5. Find the average of 1862,1430 , and 276. (a) What are the prime numbers between 80 and 90 ? (b) List the multiples of 3 that are greater than 80 and less than 90 .

Let's solve the problem step by step. ### Step 1: Find the average of 1862, 1430, and 276. To find the average, we use the formula: \[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \] **Calculating the sum:** \[ \text{Sum} = 1862 + 1430 + 276 \] Now, let's calculate the sum: \[ \text{Sum} = 1862 + 1430 + 276 = 3568 \] **Calculating the average:** Now, we divide the sum by the count of numbers, which is 3: \[ \text{Average} = \frac{3568}{3} \] Now, let's calculate the average: \[ \text{Average} = 1189.33 \] ### Step 2: Find the prime numbers between 80 and 90. The prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. The numbers between 80 and 90 are 81, 82, 83, 84, 85, 86, 87, 88, and 89. - **81**: Not prime (divisible by 3) - **82**: Not prime (divisible by 2) - **83**: Prime - **84**: Not prime (divisible by 2) - **85**: Not prime (divisible by 5) - **86**: Not prime (divisible by 2) - **87**: Not prime (divisible by 3) - **88**: Not prime (divisible by 2) - **89**: Prime Thus, the prime numbers between 80 and 90 are **83 and 89**. ### Step 3: List the multiples of 3 that are greater than 80 and less than 90. The multiples of 3 can be found by starting from the smallest multiple of 3 greater than 80 and listing them until we reach 90. The smallest multiple of 3 greater than 80 is 81 (since \(3 \times 27 = 81\)). Now, we can list the multiples of 3: - **81**: \(3 \times 27\) - **84**: \(3 \times 28\) - **87**: \(3 \times 29\) The next multiple, 90, is not included since we are looking for numbers less than 90. Thus, the multiples of 3 that are greater than 80 and less than 90 are **81, 84, and 87**. ### Summary of Results: 1. The average of 1862, 1430, and 276 is **1189.33**. 2. The prime numbers between 80 and 90 are **83 and 89**. 3. The multiples of 3 that are greater than 80 and less than 90 are **81, 84, and 87**.