Statements that fall within an exception to the hearsay rule are admissible to prove the truth of the matter asserted by the declarant (the maker of the statement).

City of Tuscaloosa v. Harcros Chemicals, Inc., 158 F.3d 548, 557-558 (11th Cir. 1998) (holding, in plaintiff Alabama municipal entities' action against defendant chemical companies for fraud and violation of antitrust law, that the trial court....A statement by an agent or an employee can be imputed to the principal or the employer (respectively) and be treated as a vicarious admission (that, like other admissions, is exempt from the prohibition against hearsay) only if the statement was made during the agency or employment relationship.

Fed. R. Evid. 804(b)(2) (""In a prosecution for homicide or in a civil action or proceeding, a statement made by a declarant while believing that the declarant's death was imminent, concerning the cause or circumstances of what the declarant believed to be impending death.").The hearsay exception for dying declarations applies only if the declarant believed that his or her own death was imminent when he or she made the statement.

United States v. Gjerde, 110 F.3d 595, 603 (8th Cir. 1997) (upholding trial court's admission of the FBI agent's testimony [about Richard Field's description of Minnewaska] as a statement against interest because (1)....If a statement is offered against a criminal defendant, the statement qualifies as a statement against interest for purposes of the federal hearsay exception for statements against interest only if there is corroborating evidence of the trustworthiness of the statement.