To find the combined capacity of the two pools, we need to sum the capacities of each pool. However, it seems the values for the capacities are incomplete because you only provided the format "8.12 x" and "5.27 x" without giving the exponent for the "x".
Assuming the full values were intended as follows:
- Olympic size pool: \( 8.12 \times 10^n \) gallons
- Smaller pool: \( 5.27 \times 10^n \) gallons
where \( n \) is the same exponent for both pools, we can combine them like this:
\[ \text{Combined capacity} = 8.12 \times 10^n + 5.27 \times 10^n \] \[ = (8.12 + 5.27) \times 10^n \] \[ = 13.39 \times 10^n , \text{gallons} \]
Next, we need to convert \( 13.39 \times 10^n \) into proper scientific notation. It should be expressed in the form \( a \times 10^b \) where \( 1 \leq a < 10 \).
Since \( 13.39 \) can be expressed as \( 1.339 \times 10^1 \), we can write the combined capacity as:
\[ 1.339 \times 10^1 \times 10^n = 1.339 \times 10^{(n + 1)} , \text{gallons} \]
Thus, if we are looking for the combined capacity in one of the provided options and the value of \( n \) can be any integer, we can select the matching format from the answers.
The options presented appear to have:
- A: \( 1.339 \times 10^4 \)
- B: \( 1.339 \times 10^6 \)
- C: \( 13.39 \times 10^{10} \)
- D: \( 1.339 \times 10^{10} \)
- E: \( 2.85 \times , \text{gallons} \)
The correct answer would be the one that matches the format \( 1.339 \times 10^{(n + 1)} \) for the proper exponent.
Hence, if \( n \) was intended to be lower than \( 10 \), option D \( 1.339 \times 10^{10} \) would be a suitable choice indicative of a combined capacity with an assumption on the exponent value.
Please verify the correct numerical values and return them if possible, to ensure accurate calculation.