Final answer:
Most metabolic activities occur in the cytoplasm and mitochondria of a cell. Mitochondria produce ATP, which powers the cell, while the cytoplasm contains enzymes for metabolism and structures for cellular support.
Step-by-step explanation:
The majority of the metabolic activity in a cell occurs in the cytoplasm and the mitochondria. While the cytoplasm is a jelly-like substance that hosts various organelles and is the site for many metabolic reactions, the mitochondria are known as the 'powerhouse of the cell'. They are involved in cellular respiration and produce ATP (adenosine triphosphate), which is vital for cellular functions.
Although the nucleus controls cell activity, it is not where most metabolic activity occurs. Ribosomes, found in both prokaryotic and eukaryotic cells, are the sites of protein synthesis, but they are not the main centers for metabolic activity. They do, however, contribute significantly to cellular energy consumption.
In the case of the particular interactions mentioned, the RNA components of ribosomes are synthesized in the nucleolus, which is within the nucleus (option c). Both prokaryotic and eukaryotic cells contain ribosomes (option d). In plant cells, the function of lysosomes is mainly carried out by vacuoles (option a). The nucleus is the structure that is surrounded by two phospholipid bilayers (option d).