Sure! Let's go through the steps to solve this problem:
1. Write down the weights in standard form:
- The first animal's weight is: [tex]\(5.12 \times 10^2 \, \text{lbs} = 512 \, \text{lbs}\)[/tex].
- The second animal's weight is: [tex]\(6.8 \times 10^2 \, \text{lbs} = 680 \, \text{lbs}\)[/tex].
2. Add the two weights together:
- Total weight [tex]\(= 512 \, \text{lbs} + 680 \, \text{lbs}\)[/tex].
- Total weight [tex]\(= 1192 \, \text{lbs}\)[/tex].
3. Convert the total weight into scientific notation:
- To convert [tex]\(1192 \,\text{lbs}\)[/tex] into scientific notation, we need to express it in the form [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex].
- [tex]\(1192 \, \text{lbs}\)[/tex] can be written as [tex]\(1.192 \times 10^3 \, \text{lbs}\)[/tex].
4. Round the coefficient to significant digits:
- Since the given options have 3 significant digits and looking at the closest answer, we round [tex]\(1.192\)[/tex] to [tex]\(1.19\)[/tex].
5. Write the final answer:
- The total weight of the two animals in scientific notation is [tex]\(1.19 \times 10^3 \, \text{lbs}\)[/tex].
Thus, the total weight of the two animals is [tex]\( 1.19 \times 10^3 \, \text{lbs} \)[/tex].
