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

1. For y — by — 0 an integrating factor is e J ocix = e ox so that — [e oxy dx L J —oo < x < oo. There is no transient term. 2. For y1 + 2y — 0 an integrating factor is eJ 2 dx = e2x so that —oo < x < oo. The transient term is ce 2x. A dx <-2xy = 0 and y = ceox for = 0 and y — ce~2x for d 3. For y' + y — eix an integrating factor is eJ dx = ex so that — [e'Ty] -- and y - ie3* + ce~x for dx * 4 —oo < x < oo. The transient term is ce x. 4. For y' -f- Ay = 4 an integrating factor is eJ 4 dx == e4x so that [e4x dx L for — oo < x < oo. The transient term is ce~4x. V = |e4x and y = A + ce -4x 49 www.Elsolucionario.Net Exercises 2.3 Linear Equations 5. For y'+3x2y = x2 an integrating factor is eJ ,ix... Continue reading "Linear Equations and Integrating Factors" »

Capital Intensity

Automation is a system, process, or piece of equipment that is self-acting and self-regulating. It substitutes labor-saving capital equipment and technology for labor. Automated manufacturing processes typically require high volumes, and costs are high. Fixed automation produces one type of part or product in a fixed sequence. Flexible automation can be changed to handle various products. Industrial robots and automated service processes.

Chapter 2 Process Analysis

DMAIC = Define, Measure, Analyze, Improve, and Control.

Process Analysis

A firm cannot gain competitive advantage with faulty processes! Processes can be analyzed and improved using certain tools and techniques. Process analysis is the documentation and detailed understanding... Continue reading "Process Analysis and Quality Management in Automation" »

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" »

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

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

Accounting Concepts: Real Value Recording

Cost Concept: To record the real value and not the estimated value.

Cost Accounting and Budgeting Fundamentals

• FOH Allocation: Single Plantwide, Departmental, and Activity-Based Rates
• Advantages of Departmental FOH Rates: It doesn't assign other costs such as depreciation.
• Characteristics of Unit, Batch, Facility, and Product Level
• Activity-Based Costing and the Importance of Activity Drivers
• Importance of ABC Costing
• Importance of Matching Strategic Planning with Pricing, Market Penetration, and Expansion
• Contribution Margin Formula: Sales - Variable Costs (VC)
• Fixed Cost and Variable Cost Behavior
• Break-Even Point Concept and Formula: Level of sales at which contribution margin matches fixed expenses, expressed in dollars.
• Direct Labor (DL) Cost per Unit: Given two different levels of production
• Differences Between