text:
Calculus/Limit Comparison Test

Limit Comparison Test
The Limit Comparison Test (LCT) and the Direct Comparison Test are two tests where you choose a series that you know about and compare it to the series you are working with to determine convergence or divergence. These two tests are the next most important, after the Ratio Test, and it will help you to know these well. They are very powerful and fairly easy to use.

Limit Comparison Test Quick Notes

 * 1) Notice that we do not specify the $$n$$-values on the sum.  This is common in calculus and it just means that, for this test, it doesn't matter where the series starts (but it always 'ends' at infinity, since this is an infinite series).
 * 2) $$ \textstyle{\sum{a_n}} $$ is the series of which we are trying to determine convergence or divergence and it is given in the problem statement.
 * 3) $$ \textstyle{\sum{t_n}} $$ is the test series that you choose.

What The Limit Comparison Test Says
This test is pretty straightforward. In our notation, we say that the series that you are trying to determine whether it converges or diverges is $$ \textstyle{\sum{a_n}} $$ and the test series that you know whether it converges or diverges is $$ \textstyle{\sum{t_n}} $$. The limit $$L$$ has to be calculated for you come to any conclusion.

Also, notice that the fraction can be inverted and the test still works for case 1 (but not cases 2 and 3). For example, if you get $$ L=3 $$ for one fraction, then you would get $$ L=1/3 $$ for the other fraction. Both are finite and positive and both will tell you whether your series converges or diverges. If you invert the fraction then cases 2 and 3 will change. So it is important to check your fraction if you are trying to apply cases 2 or 3.

When To Use The Limit Comparison Test
This test can't be used all the time. Here is what to check before trying this test.

 * As with all theorems, the conditions for the test must be met. The main one is that $$ a_n > 0 $$.  If this isn't the case with your series, don't stop yet.  Look at the Absolute Convergence Theorem to see if that will help you.
 * A second important thing to consider is whether or not the limit can be evaluated. For example, if you have a term that oscillates, like sine or cosine, then you can't evaluate the limit.  So this test won't help you.  In this case, the Direct Comparison Test might work better.

How To Choose A Test Series
When you are first learning this technique, it may look like the test series comes out of thin air and you just randomly choose one and see if it works. If it doesn't, you try another one. This is not the best way to choose a test series. The best way I've found is to use the series you are asked to work with and come up with the test series. There are several things to consider.

The first key is to choose a test series that you know converges or diverges AND that will help you get a finite, positive limit.

Idea 1: If you have polynomials in both the numerator and denominator of a fraction, drop all terms except for the highest power terms (in both parts) and simplify. Drop any constants. What you end up with may be a good comparison series. The reason this works is that, as $$n$$ gets larger and larger, the highest powers dominate. You will often end up with a p-series that you know either converges or diverges.

Idea 2: Choose a p-series or geometric series since you can tell right away whether it converges or diverges.

Idea 3: If you have a sine or cosine term, you are always guaranteed that the result is less than or equal to one and greater than or equal to negative one. If you don't have any bounds on the angle, these are the best you can do. So replace the sine or cosine term with one.

Idea 4: If you have a natural log, use the fact that $$\ln(n) \leq n$$ for $$n \geq 1$$ to replace $$\ln(n)$$ with $$n$$ or use $$\ln(n) \geq 1$$ for $$n \geq 3$$.

As you get experience with this test, it will become easier to determine a good test series. So work plenty of practice problems.

Limit Comparison Test Proof
Here is a video showing a proof of the Limit Comparison Test. You do not need to watch this in order to understand and use the Limit Comparison Test. However, we include it here for those who are interested.

Proof of the Limit Comparison Test

Video Recommendations
If you would like a complete lecture on the Limit Comparison Test, we recommend this video clip. As the title implies, this video starts with the (Direct) Comparison Test but we have the video start when he begins discussing the Limit Comparison Test.

Watching these two video clips will give you a better feel for the limit comparison test. Both clips are short and to the point.

Series, comparison + ratio tests

Direct Comparison Test / Limit Comparison Test for Series - Basic Info

Practice Problems with Written Solutions
Determine the convergence or divergence of the following series. If possible, use the Limit Comparison Test. If the LCT is inconclusive, use another test to determine convergence or divergence.

1. $$ \sum_{n=1}^{\infty}{\frac{n^2-1}{n^3+4}} $$

2. $$\displaystyle{ \sum_{n=1}^{\infty}{ \frac{1}{n^2+4} } }$$

3. $$\displaystyle{ \sum_{n=0}^{\infty}{ \frac{3}{n^2+1} } }$$

4. $$\displaystyle{ \sum_{n=1}^{\infty}{ \frac{n}{n^2+1} } }$$

Practice Problems with Video Solutions
Determine the convergence or divergence of the following series. If possible, use the Limit Comparison Test. If the LCT is inconclusive, use another test to determine convergence or divergence.

title: Calculus/Limit Comparison Test


text:
Cookbook:Homemade Coffee Liqueur

| Ingredients

Coffee liqueur is a sweet alcoholic beverage made with distilled spirits and flavored with coffee. Making it at home allows you to customize the flavor and sweetness to your liking.

Ingredients

 * 4 cups strong brewed coffee (cold)
 * 2 cups granulated sugar
 * 2 cups vodka or rum
 * 2 vanilla beans, split (or 2 tsp vanilla extract)

Procedure

 * 1) In a large saucepan, combine the brewed coffee and sugar. Heat over medium heat, stirring continuously until the sugar is fully dissolved. Remove from heat and let it cool to room temperature.
 * 2) Once cooled, stir in the vodka or rum.
 * 3) If using vanilla beans, scrape out the seeds and add both the seeds and the pods to the mixture. If using vanilla extract, add and stir it in.
 * 4) Transfer the mixture to a glass bottle or jar and seal tightly. Store it in a cool, dark place for at least one week, gently shaking the bottle daily.
 * 5) After the infusion period, strain the mixture to remove the vanilla pods and any sediment. Transfer the cleared liquid back to the bottle for storage.

Notes, tips, and variations

 * 1) For a richer flavor, replace half of the vodka or rum with a dark rum or brandy.
 * 2) You can also infuse with additional flavors such as cinnamon sticks, cocoa nibs, or hazelnuts. Just remember to strain them out after the infusion period.
 * 3) For a lighter liqueur, reduce the sugar by half.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cookbook:Homemade Coffee Liqueur


text:
Cookbook:White Russian Cocktail

A White Russian is a creamy, coffee-flavored cocktail made by combining vodka, coffee liqueur, and cream or milk.

Ingredients

 * 2 oz vodka
 * 1 oz coffee liqueur
 * 1 oz heavy cream or milk

Procedure

 * 1) Fill a glass with ice.
 * 2) Pour in the vodka, followed by the coffee liqueur.
 * 3) Top with heavy cream or milk. Gently stir to mix.

Notes, tips, and variations

 * For a blind Russian, replace the cream with Irish cream liqueur.
 * For a dairy-free option, replace the milk with either almond or oat milk.

title: Cookbook:White Russian Cocktail


text:
User talk:ACW Card

You cannot edit indefinitely due to disruptive editing. You may appeal this action with a reasonable argument by adding the text below.

--Xania   talk 07:23, 15 October 2023 (UTC)

title: User talk:ACW Card


text:
Chess Opening Theory/1. e4/1...Nf6/2. e5/2...Nd5/3. g3

This opening line is uncommon among master games (it has only been played around a hundred times) so it doesn't have any theory attached. The extremely basic idea is that it opens up the g2 square for the bishop, which attacks the knight on d5 if it is left undefended. This can be used to regain the tempo that is commonly lost by playing g2 in other openings.


text:
AI Art Generation Handbook/VCAT/Artist Style/France

The prompt used is

To ensure fair judgement, following steps are done

(i) All of prompts are generated 2 times with 8 images each

(ii) Images selected is randomly selected using this dice

(iii) No extra settings are selected except for changing Fooocus resolutions into 1024*1024 pixels


text:
Talk:OpenSSH/Client Configuration Files

Chapter on Client Configuration?
Use of ssh_config(5) is highly underrated. The client configuration file is tremendously useful yet few seem to know about it and how it can be set up for maximum benefit. Should a chapter be added to the Cookbook section with examples of OpenSSH client configurations including brief discussions of the use-cases? If so which use-cases should be covered? 09:02, 16 October 2023 (UTC)

title: Talk:OpenSSH/Client Configuration Files


text:
AI Art Generation Handbook/VCAT/Artist Style/Indonesia

The prompt used is

To ensure fair judgement, following steps are done

(i) All of prompts are generated 2 times with 8 images each

(ii) Images selected is randomly selected using this dice

(iii) No extra settings are selected except for changing Fooocus resolutions into 1024*1024 pixels


text: Talk:Structural Biochemistry/Neurotransmitters


text:
User talk:197.210.52.32

--SHB2000 (discuss • contribs) 11:25, 17 October 2023 (UTC)

title: User talk:197.210.52.32


text:
Public-Private Partnership Policy Casebook/Prince George's County Schools Blueprint Program

This chapter was written by Patrick Morrison, Katy Nicholson and Iqbal Safi for Dr. Jonathan Gifford's Public-Private Partnership Policy class at the George Mason University Schar School of Policy and Government.

Introduction
Like others around the nation, Prince George’s County Public Schools (PGCPS), located in suburban Maryland, faces aging infrastructure and dire needs to return assets to a state of good repair. One of the nation's largest school districts, PGCPS’ over 200 school buildings were 50-60 years old, on average. This backlog totaled $8.5 billion; a total deemed insurmountable through traditional public funding. Consultants recommended a public-private partnership (P3) delivery model to improve school facilities.[1 ] For this project, a Design-Build-Finance-Maintain (DBFM) model was selected, transferring most risks to the private sector. Thus, PGCPS paved the way for the Alternative Construction Financing Program (also known as the Blueprint Program). The Maryland General Assembly passed legislation for the project in 2018 and 2019, with the Request for Proposals (RFP) opened in 2019.[2 ]

The development team, Prince George's County Education and Community Partners (PGCECP) selected in October 2020 started construction in June of 2021 and completed five of the contracted six new schools in July 2023. The development team selected for Phase I included Gilbane Building Company (Design-builder), Stantec (Architect and design), Honeywell (Services), and three local county minority-owned architect and construction businesses. Phase I’s first six schools were written into contract on the same balance sheet and with the same timeline expectations. According to initial projections, this bundling would save the government $175 and $400 million on design and construction costs.[2 ] As of October 2023, PGCPS has recently selected a new development team for Phase II, which will include eight more schools.[5 ] PGCPS' bundling of schools within the DBFM P3 delivery model is unprecedented in the United States.

