That 7.25 is a nationwide floor on the minimum wage set by the Federal Government. States are free to set a higher minimum. But in states where there is no minimum wage (so the Federal wage applies), tipped workers can be paid as little as $2.13 an hour directly by their employers, as long as they get at least $5.12 per hour in tips.
Take home money is a different thing. Someone making minimum wage on a full-time (40 hr/wk) schedule would only make about $15000/yr. (Let's ignore the second jobs and overtime they are probably putting in for now.) The Federal standard deduction is currently around $16000, so if that person is single and not someone else's dependant they will likely end up owing no income taxes. But, they would owe 9.1% right off the top in Social Security and Medicare taxes. They would also have to consider health care. Some states subsidize certain health plans so low-income people can get basic coverage for very little, but that was part of the Medicare expansion that Trump shit all over....