Notes, summaries, assignments, exams, and exercises for Mathematics for Other courses

Bar Graph: Annual Sales of Product A and B

The bar chart illustrates the annual dollar sales of Product A and Product B for the years 2015, 2016, and 2017. As can be seen in the graph, between 2015 and 2017 sales of Product A were higher than sales of Product B. In 2015, sales of Product B were slightly lower than Product A, and in 2016 sales of Product A reached 80,000 USD while sales of Product B only reached 50,000 USD. For 2017, both Product A and Product B had a slight growth, increasing their sales by 10,000 USD compared to the previous year. Overall, we can see that sales of both products have grown in the last three years; however, the product that generates the most revenue is Product A.

Line Chart: Six-Year Sales Trend

The graph shows...

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

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Cost Tool Information

The Cost Tool provides the following information:

• Manufacturer
• Overall Cost (Total)
• Profit Percentage
• Overall Weight
• SKU Number
• Shipping Location (Town and State)

Payment Options

We accept the following payment methods:

• Credit Card
• Debit Card
• PayPal
• PayPal Credit
• Wire Transfer
• Check
• Money Orders
• Prepaid Credit Card
• Gift Certificates

We do not accept C.O.D (or sent-in payments).

Discount Guidelines

Do not offer discounts or gift certificates before presenting the value-added benefits:

• Low prices (already discounted off of retail)
• 1-year price match guarantee
• 24/7 Technical support
• High-quality

Tangible Fixed Assets Definition

Tangible fixed assets are a set of rights and resources intended to remain in the business for more than one financial period.

Types of Fixed Assets

• Tangible-Intangible Assets: These assets have a physical entity but are classified as intangible assets or rights subject to economic evaluation.
• Tangible Assets: These assets have a physical entity and are classified as real or personal property, except those that must be classified in other subgroups.

Understanding Depreciation

Depreciation refers to the systematic allocation of the cost of tangible items over their useful life due to three primary reasons:

1. The use made of these elements, which causes deterioration.
2. The passage of time, whether the asset is used or not.

Contribution Bases in Special Situations

Temporary Incapacity, Pregnancy Risk, and Childbirth

The obligation to contribute remains for situations of temporary incapacity, risk during pregnancy, and enjoyed periods of maternity leave, although they involve a cause of suspension of employment. The contribution base for the various contingencies is determined as follows:

a) Basis for Common Contingencies

The applicable contribution base for common contingencies will be determined by the month preceding the date of disability, the onset of risk during pregnancy, or entitlement to maternity leave, according to the following rules:

• In the event of wages being paid on a daily basis or if, having that character, the worker has remained registered with the

Review June The following data relate to the heights of 20 persons:
1.73 1.66 1.65 1.60 1.71 1.58 1.75 1.56 1.63 1.64
1.68 1.71 1.78 1.73 1.57 1.69 1.65 1.63 1.66 1.72
1. It groups these data into intervals of width 0.05, so the apparent lower limit of the former is 1.55. Make a table that appear real and perceived boundaries, the class marks and the two types of absolute frequencies.
Lim. Real
(Li, L i) N i Xini
(1.545, 1.595) 1.55 - 1.59 1.57 3 4
(1.595, 1.645) 1.60 - 1.64 1.62 4 10
(1.645, 1.695) 1.65 - 1.69 1.67 6 15
(1.695, 1.745) 1.70 - 1.74 1.72 5 18
(1.745, 1.795) 1.75 - 1.79 1.77 2 20
20
Find the average of these heights of two ways: with the data grouped and ungrouped. Which of the two means is more accurate? Why? Media...

1. Sample Space: Binary Signal Example

Definition: A sample space (S) is the set of all possible outcomes of a random experiment, usually denoted by S.

Example: In digital communication, a binary signal has only two possible values: 0 and 1. Hence, the sample space is S = {0, 1}. This means every outcome of the experiment must belong to this set.

2. Event Definitions and Types

Definition: An event (E) is any subset of the sample space, representing one or more outcomes of an experiment.

Types:

• Simple Event: Contains only one outcome. Example: E = {0}
• Compound Event: Contains more than one outcome. Example: E = {0, 1}
• Impossible Event: An event that cannot occur, represented by the empty set (∅). Example: Getting a ‘2’ in a binary system.

3. Deterministic

Investment Portfolio and CAPM Practice Solutions

• Question 1: Portfolio beta (0.6)
• Question 2: Expected return under CAPM (7%)
• Question 3: Expected return with new allocation (6.5%)
• Question 4: Passive investment strategy (Zero alpha)
• Question 5: Net Asset Value calculation ($50)
• Question 6: Definition of NAV (Market value of assets minus liabilities divided by shares outstanding)
• Question 7: Portion of market risk (64%)
• Question 8: Mutual fund return after expenses (4.5%)
• Question 9: Net Asset Value City Street Fund ($40)
• Question 10: Impact on portfolio value (Decreases to $460 million)
• Question 11: Impact on shares outstanding (Decreases to 9 million)
• Question 12: New NAV after shares sold ($40)
• Question 13: Risk premium for stocks (60%)
• Question 14: Optimal

Common Statistical Biases

• Sampling bias: The sample was not representative of the population.
• Non-response bias: Only 24% returned surveys.

Sampling Techniques

• Simple Random Sampling (SRS): 1) Every member of the population has the same chance of being included (representative). 2) Members are chosen independently.
• Random Cluster Sampling: 1) Divide into smaller geographical sectors. 2) Take an SRS of sectors. 3) Count all samples in sectors and scale appropriately.
• Stratified Random Sampling: 1) Divide population into groups based on criteria like age or income. 2) Perform an SRS of each group and scale appropriately.

Data Variables and Distributions

• Variable Types: Categorical and Numeric (discrete and continuous).
• Relative frequency: Count / sample

Probability Distributions for Discrete Events

The following table matches common scenarios to their appropriate probability distributions: