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The opposite of a city-state is a small town, i.e. part of a larger state or country. A city-state was a relatively small autonomous governmental unit in ancient Greece.
within the state
Democrary
within the state
A person can apply for a grant for a small business through government organizations like local and State governments. Small business grants may be given to companies that have 100 to 500 employees. It also depends on the type of small business. Sometimes one can apply for a small business grant through a non-profit organization.
boroughs
Parishes
yes, it is
unitary
limiting governmental powers
Either way can be used, though some unsaid rules do apply. It is usually left uncapitalized when referring commonly to it, such as "My sister is on a trip to the state of Alabama. It is usually capitalized in governmental and law-related documents, such as "The legislature of the State of Alabama hereby decrees that the Yellowhammer is its state bird." So in reality, it depends on the context.
shared by both state and federal authorities.