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To find the area of the shaded region, we need to subtract the area of the square OABC from the area of the quadrant OABQ.

To find the area of the shaded region, we need to subtract the area of the semi-circle from the area of the quadrant.

To solve this problem, we first need to find the areas of the two circles with diameters 10 cm and 24 cm. Then, we'll add these areas together to find the total area. Finally, we'll find the diameter of the larger circle whose area is equal to the sum of the areas of the two smaller circles.

To find the probability of drawing a card with a number less than 10, we need to determine the total number of favorable outcomes (cards with numbers less than 10) and divide it by the total number of possible outcomes (total number of cards).

In a standard deck of 52 playing cards, there are 2 black kings: the king of spades and the king of clubs.

1. Total number of possible outcomes (total number of cards): There are 52 cards in a standard deck.

2. Total number of favorable outcomes (black kings): There are 2 black kings in the deck.
   

To find the probability of drawing a card with an even number, we need to determine the total number of even-numbered cards in the bag and divide it by the total number of cards in the bag.

Given:

• Numbers on the cards range from 3 to 20.

To find the probability that two friends born in the year 2000 have the same birthday, we need to consider the total number of days in the year 2000 and the number of ways they could share a birthday.

Given that they were born in the same year:

1. Total number of days in the year 2000: Since the year 2000 was a leap year, it had 366 days.

2. Number of ways they could share a birthday: Each friend's birthday can fall on any of the 366 days in the year.
   

If each observation in a continuous frequency distribution is increased by 5, the median of the new data set will also increase by 5. This is because the median is the middle value of the data set, and adding the same constant to every observation simply shifts the entire data set by that constant.

Let's denote:

• b as the number of boys,
• g as the number of girls.

Given:

1. The average score of boys is 71.
2. The average score of girls is 73.
3. The average score of the school is 71.8.
   
   
4. 

To find the median for a frequency distribution, we need to use the relationship between the mean, median, and mode in a symmetrical distribution.

In a symmetrical distribution:

• The mean, median, and mode are all equal.

Given that the mode is 7.88 and the mean is 8.32, we can see that they are not equal. This suggests that the distribution is not perfectly symmetrical.

However, we can still estimate the median based on the mode and mean using the following relationship: