Final answer:
The integer representing the change in the stock's value after falling 6 points is -6. For the Darkroom Windowshade Company, investors 1 and 2 together do not hold a majority and thus cannot guarantee control over company decisions without additional support.
Step-by-step explanation:
The student is asking about an integer that represents the change in the stock's value, which is a concept from mathematics involving negative numbers. When the value of the stock falls 6 points, this is represented by the integer -6. A negative sign indicates a decrease in value, which aligns with the direction of the change.
The Darkroom Windowshade Company question involves calculating the number of votes needed to have control over the company's management, a concept related to shareholding and voting rights in a business setting. In this case, investor 1 and investor 2 together hold 38,000 shares (20,000 + 18,000). To change the top management, a majority is usually required, which would be over 50,000 shares (50% of the 100,000 outstanding shares) in this instance. Therefore, if investors 1 and 2 vote together, they cannot be certain of always getting their way, as they would need more shareholders to join them to exceed the 50,000 vote threshold.