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

Agile Methodology Fundamentals

The agile approach differs from classic project management because it is iterative and incremental.

Sprint Planning Objectives

The sprint planning meeting has two primary objectives: defining the functionalities to be developed in the next sprint and identifying the necessary tasks to complete them.

The Product Owner Role

The product owner is the person within the company who manages business needs and is responsible for the product backlog.

Estimated vs. Real Effort

Estimated effort refers to the projected time required, while real effort is the actual time spent on a task.

Scrum Daily Meeting

The main objective of the Scrum daily meeting is to monitor project status and make decisions to achieve the sprint goal. The... Continue reading "Agile and Scrum Methodology: Essential Concepts Explained" »

Ok, Georgios, let's get down to business.

Good idea. So, shall we start by discussing the first aid training package?

Well, we already have some people with first aid training.

But we need some first aid courses for beginners. We also need refresher courses, where people return every year to improve their skills. So we'd like you to provide both beginner and refresher courses for our staff.

We can agree to that. What I propose is a package of a beginner course plus refresher courses for more experienced people.

That would be fine for us.

So these are the courses that we offer. You can see all the dates and the prices here.

Yes, I see. Tell me, Martina, what is your priority here?

It's essential that our factories follow the law. We want to have all... Continue reading "Health and Safety Training Package for Factories" »

Are you happy with your current situation?

Yes, but I'd like to take advantage of it much better.

Do you have any technical skills?

No, I'm too lazy to do that.

Effective Time Management Strategies

• Plan your day
• Prioritize important tasks
• Delegate to others where possible
• Try techniques such as time audits

Ineffective Time Management Habits

• Try to push yourself to the limit
• Waste time on unnecessary activities
• Blame others for your workload
• Miss breaks and rest periods

Improving Sentence Structure

Text:

• Probably find... would probably find
• know.. knew
• work..work
• probably get..will probably get
• make..would make
• offer..offered
• not take..don't take
• move..moved
• become..will become
• stop..stop

Using Conditional Sentences in Sports

We were awful. But if the hacker had taken... Continue reading "Effective Time Management and Workplace Communication" »

Assessment is one of the most important components of education as it provides evidence of students' learning outcomes and their growth over time. This process helps not only students but also teachers, families, and other stakeholders in many ways. For example, assessment is a tool to evaluate the effectiveness of teaching and teachers, and it can provide insight into program effectiveness for program developers. According to Brookhart and Nitko (2011), assessments are used to measure, evaluate, and document learning outcomes, proficiency, and educational needs.

Assessment can be formative or summative (Crooks, 2001). Formative assessments are used to monitor day-to-day learning of students, provide feedback to both teachers (i.e., about instructions)... Continue reading "Understanding Assessment Formats and Question Types" »

Capital Budgeting and Cost of Capital Analysis

13) The company cost of capital may be an inappropriate discount rate for a capital budgeting proposal if the proposal has a different degree of risk. (ch13)

Calculating Weighted Average Cost of Capital (WACC)

1) The company cost of capital for a firm with a 65/35 debt/equity split, an 8% before-tax cost of debt, a 15% cost of equity, and a 35% tax rate would be:

Calculation: 0.65 × (1 - 35%) × 8% + 0.35 × 15% = 8.63%

Determining After-Tax Cost of Debt

2) The firm has 7,500 bonds outstanding with a face value of $1,000 per bond. The bonds carry a 7% coupon, pay interest semiannually, and mature in 8 years. The bonds are selling at 98% of face value. The company's tax rate is 34%. What is the firm'... Continue reading "WACC and Cost of Capital Calculation Examples" »

The Bayes’ theorem describes the probability of an event, based on conditions that Might be related to the event. Bayes’ theorem can also be calculated as the Joint probability divided by the marginal.
Bayes’ theorem deals with conditional probability.

????(????) ∗ ????(????|????) = ????(????) ∗ ????(????|????)

????(????|????)=P(A)P(B|A)/P(B)

????(????|????)=P(Ai)P(B|Ai)/ P(A1)P(B|A1)+ P(A2)P(B|A2)

????(????|????)=P(Ai ∩B) / P(A1∩B)+P(A2∩B)

-Discrete probab distrib(numb of students absent today, numb of books borrowed from library, number of head appering when a cons is tossed tre time)LIMITED

-Conitnous:liter of rain that occur in barcelona, the wheight of all population in spain )UNLIMITED.

Ejercicio Larry

Are indoeendent?

Not because

Fundamentals of Operations Research

Goal Programming Basics

Goal Programming aims to Minimize W, the weighted sum of deviations from the goals. The fundamental relationship is:

Level Achieved – Amount Over + Amount Under = Goal

Introduction to Queueing Theory

The basis of Queueing Theory is the trade-off between the cost of improving service and the costs associated with making customers wait. Queues arise when the short-term demand for service exceeds the capacity (i.e., arrival rates exceed the service rates).

Key Components of a Queueing System

• Calling Population: Refers to the pool of potential customers.
• Customer Behavior: Customers can be patient or impatient (those who leave the line before receiving service).
• Queue Capacity: Can be finite

Vertex Cover ≤ CLIQUE

Suppose G has a clique S with |S| = k. Consider S' = V – S. Then, |S'| = |V| - k. To show S' is a cover, consider any edge (v, w) ∈ E'. Then, (v, w) ∉ E, at least one of v or w is not in S (since S forms a clique), and at least one of v or w is in S'; hence, (v, w) is covered by S'.

Suppose G' has a cover S' with |S'| = |V| - k. Consider S = V – S'. Clearly, |S| = k. To show S is a clique, consider some edge (v, w) ∈ E'. Then, if (v, w) ∈ E', either v ∈ S', w ∈ S', or both. By contrapositive, if v ∉ S' and w ∉ S', then (v, w) ∈ E; thus, S is a clique in G.

Vertex Cover ≤ SET COVER

Given a black box that solves instances of SET-COVER, let G = (V, E) and k be an instance of VERTEX-COVER. Create a SET-... Continue reading "Complexity Theory: Reductions and NP-Completeness Proofs" »

1. Many business owners spend years trying to get their enterprise started.

2. At the rate we are going, we are lucky to break even at year's end.

3. The world's biggest stock exchange is in New York.

4. Every employee has shares in the company.

5. The stock market rose 20% today. Brokers were euphoric!

6. The dip in the market caused some investors concern.

7. There was a dramatic rise in the share price at the end of the week.

8. Dividend is the part of the company's profits which is paid to shareholders.

9. One of the most difficult parts of running a restaurant is keeping the cashflow which can be variable.

10. House prices have increased by 5%. It is too expensive to buy now.

11. Demand for this product has fallen recently. We won't manufacture... Continue reading "Understanding Business and Stock Market Terminology" »

Queueing Models

M/M/s: Exponential arrival and service with more than one server. These models are needed in the economic analysis of the system.

M/G/1: Exponential arrival with general service time.

M/D/1: Exponential arrival with deterministic (fixed) service time. Because of lower variability in service time, performance measures are better than M/M/1.

Queues with priority: Performance measures will improve for high-priority customers and worsen for low-priority customers. However, performance measures averaged across all customers (high AND low priority) will remain the same as before.

Distinguish between the number of servers and the number of queues:

1. An M/M/2 queue with two servers but a single queue of waiting customers.
2. Two M/M/1 queues where