To solve the problem, we need to find the ratio of volume ([tex]\( V \)[/tex]) to temperature ([tex]\( T \)[/tex]) for each given data pair. Then, we will calculate the average of these six ratios. Here is the step-by-step solution:
### Given Data
The data pairs are:
1. [tex]\( (V_1, T_1) = (0.72, 276) \)[/tex]
2. [tex]\( (V_2, T_2) = (1.0, 290) \)[/tex]
3. [tex]\( (V_3, T_3) = (0.57, 190) \)[/tex]
4. [tex]\( (V_4, T_4) = (1.1, 310) \)[/tex]
5. [tex]\( (V_5, T_5) = (1.2, 330) \)[/tex]
6. [tex]\( (V_6, T_6) = (0.85, 250) \)[/tex]
### Calculating the Ratios
1. For the first pair:
[tex]\[
\frac{V_1}{T_1} = \frac{0.72}{276} = 0.002608695652173913
\][/tex]
2. For the second pair:
[tex]\[
\frac{V_2}{T_2} = \frac{1.0}{290} = 0.0034482758620689655
\][/tex]
3. For the third pair:
[tex]\[
\frac{V_3}{T_3} = \frac{0.57}{190} = 0.0029999999999999996
\][/tex]
4. For the fourth pair:
[tex]\[
\frac{V_4}{T_4} = \frac{1.1}{310} = 0.0035483870967741938
\][/tex]
5. For the fifth pair:
[tex]\[
\frac{V_5}{T_5} = \frac{1.2}{330} = 0.0036363636363636364
\][/tex]
6. For the sixth pair:
[tex]\[
\frac{V_6}{T_6} = \frac{0.85}{250} = 0.0034
\][/tex]
### Ratios List
The calculated ratios are:
[tex]\[
[0.002608695652173913, 0.0034482758620689655, 0.0029999999999999996, 0.0035483870967741938, 0.0036363636363636364, 0.0034]
\][/tex]
### Calculating the Average Ratio
To find the average of these ratios, we sum them up and divide by the number of data pairs (which is 6):
[tex]\[
\text{Average Ratio} = \frac{0.002608695652173913 + 0.0034482758620689655 + 0.0029999999999999996 + 0.0035483870967741938 + 0.0036363636363636364 + 0.0034}{6}
\][/tex]
Summing the ratios:
[tex]\[
0.002608695652173913 + 0.0034482758620689655 + 0.0029999999999999996 + 0.0035483870967741938 + 0.0036363636363636364 + 0.0034 = 0.019641722006944708
\][/tex]
Average ratio:
[tex]\[
\frac{0.019641722006944708}{6} = 0.003273620374563451
\][/tex]
### Conclusion
The calculations show the average ratio of volume to temperature for the given data pairs is:
[tex]\[
\text{Average Ratio} = 0.003273620374563451
\][/tex]
