This completely depends on the intent and level of involvement of the investor whom wants to bring in pure cash. The possible branches and scenarios could get very long (almost like binomial tree), but I will iterate here two very fundamental ones.
1) The investor brings in the cash, capital, owns certain percentage of the company based on investment, and gets involved with decision making, at the board level, and provides feedback, and holds voting rights based on the involvement.
2) They become pure investor with very little involvement and you steer the ship.
At the end of the day, decisions are to be made by CEO and the board, and regardless of percentage of investors, if you (as CEO) hold control of the company, decision making lies upon you (as well as the consequences, and deliverables). Overall, the percentages are all dependent on the valuation, the money that is brought in, equity, ...etc