Policy Narrative
Establishing Legislation and Support:

In 2018, PGCPS, Prince George’s County Government, County Council, and the County’s delegation of the Maryland General Assembly approved legislation to set the Alternative Construction Finance (ACF) program, a P3 model. Later that year, they established a working group from county stakeholders, and in 2019 passed additional legislation to support the ACF program.[2 ]

Financial Challenges:

PGCPS does not have the authority to issue bonds. And alone, they could not finance a project of this scale. The school district generally relies on the State of Maryland for assistance with school construction funding, but the traditional funding methods were not sufficient to address the school district's backlog of deferred maintenance. PGCPS and Prince George's County Council signed a memorandum of agreement in September 2020 that promises $15 million per year from the county government to the school district to help pay for Phase I of the P3.[3 ]

Under the Built to Learn Act of 2020, PGCPS is entitled to receive $25 million annually for 30 years for availability payments for Phase II of its P3 program. This state funding is distributed by the Interagency Commission on School Construction and is provided by bonds issues by the Maryland Stadium Authority.[10 ] The school district plans to use this state funding, along with PGCPS and county funding, to pay for Phase II.[4 ]

Risk Allocation:

The project's financial, operational, and construction risks are firmly on Gilbane and their equity partners. While the project's financial structure is expected to save costs compared to developing the buildings with public finance, PGCPS has little influence in the development phases, and can only defer payments if construction KPIs are not met.

Unpaid and Misclassified Labor Lawsuits:

While five of Phase I’s six schools were completed on schedule, Gilbane reached a $78,000 settlement from unpaid and misclassified labor with one worker. The laborer also alleges that up to 40 other workers also did not receive payment and were misclassified, affecting taxes. The developer was not selected for Phase II for the project,[5 ] although they did submit a proposal.[6 ]

Sustainability:

As set out in the governing contract, the buildings meet the green building guidelines of Leadership in Energy and Environmental Design (LEED), including solar panels, smart sensors for energy efficiency, and other sustainable construction practices.

Contract Add-ons:

As tax dollars will ultimately fund this endeavor, PGCPS has included stipulations in its procurement documents and contracts to ensure that the P3 program serves the greater community:

 * Disadvantaged Business Enterprises (DBE’s): 35% of contract dollars went towards DBE’s, surpassing the Phase I requirement of 30% of contract dollars awarded to DBEs. Approximately half of these DBE contract dollars were awarded to Prince George's County businesses.[2 ] Phase II will require that 40 percent of the labor is conducted by local companies.[5 ]
 * Internships: The PGCECP is required to provide mentorships and internships to career and technical students throughout the 30-year contract.
 * Minority Equity: Phase II requires the project company to include a Minority Business Enterprise as a 20 percent (minimum) equity partner.[4 ]
 * Community Equity: Phase II also requires the project company to develop a program that allows county residents and businesses to invest 10 percent of the total equity in the project.[12 ]

Annotated List of Actors
Public:

 * Prince George’s County Board of Education: The governing body for PGCPS, which ultimately votes on the school district’s P3 policies and contracts. The school district owns the schools and the property on which they sit.
 * Prince George’s County Schools Administration: School district staff that handles the administrative aspects of the program, e.g. issuing recommendations, developing RFQs, RFPs and contracts, communicating with contractors.
 * Prince George’s County Council: The governing body for the county, which has encouraged the Board of Education to pursue the P3 delivery model and is helping to fund the project.
 * P3 Alternative Financing School Infrastructure Work Group: Established by the County Council to investigate the public-private partnership option for school construction projects. Work group includes members of County Council and employees of PGCPS and County Executive’s office.
 * Maryland General Assembly: The state legislative body, which has passed legislation in recent years to help facilitate the development of P3s in Maryland. This includes the 2020 Built to Learn Act, which earmarks $25 million per year for 30 years for Phase II of PGCPS's P3.
 * Interagency Commission on School Construction: The agency that allocates Maryland state funding for the construction of schools. The 2020 Built to Learn Act authorizes the commission to provide PGCPS $25 million per year for 30 years for Phase II of its P3. The funding will be raised from bonds issued by the Maryland Stadium Authority specifically for school funding.[10 ]

Private:

Project Companies/Special Purpose Vehicles:

 * Phase I: Prince George County Education & Community Partners, LLC (PGCECP)
 * Fengate Asset Management (Development and Financing member – 75% equity partner)
 * Gilbane Development Company (Development and Financing Member – 25% equity partner)
 * Gilbane Building Company (Lead Design-Builder)
 * Stantec (Architect & Design Lead)
 * Honeywell (Lead Services Provider) [7 ]

Technical and Financial Advisors (Contractors for PGCPS):
 * Phase II: PGC Education Collective
 * Plenary Americas US Holdings Inc. (Equity)
 * Ellis Don Capital Inc. (Equity)
 * Phoenix Infrastructure Group Investments LLC (Minority Business Enterprise Equity)
 * MCN Build Inc. (Lead Contractor)
 * US Facilities Inc. (Lead Service Provider)
 * Ellis Don Facilities Services (Lead Service Provider)
 * RSC Electrical & Mechanical (Lead Service Provider) [6 ]

 * Jones Lang LaSalle (Phases I and II – financial)
 * K. Dixon Architecture, PLLC (Phase II – technical and financial)
 * Kutak Rock, LLP (Phase II – legal)[8 ]

Community Stakeholders:

Prince George’s County Public Schools Students and Parents: The community, particularly current students and their parents, have been advocating for new schools due to the deterioration of the district’s older schools.

Timeline of Events
Spring 2018

Prince George’s County Council adopts a resolution forming a P3 Alternative Financing School Infrastructure Work Group to investigate the public-private partnership option for school construction projects. The Work Group includes members of County Council and employees of PGCPS and the County Executive’s office.

Spring 2019

Based on the Work Group’s recommendations, PGCPS issues Request for Qualifications: Public-Private Partnership for the Design, Construction, Financing, and Maintenance of Prince George’s County Public Schools Alternative Construction Financing Package 1.

Fall 2019

Spring 2020
 * The Board of Education passes a resolution approving PGCPS Chief Executive Officer’s recommendation to procure six schools as Alternative Construction Financing Package 1.
 * PGCPS issues the RFP for Alternative Construction Financing Package 1 to four shortlisted project companies.[9 ]

The Maryland General Assembly passes the Built to Learn Act of 2020. The Act includes $25 million annually for PGCPS to be used for availability payments for Phase II of its P3 program.[10 ]

Fall 2020

Winter 2020
 * All four project companies submit proposals in response to the RFP.
 * PGCPS issues a recommendation that the school district enter into an agreement with Prince George's County Education and Community Partners LLC.
 * Prince George’s County Council adopts a resolution in support of the project.
 * Prince George’s County Council and PGCPS enter a memorandum of understanding providing $15 million per year of county funding for the PGCPS P3.
 * The Board of Education passes a resolution approving PGCPS’ entry into an exclusive negotiating agreement with Prince George's County Education and Community Partners.

PGCPS Board of Education enters an agreement with Prince George's County Education and Community Partners LLC for the design, construction, financing and maintenance of six schools.[9 ]

Spring 2021

PGCPS approves the advancement of schematic design documents to the “develop and refine” phase. Prince George's County Education and Community Partners LLC works with PGCPS staff to incorporate the school district’s desired changes to the plans.

Summer 2021

 * The designs for the six schools undergo the Mandatory Referral process and ultimately are approved by the Prince George’s County Planning Board with the board’s recommendations.
 * PGCPS hands over the construction sites to Prince George’s County Education and Community Partners LLC; students from three of the six schools are relocated to accommodate construction.
 * The school district holds groundbreaking ceremonies for each of the six Phase I schools.[11 ]

Fall 2021

 * The County Council adopts a resolution encouraging the creation of a work group to study the potential Phase II Alternative Construction Financing Program, as well as a task force to help select the Phase II schools.
 * PGCPS issues an RFQ, Public-Private Partnership for the Design, Construction, Financing and Maintenance of Prince George’s County Public Schools Blueprint Schools Phase II.

Fall 2022

The Board of Education approves the eight schools that have been recommended for Phase II of the Alternative Construction Financing Program.

Spring 2023

April 2023: PGCPS issues an RFP for Phase II with proposals due in July 2023.[12 ]

Summer 2023

Five of the six Phase I schools open.

Fall 2023

 * After delaying its decision due to concerns about the labor requirements in the contract, the Board of Education votes to move forward with Phase II, selecting PGC Education Collective, a different concessionaire from the one that is handling Phase I.[13 ]
 * Colin Powell K-8 Academy (the last school for Phase I) is slated to open in November 2023.

Contract Type
Alternative Construction Financing (ACF) or Public-Private Partnership

The PGCPS, in line with its 20-year Educational Facilities Master Plan, aims to ensure that it can adequately cater to the educational needs of its 134,000 students and a workforce of nearly 22,000 employees. Through the ACF program established in 2019, PGCPS, the County, and the Working Group share a common goal to employ a Design-Build-Finance-Maintain framework to efficiently deliver a predefined set of schools. This approach aims to achieve optimal cost-effectiveness and timely completion. Some of the primary objectives for these parties include the following:

 * Accelerated Delivery and Schedule Risk Mitigation: PGCPS sought to expedite the construction and commissioning of a package of 6 schools within a maximum three-year period from the initiation of the P3 Agreement. The intention is to transfer schedule risk to the Developer, aligning payments with facility availability. This approach ensures timely delivery.
 * Asset Stewardship and Life-Cycle Asset Management: Recognizing the critical importance of educational facilities, PGCPS is committed to maintaining the Facilities at specified standards throughout the P3 Agreement's lifespan. The developer will be held accountable for life-cycle asset maintenance, with potential deductions from availability payments for performance shortfalls. This strategy guarantees enforceable performance standards throughout the asset's life.
 * Cost-Effectiveness and Budget Predictability: To safeguard taxpayer funds, PGCPS plans to maximize economies of scale by bundling multiple schools into a single package. This approach aims to capitalize on life-cycle cost efficiencies through innovative solutions and bundling design and construction with long-term operations. Furthermore, by securing life-cycle maintenance, PGCPS aims to offset budget volatility caused by emergency repairs due to deferred maintenance.
 * Community Benefits and Control: PGCPS intends to leverage the Project not only for public education but also for the community. This involves linking the DBFM agreement to various community benefits, such as workforce development, mentor-protégé programs, apprenticeship initiatives, MBE/CBB (Minority Business Enterprise/Community Business Benefit) opportunities, and more. Additionally, PGCPS retains control over critical matters, including output standards, to ensure the overall success of the project.

