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Mr. Potter's physical science classes conducted an experiment to determine the density of aluminum. Here are the density values each class period came up with:

- [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]

If aluminum's true density is [tex]$2.7 \, \text{g/ml}$[/tex], how would you group the class values based on accuracy?

A. Group: [tex]$1^{\text{st}}$[/tex], [tex]$3^{\text{rd}}$[/tex], [tex]$5^{\text{th}}$[/tex], and [tex]$6^{\text{th}}$[/tex] hours, with one recorded decimal place in their values.

Group: [tex]$2^{\text{nd}}$[/tex] and [tex]$4^{\text{th}}$[/tex] hours, with two recorded decimal places in their values.

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.

C. Group: [tex]$3^{\text{rd}}$[/tex] hour, with a value of 1.

Group: [tex]$4^{\text{th}}$[/tex] hour, with a value of 2.

Group: [tex]$1^{\text{st}}$[/tex] and [tex]$2^{\text{nd}}$[/tex] hours, with a value of 3.

Group: [tex]$5^{\text{th}}$[/tex] and [tex]$6^{\text{th}}$[/tex] hours, with a value of 4.

D. Group all classes as accurate.

Sagot :

To solve this problem, we must group the class periods according to their density values relative to the true density of aluminum, which is [tex]$2.7 \, \text{g/ml}$[/tex]. Here’s a detailed step-by-step solution:

1. List the given density values for each class period:
- [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]

2. Identify the true density value:
- True density of aluminum: [tex]\(2.7 \, \text{g/ml}\)[/tex]

3. Compare each class period's density value with the true density:
- [tex]\(1^{\text{st}}\)[/tex] hour: [tex]\(3.1 \, \text{g/ml}\)[/tex] (greater than [tex]\(2.7 \, \text{g/ml}\)[/tex])
- [tex]\(2^{\text{nd}}\)[/tex] hour: [tex]\(3.05 \, \text{g/ml}\)[/tex] (greater than [tex]\(2.7 \, \text{g/ml}\)[/tex])
- [tex]\(3^{\text{rd}}\)[/tex] hour: [tex]\(1.9 \, \text{g/ml}\)[/tex] (less than [tex]\(2.7 \, \text{g/ml}\)[/tex])
- [tex]\(4^{\text{th}}\)[/tex] hour: [tex]\(2.35 \, \text{g/ml}\)[/tex] (less than [tex]\(2.7 \, \text{g/ml}\)[/tex])
- [tex]\(5^{\text{th}}\)[/tex] hour: [tex]\(4.2 \, \text{g/ml}\)[/tex] (greater than [tex]\(2.7 \, \text{g/ml}\)[/tex])
- [tex]\(6^{\text{th}}\)[/tex] hour: [tex]\(4.0 \, \text{g/ml}\)[/tex] (greater than [tex]\(2.7 \, \text{g/ml}\)[/tex])

4. Group the class periods based on whether their recorded density is under the true density or over the true density:
- Values under the true density:
- [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 the true density:
- [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]

Given these groupings, the correct answer among the provided options is:
b. Group: [tex]\(3^{\text{rd}}\)[/tex] and [tex]\(4^{\text{th}}\)[/tex] hours, with values under the true density
Group: [tex]\(1^{\text{st}} \cdot 2^{\text{nd}} \cdot 5^{\text{th}}\)[/tex] and [tex]\(6^{\text{th}}\)[/tex] hours, with values over the true density

Therefore, the answer to the question is:

Option (b) is correct.
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