In 90% of the last 30 years, the rainfall at shell beach has varied no more than 6.5 of its mean value of 24 inches. Write and solve an absolute value inequality to describe the rainfall in the other 10% of the past 30 years. how do I do this problem and what is the answer?

To solve this problem, we need to first understand the given information. We know that in 90% of the last 30 years, the rainfall at Shell Beach has varied no more than 6.5 inches from its mean value of 24 inches. This means that 90% of the time, the rainfall was between 24 - 6.5 = 17.5 inches and 24 + 6.5 = 30.5 inches.

We need to find the range of rainfall in the remaining 10% of the past 30 years. Let's call this range "x". To write an absolute value inequality, we can use the following equation:

|rainfall - mean| ≤ x

Since we want to find the range of rainfall, we are looking for the maximum value of x. In this case, the maximum value of x will be when the rainfall varies the most from the mean. Therefore, we can set the value of x equal to the difference between the maximum and minimum rainfall values.

The maximum value of rainfall would occur when it is either below 17.5 inches or above 30.5 inches.

Therefore, the absolute value inequality to describe the rainfall in the other 10% of the past 30 years would be:

|rainfall - 24| > 30.5 - 17.5

Simplifying:

|rainfall - 24| > 13

This means that the absolute difference between the rainfall and the mean value of 24 needs to be greater than 13.

In conclusion, the absolute value inequality is |rainfall - 24| > 13.

To find the answer, you would need to analyze historical data or consult further information about Shell Beach's rainfall to determine the range of the remaining 10% of rainfall in the past 30 years.