Find the average of all prime numbers between 20 and 50.

Options

A. 35.857
B. 35.657
C. 34.857
D. 36.657

Answer

To find the average of all prime numbers between 20 and 50, we can follow these steps:

### Step 1: Identify the prime numbers between 20 and 50.
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. We will check each number between 20 and 50 to see if it is prime.

- The numbers to check are: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
- The prime numbers in this range are: **23, 29, 31, 37, 41, 43, 47.**

### Step 2: Sum the identified prime numbers.
Now we will add all the prime numbers we found:
- \( 23 + 29 + 31 + 37 + 41 + 43 + 47 \)

Calculating this step-by-step:
- \( 23 + 29 = 52 \)
- \( 52 + 31 = 83 \)
- \( 83 + 37 = 120 \)
- \( 120 + 41 = 161 \)
- \( 161 + 43 = 204 \)
- \( 204 + 47 = 251 \)

So, the total sum of the prime numbers is **251**.

### Step 3: Count the number of prime numbers.
Next, we count how many prime numbers we have identified:
- The prime numbers are: 23, 29, 31, 37, 41, 43, 47.
- There are **7 prime numbers**.

### Step 4: Calculate the average.
The average is calculated by dividing the total sum of the prime numbers by the count of the prime numbers:
- Average = \( \frac{\text{Total Sum}}{\text{Count}} = \frac{251}{7} \)

Calculating this:
- \( 251 \div 7 \approx 35.857 \)

### Final Answer:
The average of all prime numbers between 20 and 50 is approximately **35.857**.

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