Sure! Let's relate and perform the necessary conversions for each given item step-by-step:
1. 478: This number appears to be in base 10 and does not require any conversion. Its relation is simply:
- Relation: 478
2. [tex]\(\overline{10a}\)[/tex]: There is not enough information provided to solve this part. The value is not specified clearly or some data might be missing.
- Relation: Not Determinable
3. [tex]\(\overline{40a}_{(5)}\)[/tex]: This number seems to be in base 5, but 'a' is not a valid digit in base 5. Therefore, this cannot be determined.
- Relation: Not Valid
4. 19: This number is in base 10 and does not require any conversion. Its relation is simply:
- Relation: 19
5. [tex]\(18_{(9)}\)[/tex]: We need to convert this number from base 9 to base 10. The conversion results in the number 17.
- Relation: 17
6. [tex]\(\left(1000_{(2)}\right)^2\)[/tex]: We first convert [tex]\(1000_{(2)}\)[/tex] (base 2) to base 10, which is 8. Then we square it: [tex]\(8^2 = 64\)[/tex].
- Relation: 64
7. [tex]\(3_{(10)} 5_{(11)}\)[/tex]: The first number 3 is already in base 10, so it remains 3. The second number 5 from base 11 converts to base 10 is simply 5.
- Relation: 3 and 5
8. [tex]\(25_{(7)}\)[/tex]: We need to convert this number from base 7 to base 10. The conversion results in the number 19.
- Relation: 19
9. 17: This number is in base 10 and does not require any conversion. Its relation is simply:
- Relation: 17
So, summarizing all the relations:
1. [tex]\(478\)[/tex] relates to 478
2. [tex]\(\overline{10a}\)[/tex] is Not Determinable
3. [tex]\(\overline{40a}_{(5)}\)[/tex] is Not Valid
4. [tex]\(19\)[/tex] relates to 19
5. [tex]\(18_{(9)}\)[/tex] relates to 17
6. [tex]\(\left(1000_{(2)}\right)^2\)[/tex] relates to 64
7. [tex]\(3(10) 5_{(11)}\)[/tex] relates to 3 and 5
8. [tex]\(25(7)\)[/tex] relates to 19
9. [tex]\(17\)[/tex] relates to 17
These are the correct corresponding values and relations.
