The United States postal service charges a "nonmachinable surcharge" for first class mail if the length of the envlope (parallel to the address) divided by the height of the envolope is less than 1.3 or more than 2.5. Charlene has an envelope with the height of 3.5in. Write a compound inequality to show the lenghts in inches for which charlene will have to pay the surcharge.
we know the surcharge applies if
l/h < 1.3 or l/h > 2.5
so, with h=3.5, we find that
l/3.5 < 1.3 or l/3.5 > 2.5
that is,
l<4.55 or l>8.75
ThankYou
To determine the lengths in inches for which Charlene will have to pay the surcharge, we can write a compound inequality using the given conditions.
Let's assume the length of the envelope is represented by the variable "L" (in inches).
According to the given conditions, the envelope will be subject to the surcharge if the length divided by the height is less than 1.3 or more than 2.5.
Therefore, the compound inequality to show the lengths in inches for which Charlene will have to pay the surcharge can be expressed as:
1.3 < L/3.5 < 2.5
To determine the lengths in inches for which Charlene will have to pay the surcharge, we can set up a compound inequality using the given conditions.
Let's denote the length of the envelope as "L" (in inches) and the height of the envelope as "H" (in inches):
- The condition "the length of the envelope divided by the height is less than 1.3" can be expressed as L/H < 1.3.
- The condition "the length of the envelope divided by the height is more than 2.5" can be expressed as L/H > 2.5.
Given that the height of Charlene's envelope is 3.5 inches (H = 3.5), we substitute this value into the compound inequality:
1.3 < L/3.5 < 2.5
Therefore, the compound inequality representing the lengths in inches for which Charlene will have to pay the surcharge is 1.3 < L/3.5 <2.5.