The correct answer is a) mitochondria.
Mitochondria are often referred to as the powerhouses of the cell because they are responsible for producing adenosine triphosphate (ATP), which is the primary energy currency in biological systems. These organelles convert energy stored in carbohydrates and fats into ATP through a process called cellular respiration. This process involves several steps, including glycolysis, the Krebs cycle, and oxidative phosphorylation, which take place in the mitochondria.
In contrast, the other options do not serve the same function: b) cell membrane acts as a barrier and regulates the passage of substances in and out of the cell; c) ribosomes are involved in protein synthesis; and d) nucleus houses the cell’s genetic material and coordinates activities like growth and reproduction. Thus, the role of mitochondria as the site of ATP production solidifies its title as the powerhouse of the cell.