the freshman class ranges in height from 4'8"-6'. Write a compound inequality for the height of a freshman "f". Then write it as an absolut value inequality.
Hmm. I think I know the compound. Isn't that just 4'8" is less than or equal to 'F' is less then or equal to 6'?
4'8" ≤ f ≤ 6'
An absolute value is the distance from zero.
By translating the zero to the middle of the range of heights, the above inequality can be transformed into one with only one inequality sign using absolute value.
Average of range
=(4'8" + 6')/2 = 5'4"
Half of range
=(6'-4'8")/2= 8"
The absolute value inequality
= |f-5'4"| ≤ 8"
To write a compound inequality for the height of a freshman "f," given that the range of heights is from 4'8" to 6', we can use the inequality symbols to represent the height range as follows:
4'8" is equivalent to 4 + 8/12 = 4 + 2/3 = 4.67 feet,
and 6' is equivalent to 6 feet.
So, the compound inequality for the height of a freshman "f" is:
4.67 ≤ f ≤ 6.
To rewrite this compound inequality as an absolute value inequality, we need to find the midpoint of the interval between 4.67 and 6. The midpoint can be found by averaging the two endpoints:
Midpoint = (4.67 + 6) / 2 = 10.67 / 2 = 5.335.
Now, we can express the absolute value inequality by taking the absolute value of the difference between the height "f" and the midpoint, and setting it less than or equal to the distance between the midpoint and one of the endpoints:
|f - 5.335| ≤ 6 - 5.335.
Simplifying this, we get:
|f - 5.335| ≤ 0.665.
Therefore, the absolute value inequality for the height of a freshman "f" is:
|f - 5.335| ≤ 0.665.