Question

The arithmetic mean of three numbers is greater than 11. The first number is -4, the second is 30, and the third is n. How big is n?

Answer 1

The value of the third number, represented by n, must be greater than 7 for the arithmetic mean of the three numbers to be greater than 11.

Step-by-step explanation:

The question asks to calculate the value of a third number, represented by n, given that the arithmetic mean of three numbers is greater than 11, and the first two numbers are -4 and 30. To solve for n, we use the formula for the arithmetic mean with the provided values.

The arithmetic mean of -4, 30, and n can be found by the formula:

Arithmetic Mean = (Sum of all numbers) / (Number of numbers)

In this case, we have:

Arithmetic Mean = (-4 + 30 + n) / 3 > 11

After calculating the sum and simplifying, we get:

-4 + 30 + n > 33

n > 33 - 26

n > 7

Therefore, the value of n must be greater than 7 for the arithmetic mean of the three numbers to be greater than 11.

Answer 2

The arithmetic mean of three numbers is greater than 11. The first number is -4, the second is 30, and the third is n. The value of n is greater than 7.

Step-by-step explanation:

The arithmetic mean of three numbers is the sum of the numbers divided by the total number of numbers. In this case, the sum of the three numbers is -4 + 30 + n. To find the arithmetic mean, we need to divide this sum by 3. We know that the mean is greater than 11, so we can set up an inequality: -4 + 30 + n / 3 > 11. Multiplying both sides of the inequality by 3 gives us -4 + 30 + n > 33. Simplifying, we get 26 + n > 33. Subtracting 26 from both sides, we get n > 7.