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The **13th Amendment** to the U.S. Constitution abolished slavery. Ratified in December 1865, it states that "Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction."

Excellent question! The theory of general relativity was developed primarily by **Albert Einstein**. However, the story is a fascinating one that involves crucial collaboration and a race to the finish line. Here's a more detailed breakdown: ### 1. Albert Einstein: The Visionary Einstein is the undisputed father of general relativity. He spent nearly a decade (from 1907 to 1915) developing the theory, which fundamentally reinterpreted gravity not as a force, but as a curvature of spacetime caused by mass and energy. ### 2. Key Collaborator: Marcel Grossmann A crucial figure was Einstein's friend and colleague, mathematician **Marcel Grossmann**. In 1912, Einstein realized he needed a more advanced mathematical framework to describe his ideas. He turned to Grossmann, who introduced him to the calculus of tensors and the absolute differential calculus (now known as Riemannian geometry). Grossmann helped Einstein formulate the first draft of the theory in 1913, known as the "Entwurf" (outline) theory. ### 3. The Final Formulation and the "Race" The "Entwurf" theory had flaws. In late 1915, Einstein, working alone, corrected these errors and presented the final, correct field equations to the Prussian Academy of Sciences in Berlin over several weeks in November 1915. At the exact same time, the great German mathematician **David Hilbert** was also working on the same problem. Hilbert derived the field equations from a variational principle and sent his paper to the Prussian Academy for publication just days before Einstein's final paper was submitted. This led to a brief period of tension, but it was quickly resolved. Hilbert always acknowledged that Einstein was the originator of the physical theory, and he graciously referred to the equations as the "Einstein field equations." ### Summary of Key Milestones: * **1907:** Einstein has his "happiest thought"—the realization that a person in free fall should not feel their own weight. This is the equivalence principle, the seed of general relativity. * **1912-1913:** Einstein collaborates with Marcel Grossmann to create the first mathematical framework for the theory. * **November 1915:** Einstein presents the final, correct field equations to the Prussian Academy of Sciences. * **1916:** Einstein publishes a comprehensive paper on general relativity, titled "The Foundation of the General Theory of Relativity." So, while **Albert Einstein** is the sole creator of the physical concepts, the final theory was a product of his genius, his collaboration with **Marcel Grossmann**, and a simultaneous mathematical derivation by **David Hilbert**. **In short: The theory was developed by Albert Einstein, with essential mathematical help from Marcel Grossmann.**

That's a great question, but it's impossible to say for certain! The 2025/26 Premier League season hasn't even started yet, let alone the one after it. Football is incredibly unpredictable. However, we can make some educated guesses based on the current landscape, recent transfers, and team trajectories. Here’s a breakdown of the most likely contenders for the **2025/26 Premier League title**. ### The Top Contenders #### 1. Manchester City * **Why they're the favorite:** They are the reigning champions and have been the dominant force for years. Under Pep Guardiola, they have a squad of immense quality, tactical intelligence, and a winning mentality. As long as Guardiola is there and key players like Kevin De Bruyne and Erling Haaland remain, they will be the benchmark. * **Key Question:** Can they manage the squad's age and potential fatigue from competing on all fronts? Will they strengthen the squad further, especially in defense? #### 2. Liverpool * **Why they're a major threat:** Under Arne Slot, they've seamlessly transitioned from Jürgen Klopp's era, maintaining their intensity and adding more tactical flexibility. The squad is young, hungry, and incredibly fit. The arrival of key players like Florian Wirtz signals serious ambition. * **Key Question:** Can they sustain their high-intensity style over a long season and in the Champions League? How will the midfield evolve after the departures of key figures? #### 3. Arsenal * **Why they're contenders:** Mikel Arteta has built a young, cohesive, and physically dominant team. They have learned how to win consistently and are closing the gap to City. The additions of players like Declan Rice and Kai Havertz have added the necessary steel and experience. * **Key Question:** Can they take that final step and win the league when it matters? They need to improve their cutting edge in front of goal and avoid a late-season slump. #### 4. Chelsea * **Why they're a dark horse:** They have arguably the most talented and deepest squad in the league. Under Enzo Maresca, they are playing a possession-based style that suits their players. The blend of young stars (Cole Palmer, Moisés Caicedo) and experienced winners is formidable. * **Key Question:** Can Maresca instill the necessary discipline and consistency? The sheer number of players might need to be managed, and they must prove they can handle the pressure of a title challenge. ### Other Teams to Watch * **Manchester United:** With Ruben Amorim settled in and a major squad overhaul underway, they are a team on the rise. They have the financial power to compete but are still a few years away from being true title contenders. * **Newcastle United:** With Eddie Howe and a well-funded squad, they are a consistent top-six side. They could push for a top-four finish but challenging for the title seems a step too far for now. * **Tottenham Hotspur:** Under Thomas Frank, they will be competitive and aim for the Champions League spots, but a title charge is unlikely. ### Factors That Could Change Everything * **Injuries:** A single major injury to a star player like Haaland, De Bruyne, or Salah can dramatically alter a team's season. * **Managerial Changes:** A surprise sacking or a new appointment at a top club could completely change their trajectory. * **The World Cup 2026:** The tournament will be held in the USA, Canada, and Mexico from June 11 to July 19, 2026. This will interrupt the Premier League season, likely causing a winter break. The physical and mental fatigue from the World Cup could impact key players' performances in the crucial latter part of the 2025/26 season. * **Financial Fair Play (FFP):** How strictly FFP is enforced could limit the spending power of some clubs. ### Conclusion While **Manchester City** and **Liverpool** are the current co-favorites, the race will be closer than ever. **Arsenal** and **Chelsea** have the squads to cause an upset. **The most likely scenario is another thrilling three or four-horse race that will go down to the final weeks of the season.** *Disclaimer: This is a speculative analysis based on the situation in mid-2024. The football world is full of surprises, and anything can happen over the next 18 months!*

Josh buys the house for $80,000 and spends $50,000 on repairs, so his total investment is $130,000. The repairs increase the value of the house by 150% of the purchase price. Since 150% of $80,000 is $120,000, the new value of the house is $80,000 + $120,000 = $200,000. The profit is the selling price minus the total investment: $200,000 - $130,000 = $70,000. \boxed{70000}