A person's adult height can be guessed from knowing his/her shoe size by the equation H= 1.6s + 4.3 where H is the person's adult height in feet and s is the persons shoe size. this equation has a margin of error of ±3.5 inches.
for the problems below, the example of the shoe size used will be size 13.
write answers rounded to 3 decimal places.
A) write an absolute value inequality (tolerance) that describes the person's possible heights. (height is in feet; error is in inches - convert inches. into feet)
b) solve the inequality and find the range of heights possible
A) To find the absolute value inequality that describes the person's possible heights, we need to consider the margin of error of ±3.5 inches. First, we convert this error into feet.
Since there are 12 inches in 1 foot, the error of ±3.5 inches can be written as ±3.5/12 feet.
Now, let's write the absolute value inequality:
|H - (1.6s + 4.3)| ≤ 3.5/12
B) To solve the inequality and find the range of heights possible, we can break down the inequality into two separate inequalities, considering both the positive and negative error:
1. H - (1.6s + 4.3) ≤ 3.5/12
2. H - (1.6s + 4.3) ≥ -3.5/12
Now we can solve each inequality separately.
For the first inequality:
H - (1.6s + 4.3) ≤ 3.5/12
H - 1.6s - 4.3 ≤ 3.5/12
Add 1.6s and 4.3 to both sides:
H ≤ 1.6s + 4.3 + 3.5/12
H ≤ 1.6s + 4.633333
For the second inequality:
H - (1.6s + 4.3) ≥ -3.5/12
H - 1.6s - 4.3 ≥ -3.5/12
Add 1.6s and 4.3 to both sides:
H ≥ 1.6s + 4.3 - 3.5/12
H ≥ 1.6s + 4.266667
Therefore, the range of possible heights is:
1.6s + 4.266667 ≤ H ≤ 1.6s + 4.633333
Now we can substitute the given shoe size, which is 13, into the equation to find the range of heights:
1.6(13) + 4.266667 ≤ H ≤ 1.6(13) + 4.633333
20.866667 ≤ H ≤ 21.633333
Therefore, the range of possible heights for a person with a shoe size 13 is approximately 20.867 feet to 21.633 feet.