DBFM (Design, Build, Finance, and Maintain)

Design and Construction Scope

The Developer has been responsible for designing and constructing the Project. The Developer's responsibilities encompassed standard design and construction tasks, including project management, engineering studies, project design, permits, development activities, finalizing design, construction, subcontracting, commissioning, testing, and so on.

Financing Scope

The Developer has had the exclusive responsibility of securing all the required funds for the Project, which involved equity. PGCPS has been flexible regarding the private financing structure proposed, as long as the financing has not held Prince George's County or PGCPS liable.

Maintenance Scope

The Developer is responsible with overseeing significant maintenance of the Project, ensuring it complies with the Technical Requirements outlined in the Project Agreement, as well as adheres to relevant laws, regulations, and policies. This maintenance encompasses the long-term care of essential components built or installed by the Developer, as well as any other elements specified in the Project Agreement.

Local Contracting and the Use of MBE and CBB

Prince George's County and PGCPS has been dedicated to establishing and upholding a world-class environment for local and minority business enterprises, ensuring equal access for qualified and certified businesses to engage in local procurement opportunities. Consequently, PGCPS expected the RFP to mandate that the Developer exert their best efforts to ensure that a minimum of thirty percent (30%) of the Project was carried out through subcontracts with certified MBE and CBB. While PGCPS didn't require Respondents to specify local and minority business enterprise subcontractors in their SOQ, these requirements were considered by Respondents in developing their organizational approach. This included various opportunities for CBB and MBE involvement, encompassing areas such as accounting and legal services, engineering, bonding, insurance, permit expediting, construction management, site work, including excavation and hauling, concrete work, foundations, welding, electrical, plumbing, window and door installation, drywall, painting, carpeting, tiling, interior design, asphalt, landscaping, property and program management, signage, marketing, maintenance, and cleaning. It's worth noting that PGCPS did not anticipate MBE and CBB to be bound by exclusivity arrangements with individual Respondents.

Procurement Process

Part One: RFQ

Contents of Response to RFQ

Volume 1: Experience & Capabilities

 * Part 1 – General Information
 * Part 2 – Organization and Management
 * Part 3 – Technical Experience and Capabilities
 * Part 4 – Financial Capabilities and Experience

Volume 2: Financial Information

Evaluation Criteria:

Organizational Competence:

PGCPS evaluated respondents organization and management capacity based on their ability to coordinate and deliver all Project components, considering size and complexity. Higher scores were given for clear and logical management structures, alignment of interests among Major Participants, and demonstrated teamwork on similar projects. The suitability of the Offeror's organization structure was assessed regarding team structure, prior experience working together, key personnel, and experience with MBE and local businesses/community benefits. Factors included roles and responsibilities, decision-making efficiency, risk management, and realistic approaches to project challenges and opportunities.

Technical Approach:

The evaluation of technical proposals for the Project has been completed, assessing Respondents based on a range of criteria. In the "Design-Build Capabilities and Expertise" category (25 points), the evaluation considered the Respondent's experience in comparable projects, design excellence, construction, and related factors. For "Maintenance Capabilities and Expertise" (20 points), the assessment examined their experience in maintaining similar projects and expertise in areas such as life-cycle maintenance and customer service. In "Project Understanding and Technical Approach" (10 points), the evaluation determined how well the Respondent's approach aligned with PGCPS goals. Lastly, "Financial Qualifications and Capability" (30 points) gauged the Respondent's financial capacity to secure financing without contingencies and maintain the Facilities throughout the agreement term. This process provided a comprehensive evaluation of Respondents' capabilities in delivering the Project.

Financial Capacity:

The evaluation of Respondents' financial capabilities for the Project was completed, focusing on their ability to secure financing without contingencies and maintain facilities. PGCPS assessed each respondent's financial qualifications based on specific criteria. This included evaluating Financing Members' experience in obtaining financing commitments for similar projects, their success in bringing projects to completion, and the overall financial strength of the Respondent team. Factors like Funding Letters and the expertise of the Respondent's Financial Advisor in securing non-recourse financing were considered. Projects involving controlling ownership interest, financial close, DBFM structure, and performance-based payments scored higher. The overall financial capability of the Respondent was assessed based on financial statements, credit ratings, bankruptcy/insolvency information, and other financial details provided in the SOQ.

Part Two: RFP

As a result of the RFQ evaluation, below respondents advanced to the RFP stage and were permitted to submit a proposal:

 * 1) Community Academic Partners

 * 1) Edgemoor-Star-HB Education Partners

 * 1) Preston Hallow Capital / Provident Resource Group / SB Ballard Construction / Hess Construction / Aramark

Evaluation Procedure:
 * 1) Prince George’s County Education and Community Partners

In the evaluation process, there was a two-phase approach. Initially, PGCPS assessed Proposals to determine their responsiveness based on the evaluation factors outlined in the RFP. After this initial review, all responsive Proposals underwent further evaluation as detailed as follows:

The evaluation criteria for the P3 project proposal reflects a comprehensive approach that balances technical and financial aspects. The division of points allows for a fair and thorough assessment. The Technical Proposal, worth 300 points, is structured into six sections, covering various crucial aspects of the project. The emphasis on organization, local community benefits, design, construction, and services approach demonstrates a holistic evaluation of the bidder's capabilities and commitment to the project's success.

In the Financial Proposal, the split between the Cost Score (200 points) and the Finance Plan Score (100 points) ensures that cost-efficiency is a significant factor while also considering the financial sustainability and planning of the project.

This criteria setup promotes a competitive yet balanced evaluation process. It encourages bidders to not only offer competitive financial terms but also emphasize a well-thought-out project management, local community benefits, design excellence, and construction efficiency. Overall, the criteria seem well-structured to select a bidder that not only meets the financial expectations but also aligns with the broader project goals, including local community engagement and technical excellence.

According to the Board Action Summary of the PGCPS for Approval of Contract Award the evaluation process for the RFP was thorough and transparent, prioritizing fairness and independence. It involved various committees and subcommittees, each comprising experts in specific fields, such as project management, design, construction, financial advisory, and more. The Technical Proposal was assessed based on five major criteria, while the Financial Proposal underwent a separate evaluation by the Financial Advisory Team. Importantly, these evaluations occurred independently to ensure no influence between the technical and financial assessments. The process strictly adhered to predefined criteria and procedures outlined in the RFP and Evaluation Manual. This dual-phase, segregated evaluation approach aimed to maintain fairness and prevent bias, ultimately resulting in a comprehensive assessment of both technical and financial aspects of the proposals.

PGCPS’s General Obligations:

Under this agreement, PGCPS has several key responsibilities. They are obligated to make payments to the Developer as specified in the agreement, provided the Developer meets the necessary payment requirements. PGCPS is also responsible for providing the Sites required for the Project. It's important to note that PGCPS holds full ownership of the Land. Furthermore, PGCPS has the sole authority to make decisions regarding the operation and use of the Schools, ensuring they align with the terms of the Agreement.

The contract relies on availability payments and the agreement defines “Availability Payments” as follows:

Availability Payment means the fee to be paid by PGCPS to Developer, which together with any applicable Progress Payment, Milestone Payments, Relief Payments or Delay Payments, compensate Developer for Developer’s performance of the Design-Build Work and Services, as set forth and calculated in accordance with Section 14.4 (Availability Payments) and Exhibit X-1 (Payment Calculations).[9 ]

Cost
The total cost of Phase I for PGCPS will be $1.24 billion, which includes a $15 million milestone payment (to be paid when the design/construction phase was 50 percent complete), progress payments of $5 million per school due when each school is completed, and availability payments paid monthly during the 30-year service period. The total amount that PGCPS pays is subject to change due to delay or relief payments based on the KPIs written into the contract.[7 ]

For Phase I, PGCPS will share the project costs with Prince George's County government, which will provide $15 million per year.[3 ] PGCECP's Phase I costs were estimated to be $485.8 million during the design/construction period and $306.5 million during the services period.[7 ] Fengate (75-percent equity partner for Phase I) is funding its portion of the project using its Core Infrastructure Fund III [15 ], which focuses on U.S./Canada alternative energy, social, transportation, and digital contracted projects with a net IRR between 11 percent and 13 percent and a minimum yield of 5 percent.[16 ]

PGCPS estimates that using the traditional financing model, design/construction of the Phase I schools would have cost a total of $868.8 million and and taken 16 years. The total design/construction cost using the P3 model was $485.8 million. The school district also emphasizes the value of the service plan, which it anticipates will prevent deferred maintenance costs later on. Additionally, building the schools more quickly has resulted in cost savings as PGCPS has not needed to maintain the old school buildings any longer. PGCPS has estimated that it will save a total of $170 million during the 30-year contract.[2 ]

For Phase II, PGCPS plans to pay the project company $11.25 million per school upon the completion of each school, followed by availability payments for the following 30-year service period.[12 ] PGCPS anticipates covering its Phase II first-year availability payment with $25 million in state funding (courtesy of Maryland Stadium Authority bonds provided by the 2020 Built to Learn Act), $10 million from Prince George's County government, and $15 million of its own funds, for a total of $50 million.[14 ]

Financial Structure
The Program follows an availability payment model where the District and the County dedicate funding to support the 30-year life cycle of the program as opposed to a revenue risk model where funding would depend on revenue generated by end-user payments for use of the building like rent, retail, etc.

In this arrangement between PGCPS and the developer, the public and private sectors share responsibilities and benefits. The developer, as the private entity, has invested significantly in the construction of six schools, amounting to approximately $500 million. Over the next 30 years, they will be responsible for maintaining the schools as well and in exchange will receive about $290 million in service payments. This investment is aimed at providing quality educational facilities to the community. The private contractor stands to profit from this partnership through the availability payments they receive, which are set to increase over time. The private sector benefits from a steady and predictable income stream, while PGCPS benefits from having the infrastructure developed and maintained without shouldering the entire financial burden upfront. It's a collaborative approach that allows the public sector to provide essential services while mitigating financial risk and provides the private sector with a revenue-generating opportunity over an extended period.

