To solve the problem of listing the given absolute values from least to greatest, we need to follow several steps. Here are the detailed steps:
1. Identify the absolute values of the given numbers.
2. List out the values numerically: [tex]$|41|, |37|, |-16|, |-27|$[/tex]
3. Calculate the absolute values to convert all values to positive magnitudes as follows:
- The absolute value of [tex]$41$[/tex] is [tex]$41$[/tex].
- The absolute value of [tex]$37$[/tex] is [tex]$37$[/tex].
- The absolute value of [tex]$-16$[/tex] is [tex]$16$[/tex].
- The absolute value of [tex]$-27$[/tex] is [tex]$27$[/tex].
4. Now that we have the absolute values, we should list them in ascending order:
- [tex]$16$[/tex]
- [tex]$27$[/tex]
- [tex]$37$[/tex]
- [tex]$41$[/tex]
5. Compare the sorted list of absolute values with the given answer choices to find the correct sequence:
- A. [tex]$|-16|, |-27|, |37|, |41|$[/tex] translates to [tex]$16, 27, 37, 41$[/tex]
- B. [tex]$|-16|, |-27|, |41|, |37|$[/tex] translates to [tex]$16, 27, 41, 37$[/tex]
- C. [tex]$|-16|, |41|, |-27|, |37|$[/tex] translates to [tex]$16, 41, 27, 37$[/tex]
- D. [tex]$|-16|, |37|, |-27|, |-41|$[/tex] translates to [tex]$16, 37, 27, 41$[/tex]
By checking these sequences against the sorted order [tex]$16, 27, 37, 41$[/tex], it is clear that the correct choice is:
A. [tex]$|-16|, |-27|, |37|, |41|$[/tex]
Thus, listing the given values from least to greatest is:
[tex]$
|16|, |-27|, |37|, |41|
$[/tex]
