Final answer:
Roosevelt's references to Cuba, Panama, and the 'Open Door in China' relate to the Spanish-American War and Rough Riders, the US-backed Panamanian Revolution and Panama Canal construction, and the US policy for equal trade opportunities in China, respectively.
Step-by-step explanation:
When President Theodore Roosevelt referenced Cuba, he was likely referring to the Spanish-American War and the involvement of his cavalry unit, the Rough Riders, in the liberation of Cuba from Spanish rule. For Panama, he was discussing the United States' support of the Panamanian Revolution and the subsequent construction of the Panama Canal, a vital strategic maritime passage connecting the Atlantic and Pacific Oceans, which solidified U.S. influence in Latin America. The 'Open Door in China' refers to the policy advocated by the United States for free trade in China, which aimed at preventing any single country from monopolizing trade with China and maintaining equal market opportunities for all trading nations, though it primarily benefited the United States by allowing it to access markets without the presence of military forces.