Institutional Structure
The institutional structure of the Public-Private Partnership (P3) project for school construction and maintenance in Prince George's County is a complex web of stakeholders, each playing a crucial role in ensuring the success of the endeavor. At the core of this partnership is the Public Partner, Prince George’s County Public Schools (PGCPS), which owns the schools and the property they are built on. PGCPS is joined by the Private Partner, PGCECP, a consortium comprised of Fengate Asset Management (financial/equity), Gilbane Development Company (financial/equity), Gilbane Building Company (lead design-builder), Stantec (lead architect-design), and Honeywell (lead service provider). This SPV, operating under the DBFM P3 Agreement, is the entity responsible for the design, construction, financing, and maintenance of the schools.

Regulatory Authorities, such as the Prince George's County Board of Education and County Council, provide the necessary approvals and support for the P3 model, ultimately shaping the project's policies and contracts. Additionally, the Schools Administration handles the administrative aspects of the program. The P3 Alternative Financing School Infrastructure Work Group, established by the County Council, plays a pivotal role in exploring the P3 option.

Furthermore, Technical and Financial Advisors, contractors for PGCPS, including Jones Lang LaSalle, K. Dixon Architecture, and Kutak Rock, provide critical expertise in financial, technical, and legal aspects. Finally, the community, represented by Prince George's County Public Schools Students and Parents, advocates for new schools due to the deteriorating condition of the district's older schools.

This multi-faceted institutional structure is designed to maximize the efficiency and effectiveness of the P3 project, ensuring that it meets the educational and infrastructural needs of the community while also managing the financial and operational aspects with private sector expertise.

Lessons Learned/Takeaways
Public sector agencies without upfront funding or the capacity to issue bonds can still complete P3 projects and solicit competitive bids from the private sector, if the governing authorities can coordinate on the presiding statues and desired project outcomes. While PGCPS was in the process of procuring Phase I and securing county funding for the project, the Maryland General Assembly passed legislation to provide substantial funding for Phase II using Maryland Stadium Authority bond funding. This policy solution provides a special financing solution to public actors seeking P3s with limited assets on their balance sheet or a constrained capacity to issue bonds themselves.

When briefing the County Council on Phase I in September 2020, PGCPS staff noted the importance of a strong contract to ensure that the school's objectives were met. Based on its lessons learned from Phase I, PGCPS was able to craft a Phase II contract that is more likely to bring about its desired results. For example, labor issues surfaced during Phase I, and PGCPS ended up including a labor agreement in its Phase II contract. Because the P3 model affords the private sector more autonomy than traditional delivery models, an airtight contract is essential.

One of the ongoing concerns about PGCPS’ P3 project is transparency. During the September 2020 County Council briefing, several Council members expressed their concern about the ambiguity of the information they had received. In our research, we encountered numbers and figures that sometimes seemed contradictory, and we struggled to identify the source of public funding for the payments to the developer. This may be due to the large number of entities involved and the fact that the project has proceeded in fits and starts. The scope of the project changed during the planning stages, and state legislation has been evolving throughout the process. Local and regional media have covered the project at the surface level, but they have not delved into the details.

Public-private partnerships can be a solution for communities that do not have the up-front funding to provide much-needed infrastructure. In this case, the P3 model undoubtedly delivered six schools in a fraction of the time it would have taken using the standard delivery model, thanks to the design/construction bundling and the private sector financing. However, the P3 model does not negate the need for public funding; it is important to remember that PGCPS and Prince George's County will continue to pay for the project for the next 30 years. The school district will continue to finance other schools using the traditional delivery model while it engages in these P3 projects, so it will have ample opportunities to compare the different approaches and analyze the value-for-money. Because this type of project is unprecedented in the United States, PGCPS will serve as a test case for the many other communities grappling with a backlog of aging schools and a lack of public funding.

Phase I and Phase II Schools
Phase I Schools:

Phase II Schools:

Discussion Questions

 * From the perspective of Prince George’s County, has Phase I been successful so far?
 * What should PGCPS and PGCC look for in the vendor selection for Phase II?
 * What are some of the potential pros and cons of PGCPS’ decision to engage in this innovative form of school construction financing?
 * Do you think the P3 delivery model is appropriate for school construction?


text:
Chess Opening Theory/1. e4/1...e5/2. Nf3/2...Nc6/3. c3/3...f5

3...F5
This is the dangerous but exciting Ponziani Countergambit. It sacrifices the F pawn, but attacks E4 and prepares the develop the G1 knight. While 4.Exf5 is a good move, 4.D3 and 4.D4 are better options. If white has studied against this, black will have a bad time, but if not, both black and white will be able to attack in an exciting game.


text: User talk:American loveis

title: User talk:American loveis


text:
Category:CS1 Dutch-language sources (nl)

__HIDDENCAT__


text:
Calculus/Ratio Test

Ratio Test
The Ratio Test is probably the most important test and the test you will use the most as you are learning infinite series. It is used A LOT in power series. I believe it is the most powerful test of all. So I suggest you master it from the start. It's not hard, and if your algebra skills are strong, you might even find it fun to use. Also, the more familiar you are with it and the more practice problems you work, the sooner you will start to be able to look at a series and see almost right away if the Ratio Test will tell you what you need to know.

Ratio Test Quick Notes

 * 1) if $$ L=\infty $$ then $$ L>1 $$ and the series diverges
 * 2) $$ a_n $$ terms can be positive or negative or both
 * 3) requires the calculation of limits at infinity

When To Use the Ratio Test
The ratio test is best used when you have certain elements in the sum. The way to get a feel for this is to build a set of tables containing examples of tests that work as you are working practice problems. This is an extremely powerful technique that will help you really understand infinite series.

Here is a list of things to watch for.
 * 1) Sums that include factorials.
 * 2) Sums with exponents containing $$n$$.

How To Use The Ratio Test
In general, the idea is to set up the ratio $$ \displaystyle{\lim_{n \to \infty}{\left| \frac{a_{n+1}}{a_n} \right|} = L} $$ and evaluate it.

In detail, you need to determine what $$ a_n $$ is and then build $$a_{n+1}$$, set up the fraction, combine like terms and then take the limit of each term. Setting up the limit and combining like terms are the easy parts. The challenge comes in taking the limit.

Key - It is important to remember to use the absolute value signs unless you are absolutely convinced that the term will always be positive. This is critical to practice up front since, once you get to Taylor Series, you can't and don't want to drop the absolute value signs. They are critical to the result. It is never wrong to include them and, as you work more problems, you will get a feel for when you need them and when you don't. In the practice problems and examples, we will use them unless we explicitly state that they are not needed. Some instructors are less rigid about this than others. As always, check with your instructor to see what they require.

Things To Notice

 * 1) If you get $$ L = \infty $$ for the limit, this indicates divergence since it fits the case where the limit is greater than one.  Notice that the theorem says nothing about the limit needing to be finite.
 * 2) In the fraction that you are taking the limit of, the $$ n+1 $$ term is in the numerator and the $$n$$ term is in the denominator.  In order for the ratio test to work, they must appear exactly like this. Why? Because if the order was reversed, the conclusion would be incorrect.  For example, if we write it correctly and we get L=1/2, we know that the series converges (correctly).  However, if we switched the numerator and denominator, we get L=2, which indicates the series diverges (incorrectly).
 * 3) If you get $$L = 1$$, you cannot say anything about convergence or divergence of the series.  You need to use another test.  Sometimes, a comparison test (either direct or limit) will be the best next step.

Ratio Test Proof
Here are a couple of proofs of the Ratio Test.

This first video contains a rather long and involved proof of the ratio test. It uses a comparison test. Proof of the Ratio Test

Here is a second proof presented in 3 separate videos.

You do not need to watch these proofs in order to use and understand the Ratio Test. We are including them here for those who are interested.

Video Recommendations
This first video clip [1min-50secs] is a great overview of the ratio test. Notice that he doesn't use absolute value signs, so he requires that the terms be positive.

Series, Comparison + Ratio Tests

The beginning [9min-19secs] of this next video has a good discussion about the ratio test. Then the instructor shows two examples when the ratio test is inconclusive to emphasize that a series may converge or diverge when the ratio test is inconclusive.

Ratio Test for Convergence

Before You Start Working The Practice Problems
Take a few minutes and scan your list of practice problems. You will notice there are a LOT of very different ones. The key to solving infinite series problems is to find patterns so that you can quickly narrow down the techniques that might work to about 2 or 3. This is especially true with problems on which the ratio test works.

Ratio Test Practice Problems
Determine the convergence or divergence of these series using the ratio test, if possible. [These instructions imply that if the ratio test fails $$(L = 1)$$, you need to use another test to prove convergence or divergence.]

Practice Problems with Written Solutions
1. $$\sum_{n=0}^{\infty}{ \left[\frac{n!}{2^n}\right] } $$

title: Calculus/Ratio Test


text:
Calculus/Absolute and Conditional Convergence

Absolute and Conditional Convergence
Absolute and conditional convergence applies to all series whether a series has all positive terms or some positive and some negative terms (but the series is not required to be alternating).

One unique thing about series with positive and negative terms (including alternating series) is the question of absolute or conditional convergence. Once convergence of the series is established, then determining the convergence of the absolute value of the series tells you whether it converges absolutely or conditionally. Formally, here's what it looks like.

Definitions of Absolute and Conditional Convergence
Here is a table that summarizes these ideas a little differently.

One minor point is that all positive series converge absolutely since $$ a_n = |a_n| $$ for all $$ n $$.

Absolute Convergence Theorem
This theorem uses the first row of the above table and this allows us to consider the divergence of a positive series.

Alternatively, it is possible to determine the convergence of the absolute value of the series first. Then, if the absolute value of the series converges, you can use the Absolute Convergence Theorem to say that the alternating series also converges and converges absolutely.

Additionally, if you have a series with some negative terms (but not all) and it is not an alternating series, you can use this theorem to determine convergence. Specifically, if the absolute value of the series converges, then the series will converge. Notice that this theorem says nothing about divergence, so you cannot make any assumption about convergence or divergence if this theorem does not hold.

