To solve this problem, we first need to understand the context provided by the question and the options given. We're asked to choose an answer that relates to the statement about the density of air being 20 grams per cubic meter. Let's analyze each of the provided options and assess their relevance and appropriateness in this context.
Option A: [tex]$11.69\%$[/tex]
This option presents a percentage value. In the context of air density or other atmospheric measurements, percentages often refer to relative humidity, concentration rates, or other similar measurements. Given that the problem involves a numeric measure (20 grams per cubic meter), this percentage might be a fitting answer if the question pertains to a proportion or concentration measure.
Option B: [tex]$11.6 g / mm^3$[/tex]
This option gives a density measurement in grams per cubic millimeter ([tex]$g/mm^3$[/tex]). We need to consider if it makes logical sense alongside the provided context of 20 grams per cubic meter:
- 1 cubic meter ([tex]$m^3$[/tex]) is equal to [tex]\(1,000,000,000\)[/tex] cubic millimeters ([tex]$mm^3$[/tex]).
- Converting 20 grams per cubic meter to grams per cubic millimeter:
[tex]\[ 20 \text{ grams per cubic meter} = 20 \times 10^{-9} \text{ grams per cubic millimeter} \][/tex]
Therefore, 11.6 grams per cubic millimeter is an extremely high density and does not seem reasonable given the context.
Option C: 12.7646
This option provides a raw numerical value without units. It’s unclear how 12.7646 relates to the density mentioned in the problem. As it stands alone without context or units, it cannot be directly compared or validated.
Option D: [tex]$12.76 g^3 m^3$[/tex]
This option presents units that do not make typical physical sense. It combines units of mass ([tex]$g$[/tex]) and volume ([tex]$m^3$[/tex]) incorrectly; [tex]$g^3 m^3$[/tex] is not a standard or meaningful unit in this context and is thus implausible.
After evaluating all options:
- Option A, [tex]$11.69\%$[/tex], is the most plausible and reasonable answer given typical applications in atmospheric science (such as relative humidity).
Therefore, the correct answer is:
A. [tex]$11.69\%$[/tex]
