In Anchorage, Alaska, the temperature was [tex]$-12^{\circ} F$[/tex]. At the same time, in Miami, Florida, the temperature was [tex]$76^{\circ} F$[/tex].

Which expression represents the difference in temperatures?

A. [tex]$-12 - 76$[/tex]

B. [tex]$|-12| - 76$[/tex]

C. [tex]$-12 - |76|$[/tex]

D. [tex]$|-12 - 76|$[/tex]

Answer :

To find the difference in temperatures between Anchorage, Alaska, and Miami, Florida, we need to determine how much one temperature is from the other.

1. Identify the Temperatures:
- The temperature in Anchorage, Alaska, is [tex]\(-12^\circ F\)[/tex].
- The temperature in Miami, Florida, is [tex]\(76^\circ F\)[/tex].

2. Calculate the Difference:
- The difference in temperature is calculated by subtracting the temperature in Miami from the temperature in Anchorage:

[tex]\[
\text{Difference} = -12 - 76
\][/tex]

3. Calculate the Result:
- [tex]\(-12 - 76\)[/tex] equals [tex]\(-88\)[/tex]. This means there is an 88-degree difference, but it's negative because Anchorage is colder than Miami.

4. Absolute Value for Actual Difference:
- The absolute value of the difference gives us the actual magnitude without regard to direction:

[tex]\[
\text{Absolute Difference} = |-12 - 76| = | -88 | = 88
\][/tex]

The expression [tex]\( |-12 - 76| \)[/tex] represents the difference in temperatures, indicating a positive difference of 88 degrees. Therefore, the correct answer is option D: [tex]\( |-12 - 76| \)[/tex].