Final answer:
The true statement about the Twenty-Fifth Amendment is that President Nixon used it to appoint Gerald Ford as vice president after Spiro Agnew's resignation. The amendment was ratified in 1967 and outlines the procedures for presidential and vice presidential succession and disability. Hence, it has been used and is not limited to instances explicitly stated by the Constitution.
Step-by-step explanation:
The Twenty-Fifth Amendment
Among the statements provided, the true one is that the Twenty-Fifth Amendment was used by President Nixon when he appointed Gerald Ford as vice president. This event occurred following Vice President Spiro Agnew's resignation due to a tax scandal. Gerald Ford was then nominated by Nixon and confirmed by Congress as vice president under the authority of the 25th Amendment. Therefore, it's inaccurate to say that the 25th Amendment has never been used. Furthermore, the Amendment does not only apply when the Constitution explicitly states; it is a standing part of the Constitution that defines the procedures for presidential and vice presidential succession and disability.
It is also false that the Amendment was a result of President Carter's illness, as it was ratified in 1967. Moreover, when President Ford took office after Nixon's resignation, he became the first person to ascend to the presidency through the 25th Amendment and later nominated Nelson Rockefeller as his vice president, again utilizing the Amendment. Presidential disability and succession are critical components of the 25th Amendment, with procedures for the vice president to assume the president's duties either temporarily, as was the case when President George W. Bush underwent a medical procedure, or permanently in cases of death, resignation, or removal of the President.