Final answer:
According to Roosevelt's policies, the goals of sending American troops to Latin America were to stabilize economic affairs, prevent European intervention, and pursue broader U.S. foreign policy goals such as promoting democracy and ensuring peace and stability.
Step-by-step explanation:
According to Theodore Roosevelt's policies and actions, the three goals each time American troops were sent to Latin America were likely a mixture of economic, political, and strategic interests rather than the options provided in the student's question. While not explicitly stated in the question, Theoedore Roosevelt's involvement in Latin America can be best understood through his corollary to the Monroe Doctrine, known as the Roosevelt Corollary, which effectively allowed the United States to intervene in the region to stabilize economic affairs and prevent European intervention. This was often justified as ensuring repayment of loans and protecting American investments (economic domination), but the underlying reasons included a broader range of U.S. foreign policy goals such as spreading American influence (spread American imfluence), ensuring stability and peace (peacekeeping), and promoting certain political agendas (promote democracy). Therefore, the correct answer to the student's question, considering Roosevelt's perspective and historical context, could be interpreted as a mix of these broader goals rather than the more simplistic options provided.