Let's examine the density values provided by Mr. Potter's physical science classes and group them based on their relation to the true density of aluminum, which is [tex]\(2.7 \, \text{g/ml}\)[/tex].
Given the density values:
- [tex]\(1^{\text{st }}\)[/tex] hour: [tex]\(3.1 \, \text{g/ml}\)[/tex]
- [tex]\(2^{\text{nd }}\)[/tex] hour: [tex]\(3.05 \, \text{g/ml}\)[/tex]
- [tex]\(3^{\text{rd }}\)[/tex] hour: [tex]\(1.9 \, \text{g/ml}\)[/tex]
- [tex]\(4^{\text{th }}\)[/tex] hour: [tex]\(2.35 \, \text{g/ml}\)[/tex]
- [tex]\(5^{\text{th }}\)[/tex] hour: [tex]\(4.2 \, \text{g/ml}\)[/tex]
- [tex]\(6^{\text{th }}\)[/tex] hour: [tex]\(4.0 \, \text{g/ml}\)[/tex]
In order to group these values based on their accuracy, determine which values are under the true density and which are over the true density:
Values under [tex]\(2.7 \, \text{g/ml}\)[/tex]:
- [tex]\(3^{\text{rd }}\)[/tex] hour: [tex]\(1.9 \, \text{g/ml}\)[/tex]
- [tex]\(4^{\text{th }}\)[/tex] hour: [tex]\(2.35 \, \text{g/ml}\)[/tex]
Values over [tex]\(2.7 \, \text{g/ml}\)[/tex]:
- [tex]\(1^{\text{st }}\)[/tex] hour: [tex]\(3.1 \, \text{g/ml}\)[/tex]
- [tex]\(2^{\text{nd }}\)[/tex] hour: [tex]\(3.05 \, \text{g/ml}\)[/tex]
- [tex]\(5^{\text{th }}\)[/tex] hour: [tex]\(4.2 \, \text{g/ml}\)[/tex]
- [tex]\(6^{\text{th }}\)[/tex] hour: [tex]\(4.0 \, \text{g/ml}\)[/tex]
By comparing these groupings with the provided choices, the correct grouping is:
Group:
- [tex]\(3^{\text{rd }}\)[/tex] and [tex]\(4^{\text{th }}\)[/tex] hours, with values under the true density
- [tex]\(1^{\text{st }}\)[/tex], [tex]\(2^{\text{nd }}\)[/tex], [tex]\(5^{\text{th }}\)[/tex], and [tex]\(6^{\text{th }}\)[/tex] hours, with values over the true density
Therefore, the best answer from the choices provided is:
b. Group: [tex]\(3^{\text{rd }}\)[/tex] and [tex]\(4^{\text{th }}\)[/tex] hours, with values under the true density
Group: [tex]\(1^{\text{st }}\)[/tex], [tex]\(2^{\text{nd }}\)[/tex], [tex]\(5^{\text{th }}\)[/tex], and [tex]\(6^{\text{th }}\)[/tex] hours, with values over the true density
