Of 256 consumers polled, some like only thriller movies, some prefer just comedies, and some like both. If 78 people like only thrillers, and 116 like both, how many people prefer only comedies?
Let's denote the number of people who like only thrillers as 'T', the number of people who like both thrillers and comedies as 'B', and the number of people who like only comedies as 'C'. We are given the following information:
1. There are 78 people who like only thrillers (T = 78).
2. There are 116 people who like both thrillers and comedies (B = 116).
3. We have a total of 256 consumers polled.
To find the number of people who prefer only comedies (C), we need to calculate the total number of people who like thrillers, then subtract the number of people who like both thrillers and comedies.
We can set up the following equation:
T + B + C = Total number of people polled
Since the total number of people polled is 256, we have:
78 + 116 + C = 256
Combining like terms, we can simplify the equation to solve for C:
C = 256 - 78 - 116
C = 62
Therefore, there are 62 people who prefer only comedies.
Solve and graph the inequality -3x > 24
To solve the inequality -3x > 24, we need to divide both sides of the inequality by -3. However, whenever we multiply or divide an inequality by a negative number, the direction of the inequality sign must be flipped. So, when we divide both sides by -3, we must also flip the direction of the inequality sign.
Dividing both sides by -3:
(-3x)/(-3) < 24/(-3)
x < -8
Therefore, the solution to the inequality is x < -8.
Graphically, we represent this solution on a number line by shading all the values that are less than -8. The interval notation for this solution would be (-∞, -8).