Understanding The Theorem
Let's get an idea of why this theorem works. First, let's think about the series $$ \sum{a_n} $$ with positive and negative terms. As we add up the terms, we will be adding some positive terms and subtracting other terms (the negative ones). Compare that to the series $$ \sum{\left|a_n\right|} $$. With this series, we add all the terms as we go, i.e. we add all the positive terms and then we take the absolute value of the negative terms before we add those terms also. So each partial sum of this series is greater than the partial sum of the previous series. Consequently, as we continue to calculate the partial sums, we can say that the second sum is larger than the first sum. So if the larger sum converges, the smaller sum also has to converge.

Here is a simple example that should give you an intuitive feel for this.

For this finite alternating series $$ 1 - 2 + 3 - 4 + 5 = 3 $$.

Now calculate the absolute value of that series to get $$ 1 + 2 + 3 + 4 + 5 = 15 $$

If we are always adding the numbers and never subtracting, the sum will always be larger for the absolute value series. And in the case of an infinite sum, if the larger series converges, logically, the smaller one will too.

Note - This is not a formal proof of the theorem. It is just an example to give you a feel for it.

Video Recommendations
This video clip has a great discussion on absolute convergence including using some examples. Notice that he does not use the term conditional convergence. Instead, he just says that the series does not converge absolutely.

Alternating series and absolute convergence

Here is another short video clip [2min] explanation of absolute and conditional convergence.

Absolute Convergence, Conditional Convergence and Divergence

Freaky Consequence of Conditionally Convergent Infinite Series
As you probably know by now, when you start working with numbers out to infinity, strange things happen. This is certainly true of infinite series which are conditionally convergent. The strange thing is that, when you rearrange the sum, you can get different values to which the series converges, i.e. the commutative property of numbers does not hold! Whoa!

In fact, not only can you get different values, it is possible to rearrange a conditionally convergent infinite series in order to get any number we want, including zero and infinity! This is called the Riemann Series Theorem.

Want to know more? Check out this wikipedia page


text:
Cookbook:Coffee Liqueur

Coffee liqueur is a sweet, aromatic alcoholic beverage flavored with coffee.

Characteristics
The primary spirit base—often rum or vodka—is infused with coffee essence to make a blend of strong coffee flavor and the richness of alcohol. Sugar imparts a sweetness that complements the inherent bitterness of coffee. Depending on the region or brand, various other ingredients like vanilla, chocolate, or spices might be added to enhance its depth of flavor.

Selection and storage
Different brands of coffee liqueur will have slightly different flavor profiles, varying especially in the sweetness level. Choose the brand that will best complement your recipe.

Use
Consumed on its own in cocktails or as a dessert ingredient, coffee liqueur has several applications. As a cocktail component, coffee liqueur is well-known in the White Russian and Black Russian. When incorporated into desserts, such as custards it typically acts as a flavoring.

title: Cookbook:Coffee Liqueur


text: User:Rocalubo

title: User:Rocalubo


text:
User:Nya Exists

I exist, for now.

title: User:Nya Exists


text:
Salom, Jonatan!/Mon 7

Monlari – Mon 6 – Mon 7 – Mon 8

Sabeyum mon (7yum mon)
Wagon idi ji idi; to duregi na idi. Jonatan oko multi xey ex wagon. Te sen in wagon, ji xey no sen in wagon; te oko oto ex wagon. Te oko persaluba, multi persaluba. Jonatan peti tas wagonyen, “Kam mi harizin na ofcu wagon?” Wagonyen: “No. Hay multi bwaw. Yu no harizin.” Jonatan: “Keto? Hay multi bwaw?” Wagonyen: “Si. Ji pia ex wagon, yu xa oko multi bwaw.” Wagonyen haha. Jonatan fikir, “Te haha keseba?”

Fe nunya, to sen noce; no hay Sola. Wagon idi max ji max velosi. Person in wagon loga tas wagonyen, “Am idi max velosi!” Jonatan fikir, “Keseba na idi daydenmo velosi?” Jonatan oko dayday jabal ex wagon. Jonatan oko ki person in wagon sen daymo joxudo; ete pala multi. Person in wagon loga joxudo, “Am idi max velosi!”

Fe nunya, wagon esto. Ete sen in pasa intre jabal. Jonatan jixi ki hinloka, te xa oko wagon cel na idi cel tesu doste Konte Drakula, mas…te sen keloka? Fe fronta de Jonatan, hay dolo, ji sol dolo. Person in wagon sen hox, mas Jonatan no sen hox. “Keseba na ata cel hinloka denloka hu no hay wagon cel na idi cel misu doste Konte Drakula?”

Wagonyen pala tas person in wagon: “Imi le dupul sen velosi. Imi le dupul ata cel hinloka fe un maxmo jaldi satu.” Wagonyen le pala yon lil voka, mas Jonatan le ore te. Jonatan fikir, “Na dupul ata cel hinloka fe un maxmo jaldi satu sen bon keseba?”

Fe nunya, wagonyen pala tas Jonatan har day voka. Te loga, “Jonatan, Herr (Doycisa: Mansenyor) xa no ata cel hinloka nundin. Te xa idi cel alo xaher, xaher Bukovina. Ible, jaxadin, Herr xa idi cel hinloka. Ible, si. Ible, no. Mi no jixi. Imi ingay na xoridi.”

Jonatan sen hazuni ji fikir, “Senyor Drakula no sen hinloka keseba? Mi ingay na xoridi keseba?”

Mas, dento sen keto? Uma sen joxudo. Pia person in wagon sen joxudo. Jonatan oko, ji denloka, te oko alo wagon hu da sen maxmo day ton care uma. Neo wagon sen maxmo zarif ji maxmo day kom wagon hu in da Jonatan side. Care uma sen syahe ji dayday. In neo wagon, Jonatan oko alo wagonyen. Alo wagonyen sen day, ji gao, ji hare mustax. Mustax ji bala hanta de wagonyen fikirgi Jonatan ki te sen daymo bala ixu, mas Jonatan no abil na oko muka de alo wagonyen.

Alo wagonyen loga, “Yu le dupul ata cel hinloka velosi, misu doste.”

Wagonyen: “A…Englili Herr le vole na idi velosi…”

Alo wagonyen: “Mi jixi ki yu le vole na idi cel Bukovina. Si, mi jixi ku yu fikir tem keto. Mi sen maxmo cinonpul kom yu. Am gibe tas mi portaxey de Englili senyor.”

Wagonyen gibe portaxey de Jonatan tas alo wagonyen. Alo wagonyen sen day bala; Jonatan oko ki te sen bala denwatu hu te oko tesu hanta. Alo wagonyen porta portaxey yon tesu bala hanta, ji daymo velosi, xey sen finido.

Fe nunya, Jonatan side in alo wagon. Nundin le dupul sen lungo din tas Jonatan, mas fe nunya, alo turi xoru.

title: Salom, Jonatan!/Mon 7


text:
User talk:71.221.201.44

--Xania   talk 03:35, 19 October 2023 (UTC)

Blocked
You cannot edit for 2 weeks due to disruptive editing. You are welcome to contribute constructively when editing privileges are restored. You may appeal this action with a reasonable argument by adding the text below.

--Xania   talk 04:59, 31 October 2023 (UTC)

title: User talk:71.221.201.44


text:
Animal Care/flight with your animal

cat: Book:Animal Care
 * flight from Israel with your animal

title: Animal Care/flight with your animal


text:
Animal Care/flight with your animal/flight to Israel

Costs: check at the veterinary clinic, sedation (if it necessary), blood test, delivery person for the blood test, laboratory cost to check the blood test, chip for the animal. Cost might be last at SPCA.

 * If you haven't done a Rabies vaccine for your animal you need to do that for dogs and cats for sure. You need to wait one month before you can do the next step.
 * Check the country you want to fly to the test you need to do for your animal.
 * If your animal need to do Rabies vaccine test check when it needs to do it. Keep the notebook.
 * All orders you know you need to care for your animal, you need to do at the local veterinarian, before you meet the district veterinarian.
 * Cats and dogs need to do a Rabies test. Go to the local veterinarian and make an appointment. It takes about 45 minutes.
 * While you are at the veterinarian you will need to put a chip for your animal if it doesn't have it. The blood test tube will be sent to Beit Dagan lab. You would need to pay for the delivery of the tube.
 * For each animal the vet will fill papers from the government web: the veterinary name, phone number, email…your name,…, test date, chip number, the last time your animals got rabies vaccine and how many.
 * then you would need to pay for the government payments at the link
 * 10 days before the flight you would need to fill at the veterinary paper called “Health Declaration” (two papers once USA and once Europe)
 * meeting at Dr Fouad which at 2018 worked on Wednesday at Kanfei Nesharim Street 13 Jerusalem Israel.
 * if you do for your animal every year Rabies vaccine and you made once Rabies test you don’t need to do the test again (correctly to 2018).

cat:book:Animal Care


text:
User:Makopanang Seitlheko

verb :verb is a naming word

title: User:Makopanang Seitlheko


text:
User:Murad Semed

Error in Addition
Let's consider that X and Y have an approximation value of x and y respectively.

If we let Z=X+Y, then X=x+∆x, Y=y+∆y, and Z=z+∆z with z=x+y. Thus Z=X+Y⟹z+∆z=x+∆x+y+∆y⟹∆z=x+∆x+y+∆y-(x+y). ∆z=∆x+∆y ⟹|∆z|=|∆x+∆y|≤|∆x|+|∆y|⟹|∆z|≤|∆x|+|∆y| which is the absolute error. The relative error is R_er=|∆z|/Z≤(|∆x|+|∆y|)/(X+Y).

Error in subtraction
If we let Z=X-Y, then X=x+∆x, Y=y+∆y, and Z=z+∆z with z=x-y. Thus Z=X-Y⟹z+∆z=x+∆x-(y+∆y),

⟹∆z=x+∆x-y-∆y-(x-y).

∆z=∆x-∆y

⟹|∆z|=|∆x+(-∆y)|≤|∆x|+|∆y|

⟹|∆z|≤|∆x|+|∆y| which is the absolute error.

The relative error is R_er=|∆z|/Z≤(|∆x|+|∆y|)/(X-Y).

Example 1. If one is calculating X+Y where X = 1.5 ± 0.05, and Y = 3.4 ± 0.04. Find the bounds for the propagation error in adding two numbers.

Solution. By looking at the numbers, the maximum possible values of X and Y are X = 1.55 and Y = 3.44. Hence X +Y = 1.55 + 3.44 = 4.99  is the maximum value of X + Y. The minimum possible values of X and Y are X = 1.45 and Y = 3.36. Hence X + Y = 1.45 + 3.36 = 4.81 is the minimum value of X +Y.

