | 0.376 0.025 0.403 0.111 0.513 0.143 0.735 0.254 0.567 0.213 0.727 | 0.352 0.783 1.2 -0,1- -0.4 subject 15. Given that the equation for the regression line is ŷ = 0.00788 -0.08628, what is the residual for subject 15? ANSWER: 120arrow_forwardCan balloons hold more air or more water before bursting? A student purchased a large bag of 12-inch balloons. He randomly selected 10 balloons from the bag and then randomly assigned half of them to be filled with air until bursting and the other half to be filled with water until bursting. He used devices to measure the amount of air and water was dispensed until the balloons burst. Here are the dataarrow_forward
- A certain affects virus 0.4% of the population (in a population of 100,000 people, 400 will be infected with the virus). A test used to detect the virus in a person is positive 87% of the time if the person has the virus (true positive) and it is positive 14% of the time if the person does not have the virus (false positive). Fill in the remainder of the following table and use it to answer the questions below. Infected Not Infected Total Positive Test Negative Test Total 400 99,600 100,000arrow_forwardA certain affects virus 0.4% of the population (in a population of 100,000 people, 400 will be infected with the virus). A test used to detect the virus in a person is positive 87% of the time if the person has the virus (true positive) and it is positive 14% of the time if the person does not have the virus (false positive). Fill in the remainder of the following table and use it to answer the questions below. Infected Not Infected Total Positive Test Negative Test Total 400 99,600 100,000 Round all percents to the nearest tenth of a percent as needed. a) Examine the "Positive Test" row of the table. If a person tests positive for the virus, what is the probability that the person is really infected. (Note: in medical terminology, this probability measures the "positive predictive value" of the test) b) If a person tests negative for the virus, what is the probability that the person really is not infected. (This is called the "negative predictive value")arrow_forwardHand written please. An investigator wants to assess the association between manganese and blood pressure in pregnant women (side note: this is a study I am currently working on). The study plans to enroll 100 pregnant women. During the third trimester, each participant will have their manganese level and systolic blood pressure measured. Identify the type of study design and briefly describe its strengths and weaknesses.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY