Question

translate the verbal phrase and interpret, letting n represent the value(s). sixteen occupants or less.

translate the verbal phrase. choose the correct answer below

a. ( n = 0,1,2,3, dots, 16 )

b. ( n = 1,2,3, dots, 16 )

c. ( n = -16, -15, -14, -13, dots, 0 )

d. ( n = 16,17,18,19, dots )

interpret the phrase. choose the correct answer below

a. there can be a negative number of occupants. there could be negative sixteen, negative fifteen, ... or zero occupants. occupants cannot be represented with a fractional number.

b. there cannot be a negative number of occupants. there could be zero, one, two, ... or sixteen occupants. occupants cannot be represented with a fractional number.

c. there cannot be a negative number of occupants. there could be one, two, ... or sixteen occupants. occupants cannot be represented with a fractional number.

d. there cannot be a negative number of occupants. there could be a minimum of sixteen occupants, and there is no limit on the maximum number of occupants. occupants cannot be represented with a fractional number

Explanation:

Step 1: Translate "Sixteen occupants or less"

The phrase "sixteen occupants or less" means the number of occupants \( n \) can be 0, 1, 2, ..., up to 16 (since you can't have a negative number of occupants, and 0 is a valid number of occupants, like an empty space). Let's check the options:

• Option A: \( n = 0,1,2,\dots,16 \) – this includes 0 up to 16, which matches "or less" (including 0 and up to 16).
• Option B: \( n = 1,2,3,\dots,16 \) – this starts at 1, but 0 occupants is possible (e.g., an empty room), so B is wrong.
• Option C: \( n = -16,-15,-14,-13,\dots,0 \) – negative occupants don't make sense, so C is wrong.
• Option D: \( n = 16,17,18,19,\dots \) – this is 16 or more, which is the opposite of "or less", so D is wrong. So the correct translation is A.

Step 2: Interpret "Sixteen occupants or less"

Now, interpreting the phrase:

• Occupants can't be negative (you can't have -5 occupants).
• "Or less" means up to 16, including 0, 1, ..., 16. Occupants are whole numbers (can't have a fraction of an occupant). Let's check the options:
• Option A: Says negative occupants are possible – wrong, since you can't have negative people.
• Option B: "There cannot be a negative number of occupants. There could be zero, one, two, ... or sixteen occupants. Occupants cannot be represented with a fractional number." – this matches: no negatives, includes 0 up to 16, and whole numbers.
• Option C: Starts at 1 – but 0 is possible, so C is wrong.
• Option D: Says minimum of 16 and no limit on maximum – that's "16 or more", opposite of "or less", so D is wrong. So the correct interpretation is B.

Answer:

Translation: A. \( n = 0,1,2,\dots,16 \)
Interpretation: B. There cannot be a negative number of occupants. There could be zero, one, two, ... or sixteen occupants. Occupants cannot be represented with a fractional number.