Question

translate the verbal phrase and interpret, letting n represent the value(s)
fewer than three children

translate the verbal phrase. choose the correct answer below.
a. ( n = 0,1,2 )
b. ( n = -2, -1,0 )
c. ( n = 1,2 )
d. ( n = 3,4,5,6ldots )

interpret the phrase. choose the correct answer below.
a. there cannot be a negative number of children. there could be a maximum of three children, and there is no limit on the maximum number of children. children cannot be represented with a fractional number.
b. there can be a negative number of children. there could be negative two, negative one, or zero children. children cannot be represented with a fractional number.
c. there cannot be a negative number of children. there could be one or two children. children cannot be represented with a fractional number.
d. there cannot be a negative number of children. there could be zero, one, or two children. children cannot be represented with a fractional number.

Explanation:

Step1: Analyze "Fewer than three children"

The number of children \( n \) must be a non - negative integer (since you can't have a negative number of children or a fraction of a child) and less than 3. So \( n \) can be 0, 1, or 2.

Step2: Evaluate the options for translation

• Option A: \( n = 0,1,2 \) which matches our analysis.
• Option B: Negative numbers of children don't make sense, so B is wrong.
• Option C: It misses \( n = 0 \), so C is wrong.
• Option D: "n = 3,4,5,6..." are numbers greater than or equal to 3, which is the opposite of "fewer than three", so D is wrong.

Step3: Evaluate the options for interpretation

• Option A: Talks about a maximum of three children, but we need fewer than three (so maximum of 2), so A is wrong.
• Option B: Negative number of children is impossible, so B is wrong.
• Option C: Misses \( n = 0 \), so C is wrong.
• Option D: States that there can't be a negative number of children, \( n \) can be 0, 1, or 2, and children can't be a fractional number, which matches our analysis.

Answer:

For the translation: A. \( n = 0,1,2 \)
For the interpretation: D. There cannot be a negative number of children. There could be zero, one, or two children. Children cannot be represented with a fractional number.