Let's break down and address the problems:

Problem 12: Given that 50 pounds = 22.68 kg, we need to convert $\frac{15}{8}$ pounds into kilograms.

The conversion factor here is $\frac{22.68 \, \text{kg}}{50 \, \text{lb}}$, so: $\frac{15}{8} \, \text{lb} = \frac{15}{8} \times \frac{22.68}{50} \, \text{kg}$

Problem 13: This problem involves a clock's minute hand, which completes a full turn every 60 minutes. We need to find how many full turns the minute hand makes in 650x minutes.

The minute hand turns once in 60 minutes, so for 650x minutes, the total number of turns is: $\text{Number of turns} = \frac{650x}{60}$

Problem 14: Here, we have 15 cards and $n$ cards, and 6 people are distributing the cards equally. The number of cards each person gets will be: $\frac{n}{6}$

Let me calculate the answers for problems 12 and 13 to provide you with more details. Problem 12: Converting 15/8 pounds to kilograms given 50 pounds = 22.68 kg pounds_to_kg = 22.68 / 50 # conversion factor pounds = 15 / 8 kg = pounds * pounds_to_kg

Problem 13: Finding how many turns the minute hand makes in 650x minutes

minutes = 650 # Considering x = 1 for simplicity turns = minutes / 60 # each hour = 1 turn

kg, turnsHere are the results:

Problem 12: $\frac{15}{8}$ pounds is approximately 0.8505 kg.

Problem 13: The minute hand will make approximately 10.83 turns in 650 minutes.

Let me know if you'd like further clarification or if you'd like to solve other problems!

Related Questions:

1. How can we convert other units of weight using similar conversion factors?
2. What other factors can affect the speed of the minute hand on different types of clocks?
3. How do we calculate the total time in hours when dealing with multiple turns of the minute hand?
4. Can you solve the same type of problems with other units of time, like seconds?
5. What happens if we increase or decrease the number of people distributing the cards in Problem 14?

Tip: When converting between units, always ensure that the units are consistent and the conversion factor is correct for the units you’re working with.