To solve these problems, we will proceed step by step.
### Problem 3: Value of the Expression [tex]\(\frac{4}{11}+\frac{3}{11}-\frac{2}{11}\)[/tex]
The given expression involves three fractions with the same denominator. We can combine the numerators over the common denominator:
[tex]\[
\frac{4}{11} + \frac{3}{11} - \frac{2}{11} = \frac{4 + 3 - 2}{11} = \frac{5}{11}
\][/tex]
Therefore, the value of the expression [tex]\(\frac{4}{11} + \frac{3}{11} - \frac{2}{11}\)[/tex] is [tex]\(\frac{5}{11}\)[/tex].
### Problem 4: Total Distance Covered by a Contestant in a Race
Contestants must swim [tex]\(1 \frac{3}{8}\)[/tex] miles and then run [tex]\(7 \frac{7}{8}\)[/tex] miles. To find the total distance:
1. Convert the mixed numbers to improper fractions or decimals.
- For the swimming part:
[tex]\[
1 \frac{3}{8} = 1 + \frac{3}{8} = 1 + 0.375 = 1.375 \text{ miles}
\][/tex]
- For the running part:
[tex]\[
7 \frac{7}{8} = 7 + \frac{7}{8} = 7 + 0.875 = 7.875 \text{ miles}
\][/tex]
2. Sum these distances:
[tex]\[
1.375 \text{ miles} + 7.875 \text{ miles} = 9.25 \text{ miles}
\][/tex]
The total distance covered by the contestant in the race is:
[tex]\[
9.25 \text{ miles}
\][/tex]
### Conclusion
The correct choice for the total distance is:
D. [tex]\(9 \frac{1}{4}\)[/tex] miles
