Final answer:
The mean of x⁴, y⁴, f⁴, d⁴, z⁴, and w⁴ is 5.
Step-by-step explanation:
To find the mean of x⁴, y⁴, f⁴, d⁴, z⁴, and w⁴, we can divide the sum of these terms by the total number of terms, which is 6. The given equation is 5x⁴ + 5y⁴ + 5f⁴ + 5d⁴ + 5z⁴ + 5w⁴ = 150.
By dividing both sides of the equation by 5, we get x⁴ + y⁴ + f⁴ + d⁴ + z⁴ + w⁴ = 30. Finally, the mean can be calculated as (x⁴ + y⁴ + f⁴ + d⁴ + z⁴ + w⁴)/6
= 30/6
= 5.