Outside of wartime, the US Navy still patrols, a carrier group would be a dozen odd ships with personal numbering well over seven thousand.The US military only sends hundreds of thousand of people when going to war, I must add. Exploration missions, of which history is replete with examples, is usually composed of considerably smaller groups, and can be a single ship, or at most, a small group of them.
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Also given the massive difference in population between the Federation and the USA. Means that in context the number of personnel is probably equivalent.