Final answer:
A quorum for a corporation's nine-member board is five members, which is the majority. Investors 1 and 2 in the Darkroom Windowshade Company, with 38,000 combined shares, do not hold the majority necessary to guarantee control. To ratify an amendment, three-fourths of the states must agree.
Step-by-step explanation:
To determine the quorum for a corporation's board meetings, you would look at the company's bylaws or relevant corporate law provisions. Typically, a quorum is a majority of the number of directors that the board is required to have. Since the board in question here has nine members, a majority would be five members (since 5 is more than half of 9). This doesn't change even if some members have sold their shares or are abroad unless the bylaws specify otherwise.
For the Darkroom Windowshade Company, to change the top management, a vote from a majority of shares would be required. If investors 1 and 2 agree to vote together, they would hold 38,000 shares, which is less than the 50,001 shares required for a majority of 100,000. Therefore, even if they vote together, they cannot be certain of always getting their way.
When it comes to ratification of an amendment, three-fourths of the states must ratify an amendment before it becomes law. This is codified in Article V of the U.S. Constitution.