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.
To write an absolute value inequality to describe the rainfall in the other 10% of the past 30 years, we need to determine the maximum variation in rainfall from the mean value.
The problem states 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. Therefore, we can calculate the maximum rainfall as follows:
Maximum rainfall = Mean rainfall + Variation
= 24 + 6.5
= 30.5
So, in 90% of the last 30 years, the rainfall at Shell Beach varied from 17.5 inches (24 - 6.5) to 30.5 inches (24 + 6.5).
To represent the other 10% of the past 30 years, where the variation could exceed 6.5 inches, we can write an absolute value inequality.
Let x represent the variation in rainfall from the mean value. We want to find the range of x where the variation exceeds 6.5 inches.
Mathematically, the absolute value inequality can be written as:
|x| > 6.5
This absolute value inequality states that the absolute value of x is greater than 6.5, indicating that the variation in rainfall exceeds 6.5 inches.
To solve this inequality, we can break it down into two separate inequalities:
x > 6.5 or x < -6.5
These inequalities represent the range of variation that exceeds 6.5 inches in either the positive or negative direction.
Therefore, the absolute value inequality to describe the rainfall in the other 10% of the past 30 years is:
x > 6.5 or x < -6.5