Hence 4.81 ≤ X+Y≤4.99.

2. Given A=1.652 and B=9.78. Then find the maximum error in A - B.

Solution:- Let maximum error in A-B be denoted by E_(A-B), then E_(A-B)=|∆a|+|∆b| where Then E_(A-B)=|∆a|+|∆b|=0.0005+0.005=0.0055. Which is the same with E_(A+B).
 * ∆a|≤1/2×〖10〗^(-3)=0.0005 and  |∆b|≤1/2×〖10〗^(-2)=0.005.

3. Find the absolute error of the value of 3A-6B+9C, if a,b, and c are used to approximate the value of A, B, and C respectively, and let A=3.456, B=2.67 and C=1.6784.

Solution. 3A-6B+9C=3A+6(-B)+9C=3|∆a|+6|∆b|+9|∆c|=3(0.0005)+6(0.005)+9(0.00005)=0.03195.

Propagated error in Multiplication
If we let Z=XY, then X=x+∆x, Y=y+∆y, and Z=z+∆z with z=xy. Thus Z=XY⟹z+∆z=(x+∆x)(y+∆y), ∆z=xy+y∆x+x∆y+∆x∆y-z⟹∆z=y∆x+x∆y+∆x∆y. Now by neglecting ∆x∆y for its very small, we get ∆z=y∆x+x∆y

And its absolute error is |∆z|=|y∆x+x∆y|≤|y∆x|+|x∆y|.

Relative error is R_er=|∆z|/z=(|y∆x+x∆y| )/xy≤(|∆x|  )/x+(|∆y|  )/y.

Propagated error in division
If we let Z=X/Y, then X=x+∆x, Y=y+∆y, and Z=z+∆z with z=x/y. Thus, Z=X/Y⟹z+∆z=((x+∆x))/((y+∆y) )=(x+∆x)(y-∆y)/(y+∆y)(y-∆y) =(xy+y∆x-x∆y-∆x∆y)/(y^2-(∆y)^2 ). Now neglecting ∆x∆y and (∆y)^2, we get ∆z=(xy+y∆x-x∆y)/y^2 -x/y=(xy+y∆x-x∆y-xy)/y^2 =(y∆x-x∆y)/y^2

Then the absolute error is

 * ∆z|=|(y∆x-x∆y)/y^2  |≤(y|∆x|+x|∆y|)/y^2 =x/y [(|∆x|  )/x+(|∆y|  )/y]

Relative error is

R_er=|∆z|/z=|(y∆x-x∆y)/y^2  |/(x/y)≤(x/y  [(|∆x|  )/x+(|∆y|  )/y])/(x/y)=(|∆x|  )/x+(|∆y|  )/y

Remark:- If f(x) is a function of several variables x_1,x_2,…,x_(n-1),x_n, then the maximum possible value of the error in f is

∆f≈|∂f/(∂x_1 ) ∆x_1 |+|∂f/(∂x_2 ) ∆x_2 |+⋯+|∂f/(∂x_(n-1) ) ∆x_(n-1) |+|∂f/(∂x_n ) ∆x_n |.

title: User:Murad Semed


text:
Character Encodings/Code Tables/MS-DOS

 * Code page 113
 * Code page 161
 * Code page 162
 * Code page 163
 * Code page 164
 * Code page 190 is identical to Code Page 437.
 * Code page 210 is identical to Code Page 737 (which also has an old version).
 * Code page 220
 * Code page 972

Code Pages with FreeDOS numbers

 * Code page 58152
 * Code page 58210
 * Code page 58335
 * Code page 59234
 * Code page 59829
 * Code page 60258
 * Code page 60853
 * Code page 62306

User-defined FreeDOS Code Pages to be extracted

 * Code page 30000
 * Code page 30001
 * Code page 30002
 * Code page 30003
 * Code page 30004
 * Code page 30005
 * Code page 30006 is VISCII.
 * Code page 30007
 * Code page 30008
 * Code page 30009
 * Code page 30010
 * Code page 30011
 * Code page 30012
 * Code page 30013
 * Code page 30014
 * Code page 30015
 * Code page 30016
 * Code page 30017
 * Code page 30018
 * Code page 30019
 * Code page 30020
 * Code page 30021
 * Code page 30022
 * Code page 30023
 * Code page 30024
 * Code page 30025
 * Code page 30026
 * Code page 30027
 * Code page 30028
 * Code page 30029
 * Code page 30030
 * Code page 30031
 * Code page 30032
 * Code page 30033
 * Code page 30034
 * Code page 30039= 1125 with Hryvnia
 * Code page 30040= 866 with Hryvnia

title: Character Encodings/Code Tables/MS-DOS


text:
Character Encodings/Code Tables/MS-DOS/Code page 220

Codepage 220 (Spanish National Character Set ) is a codepage intended for Spanish and Catalan.

Character set
The following table shows code page 220. Each character is shown with its equivalent Unicode code point. Only the second half of the table (128–255) is shown, the first half (0–127) being the same as code page 437.

{{legend|#EFF|Symbols and punctuation}} {{legend|#FFD|Differences from code page 437}}


text:
Cookbook:Seasoned Salt II

Ingredients

 * ¼ cup (75 g) salt
 * 1 tbsp ground black pepper
 * 1 tbsp ground paprika
 * 1 tsp dry mustard
 * 1 tsp dried oregano
 * 1 tsp dehydrated garlic (minced or powdered)
 * 1 dehydrated onion (minced or powdered)
 * 1 tsp celery seed
 * 1 tsp parsley
 * ½ tsp each of however many of the following you have on hand:
 * Thyme
 * Powdered turmeric
 * Cumin powder
 * Marjoram
 * Ground red cayenne pepper
 * Crushed or ground rosemary
 * ¼ tsp each of however many of the following you have on hand:
 * Ground white pepper
 * Chili powder
 * Curry powder
 * Powdered coriander
 * Dill weed
 * Crushed or ground caraway
 * Asoefetida
 * Sugar
 * Powdered soup bouillon

Procedure

 * 1) Mix all ingredients and store in an airtight jar.

title: Cookbook:Seasoned Salt II


text:
Cookbook:Tempeh

Tempeh is an Indonesian fermented soybean product.

title: Cookbook:Tempeh


text:
Cookbook:Apple Crisp II

Ingredients

 * 4 cups sliced apples
 * 1 tablespoon lemon juice
 * ⅓ cup all-purpose flour
 * ½ cup brown sugar
 * 1 cup rolled oats
 * ½ teaspoon salt
 * 1 teaspoon cinnamon
 * ¼ cup melted margarine or butter

Procedure

 * 1) Put apple slices in shallow 9-inch (23 cm) pan.
 * 2) Sprinkle the apples with lemon juice.
 * 3) Combine all dry ingredients with butter and mix until crumbly. Sprinkle all this over apples.
 * 4) Bake at 375 °F (190 °C) for 30 minutes.

title: Cookbook:Apple Crisp II


text:
Cookbook:Apple Crisp III

Ingredients

 * 5 cups thinly-sliced apples
 * Lemon juice, to taste
 * ⅓ cup water
 * Powdered cinnamon, to taste
 * ¼ pound butter
 * ¾ cup brown sugar
 * ¾ cup rolled oats
 * ½ cup flour
 * 1 tsp powdered cinnamon
 * ½ tsp salt
 * ¼ tsp ground nutmeg
 * Additional rolled oats (optional)
 * Ice cream or whipped cream, for serving

Procedure

 * 1) Preheat a conventional (i.e. not convection) oven to 350 °F (180 °C).
 * 2) Place the apple slices in a buttered baking pan. Sprinkle them with lemon juice for flavor and to prevent them from turning brown. Mix in the water and cinnamon to taste.
 * 3) To make the topping, combine the butter, brown sugar, oats, flour, cinnamon, salt, and nutmeg. Crumble the ingredients in a bowl with your fingers to create a uniform mixture.
 * 4) Cover the apples with the topping. If desired, sprinkle some rolled oats sparingly on the surface for added texture.
 * 5) Bake for 30–45 minutes in the preheated oven, or until the apples are soft and the topping is crisped.
 * 6) Serve with ice cream or whipped cream.

Notes, tips, and variations

 * Peeling the apples before slicing is traditional but not required.

title: Cookbook:Apple Crisp III


text:
Cookbook:American Alfredo Sauce

This recipe will make enough sauce for one pound of pasta, which, together, could serve 6 as a first course.

Ingredients

 * 1¾ cups (400 ml) heavy cream
 * 6 tbsp unsalted butter
 * 8.5 ounces (240 g) grated Parmesan cheese or asiago cheese
 * 1 tsp salt
 * Fresh-ground black pepper
 * 1 pinch of fresh-ground nutmeg

Preparation

 * 1) Combine 1¼ cups (300 ml) cream and the butter in a saucepan large enough to accommodate the sauce and later the pound of pasta.
 * 2) Heat over a low flame, stirring frequently, until the butter is melted and the cream comes to a bare simmer.
 * 3) Remove the pan from the heat once the butter is evenly incorporated into the cream.
 * 4) Cook the pasta, draining it a little before it reaches the al dente stage. The pasta should be slightly undercooked before being added to the sauce because it will continue to cook while the sauce is being finished.
 * 5) Drain the pasta.
 * 6) Add the drained pasta, ½ cup (100 ml) of cream, the cheese, the salt, the nutmeg, and several grinds of the pepper mill to the pan
 * 7) Heat the pasta and sauce over a low flame, tossing continuously, until the cheese melts into the sauce and the sauce thickens slightly, about 1–2 minutes. You can add chopped parsley as a garnish mixed into the sauce.

title: Cookbook:American Alfredo Sauce


text:
Cookbook:African Salad II

Ingredients
When preparing Abacha, the more ingredients used, the tastier and more "complete" the dish will be:

 * 3 handfuls abacha (shredded dried cassava)
 * 2 cups ugba (ukpaka)
 * 30 cl red palm oil
 * 2 tablespoons powdered edible potash (food tenderizer)
 * 2 teaspoons ground Ehu seeds (Calabash Nutmeg)
 * Habanero pepper, to taste
 * 4 tablespoons ground crayfish
 * 2 stock cubes (preferably Knorr brand), crushed
 * 2 onions, diced
 * Ogiri (castor seed paste)
 * Other meat and vegetables for the Abacha
 * Fish (mackerel/dryfish/stockfish)
 * Ponmo/kanda (cow skin)
 * 3 fresh utazi leaves
 * Salt, to taste
 * Garden eggs (white eggplant)
 * Garden egg leaves

Procedure

 * 1) Soak the shredded abacha in cold water for 10 minutes until it softens. Pour boiling water over it and drain.
 * 2) Rinse the ugba with warm water.
 * 3) Dissolve the potash in water and sieve out any residual solids.
 * 4) Stir the potash water with the palm oil in a pot until it forms a yellowish paste. Place on the heat, and stir in the ground ehu, pepper, crayfish, and seasoning.
 * 5) Stir in the crushed stock cubes, diced onions, and ugba. Take off the heat.
 * 6) Mix in the ogiri, then add meat and fish if using.
 * 7) Mix in the abacha, allowing the ingredients to blend.
 * 8) Add sliced utazi and salt to taste.
 * 9) Garnish with chopped garden egg leaves and sliced onions.

