a hospital has 1 million in taxable income and the tax rate is 30% what would be the net income?

I am glad to see you actually attempted to work through the problem. I'm always glad to give feedback on answers, but I never actually do the problems for those just looking for an answer.

You are on the right path, but you have misread the question. The question does not ask for the tax, but rather for the profit after tax. Consequently, you need to multiply the $1M by the inverse of 30%.

The profit after taxes would be computed as:

100% - 30% = 70%

$1M x 70% = $700,000.

Your second question follows the same principles, since it asks for his after tax dividend. The computation is:

100% - 15% = 85%

$10,000 x 85% = $8,500

You're right on the first part. The 2nd part follows the exact same logic.