To determine which algebraic expression represents the phrase "the product of 50 and the number of employees," let's break down the phrase step-by-step.
1. Understand the Phrase:
- The phrase consists of two parts: "the product of 50" and "the number of employees."
- "The product of" indicates a multiplication operation.
2. Identify the Key Parts:
- 50 is the first part of the multiplication.
- "The number of employees" suggests an unknown quantity, which we typically represent with a variable, say [tex]\( n \)[/tex].
3. Form the Expression:
- To express "the product of 50 and [tex]\( n \)[/tex]" algebraically, we multiply 50 by [tex]\( n \)[/tex].
- In algebra, multiplication is represented by the symbol [tex]\( \cdot \)[/tex] or simply placing the variable next to the number without a symbol.
- Hence, the correct expression for "the product of 50 and the number of employees" is [tex]\( 50 \cdot n \)[/tex] or simply [tex]\( 50n \)[/tex].
4. Evaluate the Options:
- A. [tex]\(\frac{50}{n}\)[/tex] represents the division of 50 by [tex]\( n \)[/tex], which is incorrect.
- B. [tex]\(50 + n\)[/tex] represents the sum of 50 and [tex]\( n \)[/tex], which is incorrect.
- C. [tex]\(50 - n\)[/tex] represents the difference between 50 and [tex]\( n \)[/tex], which is incorrect.
- D. [tex]\(50 \cdot n\)[/tex] or [tex]\( 50n \)[/tex] represents the product of 50 and [tex]\( n \)[/tex], which is correct.
Therefore, the correct option is D. [tex]\( 50 \cdot n \)[/tex].
