...ESSAY: THOMAS MALTHUS Born: 13-Feb-1766 Birthplace: Rookery, near Dorking, Surrey, England Died: 29-Dec-1834 Location of death: St. Catherine, near Bath, England Cause of death: unspecified Remains: Buried, Bath Abbey, Bath, England Gender: Male Race or Ethnicity: White Occupation: Economist Nationality: England What many know, at least those with an elementary knowledge of economics or politics, is that Malthus is the surname of a man, who, a couple of hundred years back, said that man, sooner or later, universally, will run up against himself; that the population of mankind will eventually outstrip man's ability to supply himself with the necessities of life. The Malthusian doctrine, as stated in "Essay on the Principle of Population," was expressed as follows: "population increases in a geometric ratio, while the means of subsistence increases in an arithmetic ratio." Well, that seems plain enough, and perfectly understandable, if there is too many people and not enough food, then, certainly, there is going to be problems. Malthus developed his theory, at least to this extent: that left alone, no matter all the problems short of worldwide catastrophe, humankind will survive, as, nature has a natural way to cut population levels: "crime, disease, war, and vice," being, the necessary checks on population." This proposition, as was made by Malthus in 1798, was to cause quite a public stir, then, and yet today. The English economist Thomas Robert Malthus, b....
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...Review Notes for IB Standard Level Math © 2015-2016, Steve Muench steve.muench@gmail.com @stevemuench Please feel free to share the link to these notes http://bit.ly/ib-sl-maths-review-notes or my worked solutions to the November 2014 exam http://bit.ly/ib-sl-maths-nov-2014 or my worked solutions to the May 2015 (Timezone 2) exam http://bit.ly/ib-sl-maths-may-2015-tz2 or my worked solutions to the November 2015 exam https://bit.ly/ib-sl-maths-nov-2015 with any student you believe might benefit from them. If you downloaded these notes from a source other than the bit.ly link above, please check there to make sure you are reading the latest version. It may contain additional content and important corrections! April 8, 2016 1 Contents 1 Algebra 1.1 Rules of Basic Operations . . . . . . . . . . . . . . . . . . . . . 1.2 Rules of Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Rules of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Allowed and Disallowed Calculator Functions During the Exam 1.5 Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . 1.7 Sum of Finite Arithmetic Series (u1 + · · · + un ) . . . . . . . . . 1.8 Partial Sum of Finite Arithmetic Series (uj + · · · + un ) . . . . . 1.9 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . 1.10 Sum of Finite Geometric Series . . . . . . . . . . . . . . . . . . ...
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...Score: ______ / ______ Name: ______________________________ Student Number: ______________________ | 1. Elsie is making a quilt using quilt blocks like the one in the diagram. a. How many lines of symmetry are there? Type your answer below. b. Does the quilt square have rotational symmetry? If so, what is the angle of rotation? Type your answers below. | | 2. Solve by simulating the problem. You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences. | | 3. Use the diagram below to answer the following questions. Type your answers below each question. a. Name three points.b. Name four different segments.c. Write two other names for FG.d. Name three different rays. | | 4. Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground. Draw a sketch of this situation (you do not need to submit the sketch). Find the ground distance from Charlie to the plane. Type your answer below. Explain your work. | | _____ 5. Jason and Kyle both choose a number from 1 to 10 at random. What is the probability that both numbers are odd? Type...
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...simple discount P = S(1 − dt) 4 Future value at compound interest S = P(1 + i)n 5 Present value at compound interest P = S(1 + i)−n 6 Future value of n payments of R at compound rate i (1 + i ) n − 1 i S = Rsn| = R i 7 Present value of n payments of R at compound rate i 1 − (1 + i ) − n i P = Ran| = R i 8 Approximation to bond or debenture yield for given price 1 I + n (C − P ) i ≈ 1 (C + P) 2 9 Present value of an annuity with payments increasing in arithmetic progression P = R[(1 + i)−1 + 2(1 + i)−2 + ... + n(1 + i)−n] (1 + i )a i − n(1 + i ) − n n| = R i 10 Future value of an annuity with payments increasing in arithmetic progression (1 + i )s i − n n| S = R i 11 Present value of an annuity with payments increasing in geometric progression P = R[(1 + i)−1 + (1 + r)(1 + i)−2 + ... + (1 + r)n−1(1 + i)−n] = R(1 + r)−1 a j where j = i − r n| 1 + r 12 Future value of an annuity with payments increasing in geometric progression j S = R(1 + r)n−1 sn| where j = i − r 1 + r...
