Final answer:
The odds used for determining the payoff, when you bet $9 and can win $360, are 39 to 1, representing the ratio of potential profit to the amount wagered.
Step-by-step explanation:
If you bet $9 on a certain event and collect $360 when you win, the payoff odds can be calculated by subtracting your initial bet from the total payout and then comparing the profit with the amount wagered. First, let's determine the profit from winning: $360 (total payout) - $9 (your bet) which equals $351. The odds are then calculated based on the profit versus the amount bet. Therefore, for every $9 wagered, you stand to win $351. This can be expressed as 351 to 9 odds, which simplifies to 39 to 1 odds. When talking about odds, we typically reference the ratio of successes to failures, so in this case, the odds used for determining the payoff are 39 to 1.