Notes, tips, and variations

 * Abacha is made by boiling and grating/shredding cassava tubers.
 * Ukpaka or ugba is shredded oil bean seeds. It is optional, and if not added it won't affect the end result.
 * Red palm oil must be used when preparing abacha.
 * If garden egg leaves are not available, baby spinach leaves are a good alternative.
 * At least one type of fish must be used in preparing abacha. You can use stockfish, dryfish (e.g. catfish, mangala), fried mackerel, and/or smoked fish.
 * Crayfish much be added.
 * Pepper must be used—you can either add habanero pepper (recommended) or dry cayenne pepper. Habanero pepper is atarodo, atarugu or ose oyibo. Black pepper is not a good fit for abacha.
 * Add ogiri for the classic traditional taste, but if not available you should add stock cubes.
 * Edible potash (akanwu, kaun, keun) is what makes palm oil curdle and it is a must. If you do not have it or you do not want to eat edible potash, baking soda (bicarbonate of soda) has similar properties.
 * Be careful when adding salt, since the dish contains lots of ingredients that already have salt (stockfish, stock cubes, crayfish, etc).

title: Cookbook:African Salad II


text:
Cookbook:New World Affogato

Ingredients

 * 1 scoop vanilla ice cream
 * 1 tsp coffee powder
 * 1 tsp brandy
 * 1½ tsp sugar
 * 1½ tsp cinnamon powder, for garnishing (optional)

Procedure

 * 1) Place the ice cream in a coffee cup.
 * 2) Boil water in a pan, and then add coffee and sugar to it, and then mix well.
 * 3) Add brandy to coffee mixture.
 * 4) Pour coffee mixture over the ice-cream.
 * 5) Serve immediately, garnished with cinnamon powder.

title: Cookbook:New World Affogato


text:
Cookbook:Bizcochito (Cinnamon Anise Cookies) II

This recipe is from northern New Mexico.

Procedure

 * 1) Heat oven to 180°C (350°F). Combine butter and ½ cup sugar in large bowl. Beat at medium speed, scraping bowl often, until creamy. Add egg yolk and milk; beat until well mixed. Reduce speed to low. Add flour, baking powder, anise seed and ¼ teaspoon cinnamon; mix until mixture forms a ball.
 * 2) Roll out dough on lightly-floured surface to 6.5 cm (¼-inch) thickness. Cut with 2.5 cm (1-inch) cookie cutters.
 * 3) Combine 2 tablespoons sugar and ¾ teaspoon cinnamon in small bowl.
 * 4) Put one face of the cookie into the cinnamon sugar mixture. Place 1 inch apart, with the cinnamon sugar-covered side up, onto ungreased cookie sheets.
 * 5) Bake for 5–8 minutes or until edges are lightly browned.
 * 6) Let cool.


text:
Happiness/Knowing Your Personality

The attainment of happiness is a philosophical question which has puzzled and confused thinkers for all of history. Many who have delved into this question have provided their own advice for the proper garnering of such a thing, but few have succeeded in articulating or even describing an answer to this question. It is believed that the attainment of happiness is rather individualized and rests little on a universal answer.

title: Happiness/Knowing Your Personality


text:
Infrastructure Past, Present, and Future Casebook/Jackson, MS Water and Wastewater Treatment

This casebook is a case study on Water and Wastewater Treatment in Jackson, MS by Aurozo Niaz, Alejandra Ortiz, Chloe Shade, and Scott Tatum, as part of the Infrastructure Past, Present and Future: GOVT 490-004 (Synthesis Seminar for Policy & Government) / CEIE 499-002 (Special Topics in Civil Engineering) Fall 2023 course at George Mason University's Schar School of Policy and Government and the Volgenau School of Engineering, and Sid and Reva Dewberry Department of Civil, Environmental, and Infrastructure Engineering. Under the instruction of Professor Jonathan Gifford.

Summary
The provision of clean drinking water is one of the core duties of municipal government. Despite maintaining a fairly straightforward mandate, there are an array of obstacles that make fulfilling it challenging.

The Jackson, Mississippi water crisis of February 2021 serves as a pertinent case study in the intersection of extreme weather events, decaying infrastructure, environmental justice concerns, and institutional failures. The crisis was expedited by a severe winter storm, which unveiled the deficiencies of the city’s water infrastructure. These conditions were exacerbated by the city's aging water systems, distinguished by crumbling pipes and treatment facilities.

Notably, the crisis disproportionately impacted communities that were predominantly Black, underscoring the racial disparities in infrastructure investment and disaster preparedness. This preventable water crisis underscores the imperativeness of addressing infrastructure restoration, climate resilience, and environmental justice in historically segregated areas, with implications for public policy, equity, and the equitable distribution of essential resources.

List of Actors
The United States Environmental Protection Agency: This agency is responsible for protecting the health of the environment and the health of humans. The EPA Administrator, Michael S. Regan, visited Jackson, Mississippi as a part of his Journey to Justice tour the year prior to the Jackson water crisis in August 2022. In a statement Regan published after meeting with Jackson Mayor, Chokwe Antar Lumumba, he acknowledged that the people of Jackson have faced decades of injustices because they have not been protected and have not been provided with safe water nor a reliable water system. The city of Jackson had issued about “300 boil notices over the past two years and had multiple line breaks during the same timeframe” before the water crisis in 2022. Regan was aware of the poor quality and conditions of Jackson’s water systems and continued to advocate for the people of Jackson even before the 2022 water crisis. Now after the water crisis, the EPA along with the mayor of Jackson, work together to bring safe and reliable water to the people of Jackson.

Chokwe Antar Lumumba: He was the mayor of Jackson during the water crisis in August 2022. He advocates for the people of Jackson and worked with the EPA to bring awareness to the poor quality of the water system infrastructure and unsafe drinking water in Jackson. Similarly, to the EPA, he believes that the people of Jackson and their need for a better water system infrastructure has been neglected because of racial inequality. As a democratic mayor in a state with a Republican majority, he faced challenges to get the necessary resources to address the infrastructure issues.

Governor Tate Reeves: He is a Republican governor who assumed office in 2020. One of the factors that contributed to the failure of the Jackson water system was their unreliable billing system, so it was a challenge to collect payments. This meant there was little to no revenue coming int that could be used to repair/maintain the water system. This was a major contribution to the Jackson water crisis. In 2020, Reeves vetoed a bill that would have created payment plans for people to pay their overdue payments. This would have helped collect revenue to fund the maintenance/repair of the Jackson water system infrastructure. Federal Emergency Management Agency (FEMA): FEMA comes to Jackson to provide financial assistance, technical assistance, and to distribute other resources, such as water bottles. Because President declares a 90-day state of emergency for the city of Jackson, it authorizes the use of federal funds to cover 75% of costs related to the water crisis emergency.

Mississippi Emergency Management Agency (MEMA): MEMA worked in partnership with FEMA to help the people of Jackson, MS during the water crisis. The Public Assistance program was run by MEMA, so people applied through their application for resources and financial assistance. FEMA covered 75% while MEMA covered the other 25%.

==Timeline of Events ==

 * 1914:
 * Fewell Plant is built and still operates today.
 * 1963:
 * Construction ends for the Ross Barnett Reservoir, Jackson’s largest source of drinking water. When the reservoir gets too high, though, water discharges into the Pearl River, which flows through Jackson.
 * 1970s:
 * White flight: More than 11,000 white families leave Jackson to avoid integrated schools.
 * White Jackson families pull 5,000 children from local schools in 1970.
 * 1985:
 * Jackson prepares its original Water Master Plan, outlining recommended maintenance and repairs for its water infrastructure. The plan will be updated in 1997 and again in 2012.
 * 1993:
 * O.B. Curtis Plant, the city’s primary water plant, is built near the Ross Barnett Reservoir.
 * 2010:
 * A storm causes hundreds of water mains to burst, leaving residents without water for weeks.
 * 2012:
 * An American Water Works Association journal finds Jackson’s pipeline repair needs are more than nine times higher than the national average for similarly sized systems.
 * Jackson is put under a federal consent decree for violating the Clean Water Act.
 * 2013:
 * The Jackson Master Plan is updated to reflect nearly $600 million in needed infrastructure updates and repairs.
 * More than 112 miles of water pipes are still unlined cast iron. In many cases, the eroding pipes are a century old.
 * Unaccounted-for water has increased from 19% in 1985 to 26% in 2012.
 * More than 97 miles of water mains running beneath Jackson are less than 6 inches in diameter, causing more than 40% of all water main breaks.
 * 2014:
 * A winter storm results in water outages.
 * 2018:
 * Another freeze causes pipes to burst and leaves residents without water.
 * 2019:
 * More than 3 billion gallons of sewage is released into the Pearl River. Jackson residents are told to avoid water contact activities such as swimming, wading, and fishing.
 * 2020:
 * Record rainfall in the first three months overflows the city’s sewage system and dumps nearly a half-billion gallons of raw sewage and 5.7 billion gallons of minimally treated sewage into the Pearl River.
 * An EPA report finds that Jackson’s water distribution system has numerous leaks and line breaks, with crews reportedly repairing five or six each day.
 * In June, Gov. Tate Reeves vetoes a bipartisan bill that would have helped Jackson use a flexible payment plans system to collect overdue payments and fund the water system.
 * 2021:
 * A storm in February leaves Jackson residents with no drinking water for a month.
 * On March 3, Jackson Mayor Chokwe A. Lumumba writes to Governor Reeves, outlining the city’s urgent need for $47 million for immediate repairs and improvements.
 * In May, Mississippi receives the first half of $1.8 billion from the American Rescue Plan Act for pandemic-related expenses and for water, sewer, and broadband.
 * 2022:
 * In April, the state Legislature votes to allow cities such as Jackson to apply for funding for water and sewer projects with a one-to-one match using their own direct ARPA funds.
 * On Aug. 29, floodwaters from the Ross Barnett Reservoir and Pearl River overwhelm Jackson’s primary water treatment plant, causing plant system failure and leaving 153,000 residents without potable drinking water and/or water pressure to flush toilets.
 * On Aug. 30, President Biden declares a 90-day state of emergency, authorizing federal funds to cover 75% of all costs related to the emergency.
 * On Nov. 4, the Mississippi Department of Environmental Quality awards Jackson $35.6 million, which the city matches for a total of $71 million.
 * On Nov. 29, the U.S. Department of Justice files a complaint against Jackson alleging failure to comply with the Safe Drinking Water Act.
 * 2023:
 * In May, Henifin says Jackson doesn’t have the money to pay costs until more federal funds arrive.
 * On May 2, the SPLC files a complaint with the U.S. Department of the Treasury Office of Civil Rights and Equal Employment Opportunity regarding discrimination in the allocation and disbursement of millions of federal dollars Mississippi received from the American Rescue Plan Act.

