Certainly! Let's translate the verbal phrase "The number of ducks in the pond, [tex]\( d \)[/tex], is between 14 and 19" into a mathematical expression step-by-step.
1. Identify the variable and the range: The problem refers to the number of ducks in the pond and denotes it by the variable [tex]\( d \)[/tex].
2. Understand the phrase "between 14 and 19": This phrase implies that [tex]\( d \)[/tex] is greater than 14 but less than 19. It is not inclusive of 14 and 19 - in other words, [tex]\( d \)[/tex] lies strictly within the bounds of 14 and 19.
3. Write the mathematical expression: The correct way to express that a variable lies strictly between two numbers is by using inequalities. Therefore, the appropriate mathematical expression is:
[tex]\[ 14 < d < 19 \][/tex]
This reads as "14 is less than [tex]\( d \)[/tex] and [tex]\( d \)[/tex] is less than 19," accurately capturing the given verbal phrase.
