Chapter 1/2 – Basics
1. Basic notations 1.1. Sum of: ∑ 1.2. Product of: ∏ 2. Sets A = {1,2,3} describes the set A containing members 1, 2, and 3. A={n | n is a whole number and 1≤n≤3} x A denotes that x is a member of set A S T denotes that S is a subset of T A B is the set whose members belong to either set A, set B or both i.e. A B = {x | x A or x B} A B is the intersection of 2 sets where A B = {x | x A and x B} denotes an empty set

3. Functions Given two sets A and B, a function from A to B is a rule which assigns to each member of A precisely one member of B.

A function is a one-way relationship: the function number, (x).

takes a number x as input and it returns another

An inverse function takes as input a number y and returns the number x such that ( ) ( ) Not all functions have an inverse. Ex. ( ) A composite function is one where two functions that; ( ) ( ( )) 4. Powers Rules ( )

is given by

are applied consecutively to obtain h such

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MT105a Study Notes – J.Fenech

Chapter 3 – Differentiation
1. Definition The derivative is a measure of the instantaneous rate of change of a function 1.1. Derivative from first principles ( ) ( )

1.2. Alternative notation ( ) 1.3. Standard Derivatives Table

2.4. Chain Rule or Composite function rule ( ) ( ( )) ( ) ( ( )) ( )

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MT105a Study Notes – J.Fenech 3. Differentiation by taking logarithms 4. Local Maxima and Minima Derivatives are very useful for finding the maximum and minimum values of a function In particular; If ’(x) > 0 then is increasing at x If ’(x) < 0 then is decreasing at x 4.1. First derivative test At a point c for which ’(c) =0, is neither increasing nor decreasing. C is the...

...less-skilled workers than a continuous pro- cessing system. F In cellular manufacturing, machines and equipment are grouped by type (e.g., all grinders are grouped into a cell). (T/F) T 12. ”Balance delay” is another name for the percentage of idle time in a product layout. (T/F)T Location decisions are basically one-time decisions usually made by new organizations. (T/F)F 14. For service and retail stores, a prime factor in location analysis is customer access. (T/F)T 15. Averaging techniques are useful for: B. smoothing out ﬂuctuations in time series. 16. Maximum capacity refers to the upper limit of: D. rate of output. 17. Utilization is deﬁned as the ratio of B. actual output to design capacity. 18. In decision theory, Sensitivity analysis is required because: A A. payoﬀs and probabilities are estimates. 19. Job shops tend to be ( ) while continuous processes tend to be ( ). C. small scale and ﬂexible; large-scale and inﬂexible 20. Which of the following is the last step in the...

...Determination of the Angle Repose
Based on the gathered data in Table 1, adding smaller weights on top of the block and adjusting the weights on the pan will make the coefficient friction a little constant.
The second part of the experiment is “Determination of the Angle of Repose” as shown in Figure 6. The first procedure is to remove the string that is tied to the block then place the block, facing its wider side, to the center of the plane’s surface then gradually incline the plane until such time that you observe the same type of motion the block had. Next is to measure the corresponding vertical height (h) and horizontal (b) then record them. Just repeat measuring until you get five (5) trials. Lastly, compute the coefficient of motion by getting the tangent of the angle.
Table 2. Determination of the Angle Repose
TRIAL Vertical Height
h Horizontal Distance
b tan𝜽 𝜽
1 30 cm 119.00 cm 30/119.00 14.15o
2 33 cm 117.80 cm 33/117.80 15.65o
3 37 cm 114.20 cm 37/114.20 17.95o
4 35 cm 116.10 cm 35/116.10 16.78o
5 39 cm 115.10 cm 39/115.10 18.72o
Based on the gathered data in Table 2, increasing the vertical height and the horizontal distance will make the coefficient friction a little constant just like in the first part of the experiment.
301625043287950033554816040854Figure 9
Figure 9
4275115530355Figure 8
Figure 8
36810953192310Figure 7. Set up for Determination of Maximum Force that cause Uniform Motion
Figure 7. Set up for...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...TERMPAPER
ON
APPLICATION OF BUSINESS MATH IN BUSINESS
[pic]
U N I V E R S I T Y O F D H A K A
Submitted to:
Md. Ariful Islam
Lecturer
Dept. of Banking and Insurance
Dhaka University
Submitted by:
Md. Mahfuzur Rahaman Biswas
ID No. 51221068
Batch-21st
Department of Banking
Faculty of Business Studies
Letter of Transmittal
12th December 2012
To
Md. Ariful Islam
Lecturer
Department of Banking & Insurance
University of Dhaka
Subject: Submission of Term Paper on Business Mathematics
Dear Sir:
With due to respect, we would like to inform you that I have completed the term paper on the topic of “Application of Business Mathematics ” It is immense pleasure for us to place the same before you.
I made every endeavor to prepare this paper and tried my level best to accumulate relevant and intuitive information.
It is a great experience for me to work with this topic. I have tried to make the report vivid and comprehensive within the limited resources.
Thanking you
Sincerely yours,
Md.Mahfuzur Rahman Biswas
I.D. - 51221068
Table of Context
|Title |Page No |
|Acknowledgement |5...

