To determine which of the given options represents the possible GPAs Diana can earn in order to remain on the Dean's list, we first need to express Diana's GPA range mathematically.
Diana wants her GPA "g" to be between 3.5 and 3.8, which can be written as:
\[ 3.5 \leq g \leq 3.8 \]
We can find the midpoint of this interval and the distance from this midpoint to the endpoints:
Midpoint = \(\frac{3.5 + 3.8}{2} = 3.65\)
The distance from the midpoint (3.65) to either endpoint (3.5 or 3.8) is:
Distance = \(3.8 - 3.65 = 0.15\) (or \(3.65 - 3.5 = 0.15\))
This means that Diana's GPA can be represented in terms of absolute value as:
\[ |g - 3.65| \leq 0.15 \]
This expression indicates that Diana's GPA is within 0.15 units from the midpoint of 3.65, thus including all values between 3.5 and 3.8.
Now let's evaluate the options:
A. \( |g - 3.65| \leq 0.15 \) (This is correct and matches our derived condition.) B. \( |g - 0.15| > 3.65 \) (This does not pertain to her GPA range.) C. \( |g - 3.65| > 0.15 \) (This represents an area outside of the GPA range, which is incorrect.) D. \( |g - 0.15| \leq 3.65 \) (This does not relate to her GPA limits.)
Therefore, the correct answer is:
A. |g - 3.65| ≤ 0.15
1 answer