Sure, let's determine the sum of the masses and ensure we report it to the appropriate number of significant figures. Here's the step-by-step solution:
1. Write down the given masses of the three chalk samples:
[tex]\[
\text{Mass}_1 = 15.673 \text{ g}
\][/tex]
[tex]\[
\text{Mass}_2 = 8.4568 \text{ g}
\][/tex]
[tex]\[
\text{Mass}_3 = 14.75 \text{ g}
\][/tex]
2. Add the three masses together to find the total mass:
[tex]\[
\text{Total Mass} = \text{Mass}_1 + \text{Mass}_2 + \text{Mass}_3
\][/tex]
[tex]\[
\text{Total Mass} = 15.673 \text{ g} + 8.4568 \text{ g} + 14.75 \text{ g}
\][/tex]
[tex]\[
\text{Total Mass} = 38.8798 \text{ g}
\][/tex]
3. Determine the appropriate number of decimal places for the final result. This is based on the input with the smallest number of decimal places. Here:
- [tex]\( \text{Mass}_1 \)[/tex] has 3 decimal places (15.673 g).
- [tex]\( \text{Mass}_2 \)[/tex] has 4 decimal places (8.4568 g).
- [tex]\( \text{Mass}_3 \)[/tex] has 2 decimal places (14.75 g).
Therefore, the sum should be reported to the smallest number of decimal places, which is 2 decimal places (from [tex]\(\text{Mass}_3\)[/tex]).
4. Round the total mass to the appropriate number of decimal places:
[tex]\[
38.8798 \text{ g} \approx 38.88 \text{ g}
\][/tex]
So, the sum of the masses, reported to the appropriate number of significant figures, is:
[tex]\[
\boxed{38.88 \text{ g}}
\][/tex]
