To determine which statement correctly describes the given expression [tex]\( 2m^3 - 11 \)[/tex], let's analyze each option one by one:
Given Expression:
[tex]\[ 2m^3 - 11 \][/tex]
Option A: "Twice the cube of a number subtracted from 11"
- This statement implies:
[tex]\[ 11 - 2m^3 \][/tex]
This is incorrect because it reverses the order of subtraction.
Option B: "The difference of twice the cube of a number and 11"
- This statement implies:
[tex]\[ 2m^3 - 11 \][/tex]
This matches exactly with the given expression.
Option C: "The difference of twice a number and 11 cubed"
- This statement implies:
[tex]\[ 2m - 11^3 \][/tex]
This is incorrect because it involves cubing 11 and not [tex]\( m \)[/tex], and also it's twice the number [tex]\( m \)[/tex] and not its cube.
Option D: "The cube of twice a number decreased by 11"
- This statement implies:
[tex]\[ (2m)^3 - 11 \][/tex]
This is incorrect because it involves cubing [tex]\( 2m \)[/tex] rather than [tex]\( m \)[/tex], then subtracting 11.
Conclusion:
The correct statement that describes the expression [tex]\( 2m^3 - 11 \)[/tex] is:
Option B: "The difference of twice the cube of a number and 11."
Thus, the correct choice is:
[tex]\[ \boxed{2} \][/tex]
