Final answer:
Zeke's both clubs will first meet on the 16th day of the month, as it is a common day for both his bi-daily and every 8 days schedule. Jessica's swimming pattern increases by 100 meters daily, so she will swim 2.05 km on the fifth day. Mrs. Roth can lift the computer weighing 2.55 kg as it is the only item within her lifting capacity.
Step-by-step explanation:
The question involves finding the least common multiple (LCM) for Zeke's swim and robotics club schedule and understanding conversions of different measurements of distance for Jessica's swimming practice. To answer Zeke's query, we need to note that while the LCM of 2 and 8 is indeed 16, this doesn't necessarily mean that the clubs will first meet on the 16th day. We must consider the actual days he starts each club: since the robotics club starts on the 8th day and it happens every 8 days, the next occurrence will be the 16th day, which suits the condition of the swim club as well since it occurs every 2 days. For Jessica's swim pattern, she increases the distance every day as follows: 1.65 km (same as 1650 m), 1,750 m, 185,000 cm (which is 1.85 km), and 1,950,000 mm (which is 1.95 km). To find the pattern, we observe that the distance increases by 100 meters (or 0.1 km) each day, so on the fifth day, Jessica will swim 2.05 km.
Regarding Mrs. Roth's situation, the comparison requires converting all measurements to kilograms to determine if she can lift them. A box of books weighing 23,500 grams is equivalent to 23.5 kg, a statue weighing 2,450,000 centigrams is 24.5 kg, a computer weighing 2,550,000 milligrams is 2.55 kg, and a potted plant weighing 22.55 kg is just above her lifting capacity. Therefore, the only item Mrs. Roth can lift is the computer.