Final answer:
The density of the 75-gram gold sample with a volume of 3.9 cm³ is calculated to be 19.23 g/cm³, which is option (a) and confirms that the sample is likely gold, as it matches the known density of gold.
Step-by-step explanation:
To determine the density of a 75-gram sample of gold with a volume of 3.9 cm³, we use the formula for density, which is mass divided by volume.
Density = Mass / Volume
Plugging in the values for this sample:
Density = 75 g / 3.9 cm³
Doing the calculation:
Density = 19.23 g/cm³
The answer is 19.23 g/cm³, which matches choice (a). Given that the density we calculated is very close to the known density of gold (19.3 g/cm³), we can say with confidence that the sample is likely gold.