Final answer:
Payments by the federal government to support specific activities are known as grants-in-aid, which are conditional funds provided to state and local governments for designated projects.
Step-by-step explanation:
Payments by the federal government to carry out specific activities are called grants-in-aid. These are monetary transfers from the federal level to state and local governments, earmarked for particular projects such as road construction, education, and urban renewal. Grants-in-aid have particular conditions or "strings attached" to ensure that funds are used for their designated purpose. If not used correctly, the allocated money must be returned to the federal government. Through such mechanisms, the federal government not only funds critical projects but also exerts influence, encouraging states to align with federal policy goals.