What are statements made by the applicant that are believed to be true to the best of their knowledge?

The correct choice is representations because in the context of insurance applications, representations refer to statements made by the applicant that they believe to be true based on their knowledge at the time of providing that information. These are assertions about factual matters that are not guaranteed to be accurate but reflect the applicant's honest understanding and belief.

In insurance, representations play a crucial role as they help insurers assess the risk associated with providing coverage. If it later turns out that a representation was false, it may impact the insurer's decision on coverage, but only if the falsehood was material to the underwriting process. This underscores the importance of providing accurate information during the application process.

While declarations are formal statements often found within insurance policies and documents, they differ from representations as they are typically definitive and acknowledged by both parties. Guarantees imply a promise of certain outcomes, which is not the nature of the claims made in insurance applications. Affirmations usually pertain to strong confirmations rather than the subjective belief component found in representations. Therefore, representations is the term that best captures the essence of the statements made by applicants in this context.