**Explanation:**

**1. Understanding Specific Rotation:**
Specific rotation is a property of chiral compounds that measures the degree to which they rotate plane-polarized light. It is denoted by the symbol [α]. The specific rotation is defined as the angle in degrees through which the plane of polarized light is rotated when it passes through a sample of a compound in a standard concentration (1 g/mL) and a specified path length (1 dm) at a given temperature (usually 20°C).

**2. Relationship between Enantiomers and Specific Rotation:**
Enantiomers are mirror images of each other and have equal and opposite specific rotations. In other words, if the (R)-enantiomer has a specific rotation of +48°, then the (S)-enantiomer would have a specific rotation of -48°.

**3. Calculating the Specific Rotation of the Mixture:**
In this question, we are given that the sample of the compound contains 25% of the (S)-enantiomer. To calculate the specific rotation of this mixture, we can use the following formula:

[α]mixture = (%(R) × [α](R)) + (%(S) × [α](S))

where [α]mixture is the specific rotation of the mixture, [α](R) is the specific rotation of the (R)-enantiomer, [α](S) is the specific rotation of the (S)-enantiomer, %(R) is the percentage of the (R)-enantiomer, and %(S) is the percentage of the (S)-enantiomer.

Substituting the given values into the formula:

[α]mixture = (75% × +48°) + (25% × -48°)

**4. Calculating the Specific Rotation of the Mixture (Continued):**
To calculate the specific rotation of the mixture, we can simplify the equation:

[α]mixture = (0.75 × 48°) + (0.25 × -48°)
= 36° - 12°
= 24°

Therefore, the specific rotation of the sample containing 25% of the (S)-enantiomer is 24°.

**5. Conclusion:**
The specific rotation of the sample containing 25% of the (S)-enantiomer is 24°. This is obtained by calculating the weighted average of the specific rotations of the (R)- and (S)-enantiomers based on their percentages in the mixture.