...pp. 737-738. Please note that entries must be alphabetized and that the first line of each entry should be flush with the margin, but all successive lines should be indented 5 spaces. This is called a “hanging indent.”
Assignment: Write an essay about a concept that interests you and that you want to study further. When you have a good understanding of the concept, explain it to your readers, using definition, comparison and contrast, cause and effect and/or any other appropriate rhetorical strategies, considering carefully what your readers already know about the topic and how your essay might add to what they know. Be sure to support your explanation with specific facts and examples.
You are required to cite at least seven (7) sources. Two (2) of these may be approved websites and four (4) must be articles originally published in a reputable magazine, newspaper or peer-edited journal. Use the library’s online databases to find such articles. A handout posted on Bb under Content explains how to do this, and we will have a day in the computer lab, or classroom, where I walk you through the process. Please note that, without an individual exception approved by me, you may use no more than two (2) books. All information taken from your sources must be properly documented, using MLA style parenthetical citations along with a Works cited page. SMG, Ch. 27 shows you how to do this. If you have questions at any stage of the process,...

...of National Income Monetary and Fiscal Policies Economic Systems 9 10 Capitalism, Socialism and Mixed Economic System Islamic Economic System
74 81 33 39 62 69 2 7 15 21
1
ECONOMICS: It is a social science (social science is a science, which studies any aspect of human life) which studies as to how the scarce resources, which have alternative uses should be allocated/utilized so that maximum goods are produced i.e., maximum wants are satisfied. Basic concept Goods/resources: Anything that provides satisfaction or utility is called goods/resources. Characteristics of resources: • They are scarce • They have alternative uses. Scarcity of resources When demand for a resource exceeds its existing supply that resource is said to be scarce. Note: scarcity and shortage are the two different things. Shortage is a temporary phenomenon i.e., when supply falls short of the demand temporarily. The problem of scarcity leads to 3 issues (I) What (II) How (III) for whom to produce. Alternative uses When a man can satisfy more that one want with the same resource or can produce more than one product from one resource then the resource is said to have alternative uses. Equilibrium: It is a state when the economy is making full use of resources or when maximum goods are produced. Opportunity cost: The cost of an item measured in term of the alternative forgone is called its opportunity cost. For instance, if government decides to produce more hospitals and fewer schools,...

...MODERN MANAGEMENT THEORIES
INTRODUCTION
Management is one or the other form has existed in every nook and corner of the world since the dawn of civilization. Modern Management has grown with the growth of social-economics and scientific institution. Modern view consists that a worker does not work for only money. They work for their satisfaction and happiness with good living style. Here Non- financial award is most important factor.
Modernmanagement theories started after 1950s. Modern management theory focuses the development of each factor of workers and organization. Modern management theory refers to emphasizing the use of systematic mathematical techniques in the system with analyzing and understanding the inter-relationship of management and workers in all aspect.
It has following three Streams - Quantitative Approach, System Approach and Contingency Approach.
QUANTITATIVE APPROACH
Quantitative approach also called Operation Research. Quantitative approach is a scientific method. It emphasizes the use of statistical model and systematic mathematical techniques to solving complex management problems. Its helps the management to making decisions in operations. It can only suggest the alternatives based on statistical data. It cannot take final decision.
Characteristics of Quantitative Approach:
* Decision-making focus -...

...
PROJECT PART B: Hypothesis Testing and Confidence Intervals
Math-533 Applied Managerial Statistics
Prof. Jeffrey Frakes
December 8, 2014
Jared D Stock
A.) The average (mean) annual income was greater than $45,000
Null Hypothesis: The average (mean) annual income is greater than or equal to $45,000.
Ho: u > $45,000
Alternative Hypothesis: The average (mean) annual income was less than $45,000
Ha: u < $45,000
I will use a = .05 as the significance level, and observing the sample size of n < 30 which tells me I need to use a Z-Test to find the mean of this test and the hypothesis. As the alternative hypothesis is Ha: u < $45,000, the given test is a one-tailed Z-Test.
The critical value for the significance level, α=0.05 for a one-tailed z-test is -1.645.
Decision Rule: We must reject the hypothesis if z >1.645
Test Statistics from Minitab:
One-Sample Z: Income ($1000)
Test of mean = 45, < 45
The proposed standard deviation = 14.64
95% Upper
Variable N Mean StDev SE Mean Bound Z P
Income ($1000) 50 43.48 14.55 2.06 46.86 0.49 0.311
Confidence Intervals from MiniTab:
One-Sample Z
The assumed standard deviation = 14.64
N Mean SE Mean 95% CI
50 42.61 2.06 (39.45, 47.51)
Summary
Since the...