Final answer:
In many sports, a Captain not serving a penalty and a Designated Alternate have the authority to call a Team Timeout. A fouled-out Captain cannot, and the Pivot usually cannot unless they hold a specific leadership role.
Step-by-step explanation:
The Team Timeout in many team sports contexts can usually be called by individuals in official positions or roles on the team. Based on the options provided A fouled-out Captain is typically no longer active in the game, and therefore, would not be able to call a timeout.A Captain not serving a penalty is usually active in the game and retains their leadership responsibilities, including calling a Team Timeout.A Designated Alternate, who is appointed to take on certain leadership responsibilities, may be able to call a Team Timeout.The Pivot is a position specific to certain sports, for example, roller derby, and may not hold the authority to call a timeout unless they also have a leadership role such as captain or designated alternate.In conclusion, both the Captain not serving a penalty and the Designated Alternate generally have the authority to call a Team Timeout. To determine the exact rules for your specific sport, reference the official rule book or sport's governing body.