Notes, summaries, assignments, exams, and problems for Mathematics

Profit and Loss Fundamentals

Formula: Profit or Gain = S.P. – C.P.

• Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.

Formula: Loss = Cost Price (C.P.) – Selling Price (S.P.)

• Profit or Loss is always calculated on the cost price.
• Marked Price: The price marked as the selling price on an article, also known as the listed price.
• Discount or Rebate: The reduction in price offered on the marked or listed price.

Basic Profit and Loss Formulas

Below is a list of essential formulas used in solving profit and loss problems:

• Gain % = (Gain / CP) × 100
• Loss % = (Loss / CP) × 100
• SP = [(100 + Gain%) / 100] × CP
• SP = [(100 – Loss %) / 100] × CP

The above two formulas can be simplified as:

• If an article

Product Information and Constraints

Fran Farnsworth sells three health care products: Flex, Feelgood, and Firmup. Her costs, sales time, delivery costs, and commission for each product are as follows:

• Flex: $3 cost, 10 minutes to sell, $0.50 delivery cost, $2 commission
• Feelgood: $5 cost, 20 minutes to sell, no delivery cost, $4 commission
• Firmup: $4 cost, 12 minutes to sell, $1 delivery cost, $3 commission

Fran's weekly constraints are:

• Maximum $1500 worth of products
• Maximum $85 delivery expense
• Maximum 40 hours (2400 minutes) for sales

Linear Programming Model

Let x, y, and z represent the number of boxes of Flex, Feelgood, and Firmup sold per week, respectively. Let C be Fran's weekly commission. The LP model is:

Maximize:

C = 2x + 4y + 3z

Subject

What is a Shapefile?

A shapefile is an Esri vector data storage format for storing the location, shape, and attributes of geographic features. It is stored as a set of related files and contains one feature class. Google Earth, an Online Satellite Imagery (OSI) Technique, is a tool for generating shapefiles.

Geometric Analysis Tools in Projects

Example 1: Population Maps of To Kwa Wan using ArcGIS

We used ArcGIS to create population maps of To Kwa Wan.

1. Selected population and working population data from the C&SD department.
2. Opened TPUs with the population data in ArcGIS.
3. Calculated the area of the TPUs based on Hong Kong 1980 Grid, determining population densities.
4. Created maps with different population densities, using graduated colors to represent

Formal letter

We are writing in reference to your new products advised in March 23 edition of “Info Globe”. We are a software company based in Berlin which specializes in Games Development.

Our company is currently developing a new software to improve old games quality. We are interested in designing a new video game console which would works with old games with a better graphics quality.

 We would like to request a catalogue of your lasted collection that was advised in Info Globs. Please let us know if you would be interested in scheduling a meeting.

 I look forward to hearing from you.

Yours sincerely, M Walton

Faculty and Student Responses

A university president proposed that all students must take a course in ethics as a requirement for graduation. The table below gives the responses of a sample of faculty and students at the university when asked their opinion on this issue.

Y: FAVOR O: Oppose N: Neutral

Totals

F: Faculty         45             15             10                    70

S: Student        90             110             30                  ₂₃₀ 

 Totals   135               125                40

Probabilities

1. Find the following probabilities; each time ONE person is being randomly selected.

P(S or Y) = (230 + 135 – 90)/... Continue reading "Calculating Probabilities from a Table: Ethics Course Requirement" »

Systematic Sampling: Type of Probability Sampling Method

In systematic sampling, sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. The sampling interval, calculated by dividing the population size by the desired sample size, determines the selection.

Oversampling: Techniques to Adjust Class Distribution

Oversampling is a data analysis technique used to adjust the class distribution of a data set, ensuring a balanced representation of different classes/categories.

P Value: Probability of Obtaining Extreme Test Results

The p value represents the probability of obtaining test results at least as extreme as the observed results during the test, assuming the null hypothesis... Continue reading "Understanding Systematic Sampling and Statistical Significance" »

Worksheet: Revisiting Calculating Probabilities from a Table

1. Goals

P(F) = 251/478 = 0.525

The probability that a randomly selected student is a girl is 0.525.

P(P^C) = (247 + 90)/478 = (478 – 141)/478 = 337/478 = 0.705

The probability that a randomly selected student did not indicate being popular as a primary goal is 0.705.

P(B or S) = (227 + 90 – 60)/478 = 257/478 = 0.538

The probability that a randomly selected student is a boy or indicated a primary goal is to excel at sports or both is 0.538.

P(B and S) = 60/478 = 0.126

The probability that a randomly selected student is a boy and indicated a primary goal is to excel at sports is 0.126.

P(S|B) = 60/227 =... Continue reading "Calculating Probabilities from a Table" »

Operating Segments & Disclosures

Revenue Test Criteria

Both external and intersegment revenue are included in the revenue test.

Profit & Loss (P&L) Test

The P&L test includes 10% of the higher absolute value of intersegment revenue and expenses.

Management's Business Evaluation

Management evaluates business results along product, customer, or geographic lines, not based on legal entity results.

Defining an Operating Segment

• Includes state
• Reviewed by the chief decision maker
• Discrete information available
• Product is the primary breakdown, with geographic and customer as secondary.

Operating Segment Disclosure Rules

• Must reconcile to GAAP.
• For immaterial operating segments, revenue, P&L, and assets must be disclosed.

Non-Operating Segment

In the examples C = {1,2,3,4} and D = {3,4,5}

SymbolMeaningExample{ }Set: a collection of elements{1,2,3,4}A ∪ BUnion: in A or B (or both)C ∪ D = {1,2,3,4,5}A ∩ BIntersection: in both A and BC ∩ D = {3,4}A ⊆ BSubset: A has some (or all) elements of B{3,4,5} ⊆ DA ⊂ BProper Subset: A has some elements of B{3,5} ⊂ DA ⊄ BNot a Subset: A is not a subset of B{1,6} ⊄ CA ⊇ BSuperset: A has same elements as B, or more{1,2,3} ⊇ {1,2,3}A ⊃ BProper Superset: A has B's elements and more{1,2,3,4} ⊃ {1,2,3}A ⊅ BNot a Superset: A is not a superset of B{1,2,6} ⊅ {1,9}A^cComplement: elements not in AD^c = {1,2,6,7}
When  = {1,2,3,4,5,6,7}A − BDifference: in A but not in B{1,2,3,4} − {3,4} =