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...Math is used everyday – adding the cost of the groceries before checkout, totaling up the monthly bills, estimating the distance and time a car ride is to a place a person has not been. The problems worked this week have showed how math works in the real world. This paper will show how two math problems from chapter five real world applications numbers 35 and 37 worked out. Number 35 A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the nest 10 feet will cost $125; the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower? Solving this problem involves the arithmetic sequence. The arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount (Bluman, 2011). n = number of terms altogether n = 9 d = the common differences d = 25 ª1 = first term ª1 = 100 ªn = last term ª2 = ª9 The formula used to solve this problem came from the book page 222. ªn = ª1 + (n -1)d ª9 = 100 + (9-1)25 ª9 = 100 + (8)25 ...
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...Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence. The number added to each term is constant (always the same). The fixed amount is called the common difference, d,referring to the fact that the difference between two successive terms yields the constant value that was added. To find the common difference, subtract the first term from the second term. 1. Find the common difference for this arithmetic sequence 5, 9, 13, 17 ... | 1. The common difference, d, can be found by subtracting the first term from the second term, which in this problem yields 4. Checking shows that 4 is the difference between all of the entries. | 2. Find the common difference for the arithmetic sequence whose formula is an = 6n + 3 | 2. The formula indicates that 6 is the value being added (with increasing multiples) as the terms increase. A listing of the terms will also show what is happening in the sequence (start with n = 1). 9, 15, 21, 27, 33, ... The list shows the common difference to be 6. | 3. Find the 10th term of the sequence ...
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...A Free Exam for 2006-15 VCE study design Engage Education Foundation VCE Revision Seminars As a not for profit, this free exam was made possible by our VCE Exam Revision Seminars. Sept 19 - Oct 18 2015. • 24 different subjects • VCAA Assessors • Huge set of notes, teacher slides and an exam • 6.5hrs all located at the University of Melbourne Visit http://ee.org.au/enrol to enrol now! Units 3 and 4 Further Maths: Exam 1 Practice Exam Question and Answer Booklet Duration: 15 minutes reading time, 1 hour 30 minutes writing time Structure of book: Section A B Number of questions 13 54 Number of questions to be answered 13 27 Total Number of Modules Number of modules to be answered 6 3 Number of marks 13 27 40 Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers and rulers. Students are not permitted to bring into the examination room: blank sheets of paper and/or white out liquid/tape. No calculator is allowed in this examination. Materials supplied: This question and answer booklet of 25 pages. Instructions: You must complete all questions of the examination. Write all your answers in the spaces provided in this booklet. Units 3 and 4 Further Maths: Exam 1: Free Exam A The Engage Education Foundation Section A – Multiple-choice questions Instructions Answer all questions by circling your choice. Choose the response that is correct...
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...1. Write the first four terms of the sequence whose general term is an = 2( 4n - 1) (Points : 3) | 6, 14, 22, 30 -2, 6, 14, 22 3, 7, 11, 15 6, 12, 18, 24 | 2. Write the first four terms of the sequence an = 3 an-1+1 for n ≥2, where a1=5 (Points : 3) | 5, 15, 45, 135 5, 16, 49, 148 5, 16, 46, 136 5, 14, 41, 122 | 3. Write a formula for the general term (the nth term) of the arithmetic sequence 13, 6, -1, -8, . . .. Then find the 20th term. (Points : 3) | an = -7n+20; a20 = -120 an = -6n+20; a20 = -100 an = -7n+20; a20 = -140 an = -6n+20; a20 = -100 | 4. Construct a series using the following notation: (Points : 3) | 6 + 10 + 14 + 18 -3 + 0 + 3 + 6 1 + 5 + 9 + 13 9 + 13 + 17 + 21 | 5. Evaluate the sum: (Points : 3) | 7 16 23 40 | 6. Find the 16th term of the arithmetic sequence 4, 8, 12, .... (Points : 3) | -48 56 60 64 | 7. Identify the expression for the following summation:(Points : 3) | 6 3 k 4k - 3 | 8. A man earned $2500 the first year he worked. If he received a raise of $600 at the end of each year, what was his salary during the 10th year? (Points : 3) | $7900 $7300 $8500 $6700 | 9. Find the common ratio for the geometric sequence.: 8, 4, 2, 1, 1/2 (Points...
