Final answer:
Lisa can score between 0 and 73 on the fourth test to maintain a C average for the semester, which is an average of 70 to 79, inclusive. The closest correct option based on the intervals provided in the question is [65, 100], but the precise range should be [0, 73].
Step-by-step explanation:
To calculate the range of scores Lisa can receive on the fourth test to achieve a C for the semester, we need to determine what her average needs to be. Given that a C is between 70 and 79, inclusive, we aim for her average to be within this range after all four tests.
Lisa has scores of 87, 86, and 74 on her first three tests. The sum of these scores is 247. If Lisa wants at least a 70 average, the total after four tests needs to be at least 280 (since 70 × 4 = 280). The minimum score she needs on the fourth test is therefore 280 - 247 = 33. However, this is a non-issue since all test scores are non-negative and the minimum score for a test is 0, which is below 33.
For the upper limit, if we want to keep the average below 80 to secure a C, the sum after four tests must be less than 320 (since 80 × 4 = 320). Therefore, the maximum score Lisa can receive on the fourth test is 320 - 247 = 73.
In interval notation, the range of scores Lisa can get on the fourth test to maintain a C average is [0, 73].
However, the options provided do not include this correct interval, suggesting a possible error in the question or answer choices. Based on the options given, the closest correct interval that includes scores Lisa could receive on the fourth test to still obtain a C would be [65, 100]. Nevertheless, the correct answer based on the calculations above is [0, 73].