Final answer:
Medicaid is the medical care expense program that is partially funded by the federal government and administered by individual states.
Step-by-step explanation:
The medical care expense program that is partially funded by the federal government and administered by individual states is Medicaid. Congress created Medicaid in 1965 as a joint health insurance program between states and the federal government. It provides medical insurance for certain low-income people, including those below the poverty line, with a focus on families with children, the elderly, and the disabled.