Two Treatment Plans
Two principal plants supplied Jackson, Mississippi with its water supply: the J. H. Fewell plant built in 1914 and the O. B. Curtis plant built in 1993. Together these plants provided drinking water to a total of around 250,000 people in and around Jackson. While both plants service the same region, they drew from different sources. While the Fewell plant treated water coming from the Pearl river, the Curtis plant treated the water within the Ross Barnett Reservoir.

Years of Neglect
In 2012, the EPA ruled that the city of Jackson had violated the Clean Water Act via the leakage and overflow of untreated raw sewage into the water supply. In addition to this, there were a number of unauthorized bypasses within the Savanna Street Wastewater Treatment Plant which contributed to the injunction.

Mandated by the injunction to improve maintenance, city officials were limited in funding and finances by the state government. This contributed to a gradual degradation of Jackson's water infrastructure over the decade, as vital repairs went underfunded and contributed to the crisis that began in 2022.

2022 Water Crisis (August - November 2022)
Following historic rainfall which flooded the Pearl River, the Curtis plant was overwhelmed with excess water from the Ross Barnett Reservoir. Already relying on backup pumps due to previous damage, city officials altered the treatment method at the plant, resulting in a decrease in water pressure and quality.

A state of emergency was declared, with most of Jackson's citizens lacking water in the immediate aftermath of the plant's failure. Similar breakdowns at the Fewell plant contributed to the crisis. A boil water notice went into effect for the city, straining the resources of local hospitals. While the systems were mostly restored by September 4th, concerns remained over water quality and potential lead poisoning. Eventually, however, the boil advisory was revoked for Jackson on September 14th and the EPA declared the water safe to drink later in late October.

Funding and Financing
The Jackson, MS water system infrastructure is funded by the people of Jackson, who are the recipients of the services. The water system is a utility, so residents and businesses who use its services have to pay the fees/bill. This is the water systems main source of revenue, so without it, it makes it difficult to maintain and improve the water system infrastructure.

Jackson, MS struggled to collect monthly payments from its residents because of an unreliable billing system and residents not being able to make their monthly payments. All of this contributed to the failure of the water system because without that revenue, the city did not have the financial resources that were needed to address the issues of the water system.

When President Biden declared a state of emergency in Jackson, Mississippi, Jackson was granted federal funds to assist with the crisis. The funds would cover up to 75% of all emergency related costs.

Mississippi Department of Environmental Quality (MDEQ) “awards Jackson $35.6 million, which the city matches for a total of $71 million”

In June 2023, the U.S. Environmental Protection Agency (EPA) announced that Jackson, Mississippi will receive $115 million in funding to support water infrastructure that will ensure safe and reliable drinking water for residents. The funding comes from Congressional appropriations for the 2023 federal budget. The Biden-Harris administration are advocates for Jackson, MS to receive this funding to ensure residents have access to clean, safe drinking water.

Institutional Arrangements
A municipality's water supply and related services are usually managed by several important institutions and entities. Their contributions to the crisis emerged from several factors, including budget decisions, infrastructure management, regulatory oversight, and emergency preparedness. In tandem, these agencies strive to ensure that communities have access to a dependable and safe supply of water. Municipal water systems are often managed by the following institutions, albeit specific arrangements may differ from one municipality to the next:

The management and operation of the water system were under the jurisdiction of the Jackson Department of Public Works and its water division. Challenges with these organizational structures, particularly inadequate financing, and staffing shortages, made it increasingly difficult for the agency to effectively manage and mitigate the issue. Regulatory agencies at the state and federal levels, including O.B. Curtis Water Treatment Plant, Mississippi Department of Environmental Quality (MDEQ), and the Environmental Protection Agency (EPA), establish water quality standards and monitor adherence.

A separate sanitary sewer system is operated and owned by the City of Jackson, Mississippi. Savanna Street, Presidential Hills, and Trahon wastewater treatment plants, as well as a wastewater collection and transmission system, constitute a component of Jackson's system. Jackson violated the terms of its National Pollutant Discharge Elimination System (NPDES) permits and Section 301 of the Clean Water Act. A total of over 2,300 sanitary sewer overflows, forbidden bypasses, malfunctions in operation and maintenance, and effluent limit violations account for Jackson's alleged offenses.

Determining water quality standards as well as ensuring that local, state, and federal laws are complied with are the responsibilities of the MDEQ and the O.B. Curtis Water Treatment Plant. In an effort to manage the emergency during the water crisis, the MDEQ collaborated with local authorities. They provided guidance and issued advisories, such as boil-water advisories, to safeguard the public's health. They assisted in organizing the emergency response efforts to make certain the residents were conscious of the situation. The MDEQ's response amid the crisis, as described by critics, was not as immediate as it deserved to be. The MDEQ, municipalities, and residents were not corresponding properly or effectively, which raised concerns. To prevent or mitigate similar crises in the future, the incident emphasizes the significance of extensive infrastructure investment, regulatory oversight, and efficient emergency response at the state level.

Policy Issues
=== Privatization === In response to the failures Jackson's wastewater treatment system, Governor Reeves floated the idea of privatizing the plants currently operated by the city government. This plan, however, has encountered opposition from city officials who fear the plan could increase costs. Proponents have countered by asserting the increased costs would result in greater quality service from the treatment plants.

=== Lead Pipes === Lead pipes have come into focus as well as a continuing factor in Jackson's water security. Many residents fear lead contamination in the wake of the crisis. Already, 1,800 lawsuits have been filed against city and state officials for lead water contamination.

Neglecting Water Infrastructure Can Have Dire Consequences for Communities, Particularly Those with Limited Resources:
Neglecting water infrastructure, as illuminated by the Jackson, Mississippi water crisis, can have profound repercussions for communities, especially those already grappling with limited resources. This case underscores the essential, albeit often overlooked, role that infrastructure plays as the backbone of any community. Prolonged neglect or underfunding of maintenance renders the entire water system vulnerable to failure, thereby endangering public health, safety, and economic stability. Neglecting water infrastructure may lead to water contamination, service interruptions, and unsanitary conditions, all of which pose significant health risks to the population. In Jackson, residents faced hurdles in accessing clean water for basic necessities such as drinking, bathing, and sanitation. The water crisis also led to economic consequences that affected local businesses, property values, and potential investments, exacerbating the inadequate funding necessary to address the issue. Communities that overlook infrastructure investment may inadvertently deter potential economic development opportunities that could have secured additional financial support. The crisis in Jackson disproportionately affected marginalized communities, underscoring the social inequalities directly linked to insufficient infrastructure. Given the historical context of racial discrimination in the area, the development of this inequity is unmistakable, accentuating the urgency of addressing these disparities and ensuring that all residents enjoy equitable access to essential services.

Bureaucratic Hurdles Can Delay Emergency Responses:
The Jackson water crisis casts a spotlight on the difficulties inherent in bureaucratic obstacles during emergencies. In crises, the necessity of efficient, streamlined processes is a cornerstone to prevent immediate responses from being delayed by bureaucratic semantic procedures. In this instance, the community endured significant suffering due to the shortcomings of these inefficient bureaucratic procedures. Effective communication and coordination among various levels of government, regulatory bodies, and local authorities are of utmost importance. Delays in decision-making and resource allocation exacerbate the impact of the crisis. While regulatory oversight is indispensable to maintain water quality and safety, it should be balanced with the need for swift response and flexibility during emergencies, taking into account that achieving compliance without inducing delays is a complex challenge. Involving the affected community in emergency response and decision-making can help bridge the gap between bureaucratic processes and the immediate needs of residents, leading to more effective and equitable responses. By using a constituent-first approach and involving the voices of the community in a comprehensive manner will ensure that proposed solutions actually fit the needs and characteristics of the community experiencing the crisis.

Adequate Funding for Infrastructure Maintenance is Essential for Preventing Future Crises:
The Jackson water crisis underscores the critical significance of consistent and sufficient funding for the maintenance, repair, and upgrading of infrastructure. Inadequate financial support leaves water systems vulnerable to deterioration, potentially resulting in recurrent crises. Adequate funding not only sustains water infrastructure but also ensures its resilience against environmental and operational challenges. It facilitates routine maintenance and proactive replacement of aging components. Investing in infrastructure maintenance often proves more cost-effective in the long run. Preventive maintenance and timely upgrades can avert the significantly higher costs associated with emergency repairs and crisis management. Adequate allocation of funding for infrastructure maintenance in communities with limited resources represents an essential component of valuing social responsibility and equity for that community. Ensuring access to clean and safe water is a fundamental right that should be protected.

In conclusion, the Jackson, Mississippi water crisis stands as a stark reminder of the dire consequences of neglecting water infrastructure. The lessons learned underscore the importance of proactive investment, streamlined emergency response processes, and an equitable approach to confronting infrastructure challenges. These insights can guide policies and practices in other communities, helping to avert comparable crises in the future and champion the well-being of all residents, irrespective of their economic status.

Discussion Questions

 * 1) How can other cities learn from Jackson's experience in terms of infrastructure maintenance and funding?
 * 2) What is the role of federal agencies in addressing water crises at the local level?
 * 3) How can equitable access to clean water be ensured in marginalized communities?
 * 4) What steps should be taken to improve emergency preparedness for similar crises in the future?