Final answer:
The density of the quartz is calculated by dividing its mass (160 g) by the volume of water it displaces (38.5 mL), resulting in a density of approximately 4.16 g/mL.
Step-by-step explanation:
The density of an object can be calculated using the formula density = mass ÷ volume. In the given question, a quartz rock has a mass of 160 g and displaces 38.5 mL of water. To find the density of the quartz, you divide the mass by the volume of water displaced, which represents the volume of the quartz. So, the calculation would be:
Density = 160 g ÷ 38.5 mL = 4.155844155844156 g/mL. When rounding to two decimal places, the density is approximately 4.16 g/mL. Therefore, option (a) 4.16 g/mL is the correct answer.