Final answer:
The duty that is not a responsibility of the U.S. Senate is coining money. This power is given to the legislative branch as per the U.S. Constitution, and is not a Senate-specific duty.
Step-by-step explanation:
The duty that is not a responsibility of the Senate is d) Coining money. This is actually a power enumerated to Congress as a whole, specifically to the legislative branch, and is mentioned in the U.S. Constitution. The Senate does have many responsibilities, including a) passing bills (proposed laws), b) approving treaties made by the President, and c) approving the selection of certain federal officers by the President, which includes federal judges, ambassadors, and heads of executive departments.