To find the weight of the dump truck after adding 15,300 pounds of trash, we start by adding the weight of the empty dump truck to the weight of the trash.
- Weight of the empty dump truck: \(2.8 \times 10^5\) pounds
- Weight of trash added: \(15,300\) pounds
Now let's convert \(15,300\) to scientific notation:
\[ 15,300 = 1.53 \times 10^4 \]
Now we'll add the two weights. To do that, we need to express them in the same power of ten:
\[ 2.8 \times 10^5 = 280,000 \text{ pounds} \] \[ 15,300 \text{ pounds} = 15,300 = 0.153 \times 10^5 \text{ pounds} \]
Now we add:
\[ 280,000 + 15,300 = 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 \]
Calculating the sum:
\[ 2.8 + 0.153 = 2.953 \]
Therefore:
\[ 2.8 \times 10^5 + 0.153 \times 10^5 = 2.953 \times 10^5 \]
So the total weight of the dump truck with the trash is:
\[ \text{Weight} = 2.953 \times 10^5 \text{ pounds} \]
Thus, the correct answer in scientific notation is:
\[ \boxed{2.953 \times 10^5 \text{ pounds}} \]