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...Arithmetic and geometric progressions mcTY-apgp-2009-1 This unit introduces sequences and series, and gives some simple examples of each. It also explores particular types of sequence known as arithmetic progressions (APs) and geometric progressions (GPs), and the corresponding series. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: • recognise the difference between a sequence and a series; • recognise an arithmetic progression; • find the n-th term of an arithmetic progression; • find the sum of an arithmetic series; • recognise a geometric progression; • find the n-th term of a geometric progression; • find the sum of a geometric series; • find the sum to infinity of a geometric series with common ratio |r| < 1. Contents 1. Sequences 2. Series 3. Arithmetic progressions 4. The sum of an arithmetic series 5. Geometric progressions 6. The sum of a geometric series 7. Convergence of geometric series www.mathcentre.ac.uk 1 c mathcentre 2009 2 3 4 5 8 9 12 1. Sequences What is a sequence? It is a set of numbers which are written in some particular order. For example, take the numbers 1, 3, 5, 7, 9, . . . . Here, we seem to have a rule. We have a sequence of odd numbers. To put this another way, we start with the number 1, which is an odd number, and then each successive number is obtained...
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...MCR 3U Exam Review Unit 1 1. Evaluate each of the following. a) b) c) 2. Simplify. Express each answer with positive exponents. a) b) c) 3. Simplify and state restrictions a) b) c) d) 4. Is Justify your response. 5. Is Justify your response. Unit 2 1. Simplify each of the following. a) b) c) 2. Solve. a) b) c) 3. Solve. Express solutions in simplest radical form. a) b) 4. Find the maximum or minimum value of the function and the value of x when it occurs. a) b) 5. Write a quadratic equation, in standard form, with the roots a) and and that passes through the point (3, 1). b) and and that passes through the point (-1, 4). 6. The sum of two numbers is 20. What is the least possible sum of their squares? 7. Two numbers have a sum of 22 and their product is 103. What are the numbers ,in simplest radical form. Unit 3 1. Determine which of the following equations represent functions. Explain. Include a graph. a) b) c) d) 2. State the domain and range for each relation in question 1. 3. If and , determine the following: a) b) 4. Let . Determine the values of x for which a) b) Recall the base graphs. 5. Graph . State the domain and range. Describe...
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...Electric Counterpoint, by an American composer named Steve Reich, is a Minimalist piece which was written in the 1980s. It is the last in a series of three compositions for soloists playing along with pre-recorded multi-track tape loops. These loops being repeated leaves the note addition and resultant melody to the performer and the performing of it has been compared to playing in an ensemble with yourself. The piece is in binary form (AB) with 4 sections within the A and B sections and it ends with a Coda. At the start of the piece there is tonal ambiguity with hints at the key of E minor but this does not become clear until the bass guitar is introduced in part two of the A section. The three chord progressions used in A-3 are C Bm E5, C D Em and C D Bm. These chords make it clearer that the piece’s tonality is modal, specifically the E aeolian mode, because there is no F# in Em (as in the D chord) but there is in the aeolian mode. The most obvious indicator that the B section has begun is the change in key from E minor to C minor- and the piece switches between these keys frequently as the B section develops. The texture of the piece begins monophonically with a single guitar which starts as a one bar ostinato and then is full by bar six by using the note addition technique. Then layers are added and it becomes a four part guitar canon where the live guitar plays the resultant melody and it becomes polyphonic overall. In A-2 the bass guitar is introduced using the...
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...F.A.M.I.L.Y. (Hook) F.A.M.I.L.Y. What does it mean? F.A.M.I.L.Y. Who they supposed to be? Fake Ass Mutherfuckers I Love You Failing At Making Intelligent Logical Youth 1. Fake Ass Mutherfuckers I Love You 2. Forget All Meaningless I Love You’s 3. Failing A Million infinite long Years 4. Frequently Ask M I L Y 5. Forever and Miserable I L Y 6. Fight And Make-up In lost Years 7. Fight Apologize Make-up Imitating Little Young 8. Forming/form A Multitude in lost year 9. Finding A Moment In Life Year 10. Forgot about Madly In Love Yeah-yeah 11. Fight after missing in love yeah-yeah Verse 1 Take my words as verbal abuse because these are things you can’t define For where were the grandparents that created my Leviathans Grandparents are like the first beginning of the entity Without the beginning there is no origination to learn from Take the Keynesian view, aggregate demand does not necessarily Equal the productive capacity of the economy; Instead, it is influenced by a host of factors And sometimes behaves erratically, Affecting production, employment, and the biggest part A Generation, for what does a F.A.M.I.L.Y. mean if you can’t theoretically explain it? Verse 2 I’m hearing the wedding bells, all of a sudden that ship sails They took vows, it was never carry out, What started as intimacy turn to intimidating And the wedding ring on their finger don’t signify a thing Nor does that marriage certificate...
