Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.

Find the ratio of the volume divided by the temperature for the first data pair. Use significant figures.

[tex]\[ \frac{V}{T} = \frac{0.72}{276} = 0.0026 \][/tex]

Now do the same computation for all six pairs of values. What is the average of all six fractions [tex]\( \frac{V}{T} \)[/tex]?

[tex]\[ \boxed{\text{Answer}} \][/tex]

Sagot :

GinnyAnsweridn
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]
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.