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...WEEK ONE Week One Writing Assignment Name MAT 126 Professor Date WEEK ONE Week One Writing Assignment In the 5th chapter of Mathematics in our world, we have read about sequence numbers. We went over two basic types of sequence numbers which are arithmetic and geometric sequence. Both sequence styles have their own rule that must be followed in order to determine what category the sequence falls in. By following these rules we can successfully solve real life problems. The first sequence we will discuss is the arithmetic sequence. Each single number in the arithmetic sequence is called a term. Every term is evenly spaced by the same amount i.e, 2, 4, 6, 8… are evenly spaced by adding 2 and 5, 10, 15, 20… are spaced by adding 5. This number that spaces or succeeds the term is known as the common difference. The common difference stays the same throughout the sequence. It is generally written as a1, a2, a3,…,an, where a1 is the first term. Here is an example of real world arithmetic sequence problem where we will find the term. “A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $25 more that the preceding 10 feet. That is, the next 10 feet will cost $125; the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower?” (Bluman, 2005). To solve this arithmetic sequence problem, we are going to the formula...
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...ALGEBRA - Tips and Hints * Level 1 * Level 2 * Level 3 Browse Topics * 1. Quadratic Equations * * 1.1. Discriminant * 1.2. Complex Solutions? * 1.3. Remainder Theorem * 1.4. Factor theorem * 2. Functions * * 2.1. Defining the Graph of a Function * 2.2. Some of the important functions * 2.3. Even and Odd Functions * 3. Inequalities * * 3.1. Solving Inequalities * 3.2. Method to Solve Linear, Polynomial or Absolute Value Inequalities * 3.3. Method to Solve Rational Inequalities * 4. Progressions * * 4.1. Series * 4.2. Arithmetic progressions * 4.3. The sum of an arithmetic series * 4.4. Geometric progressions * 4.5. The Sum of a Geometric Series * 4.6. Convergence of geometric series 1. Quadratic Equations A quadratic equation is a second-order polynomial equation in a single variable x. ax2+bx+c=0 -------- (1) with a≠0 Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has two solutions. These solutions may be both real or complex. The roots x can be found by completing the square, x2+bax=−ca -------- (2) (x+b2a)2=−ca+b4a2=b2−4ac4a2 -------- (3) x+b2a=±b2−4ac2a -------- (4) Solving for x then gives x=−b±b2−4ac2a -------- (5) This equation is known as the quadratic formula. The letters a, b and c are coefficients (we know those values). They can have any...
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...BACHELOR OF BUSINESS (HONS) IN INTERNATIONAL BUSINESS Title : GROUP ASSIGNMENT Submission Date : 21/11/2014 Lecturer : Ms.Hannah Title : GROUP ASSIGNMENT Submission Date : 21/11/2014 Lecturer : Ms.Hannah BBI1214 / BBI1213 ● BUSINESS MATHEMATICS Name : YAZID MUHAMMAD BAJAMAL 110041112 WADAH MOHAMED HAMAD ELNEEL 110039251 MOHAMMED SALEH BAHUBAISHI 110037771 UNAL KAVASTAN 110037858 MONIRUL HASAN 110040569 Semester : 1 Academic Honesty Policy Statement I, hereby attest that contents of this attachment are my own work. Referenced works, articles, art, programs, papers or parts thereof are acknowledged at the end of this paper. This includes data excerpted from CD-ROMs, the Internet, other private networks, and other people’s disk of the computer system. Student’s Signature : _____________________________ SUPERVISOR’S COMMMENTS/GRADE: | for office use only DATE : ______________ TIME : ________________ RECEIVER’S NAME : _____ | Assigment 1 ● Question 1 ● An Invoice of RM 45.000 dated 28/03/2014 with cash discount terms of 2/15, 1/40, n/60. What would be the discount amount if : I. Payment is made on the 10/04/2014 2100x RM 45,000 =RM 900 Discount amount : RM 45,000 – RM 900 = RM 44,100 II. Payment is made on the 1/05/2014 1100 x RM 45,000 =RM 450 Discount amount : RM 45,000 – RM 450 ...
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