Given the problem, we need to identify the correct statements about the array [tex]\( M \)[/tex].
### Step-by-Step Solution:
1. Find the Length of Array [tex]\( M \)[/tex] and Ensure [tex]\( M[5] \)[/tex] Exists:
The description indicates that [tex]\( M \)[/tex] has a length of [tex]\( B \)[/tex] such that [tex]\( M[5] \)[/tex] exists and has the value 50. Therefore, the smallest possible value of [tex]\( B \)[/tex] must be at least 6 (since [tex]\( M[5] \)[/tex] would be the 6th element, considering a 1-indexed array).
- [tex]\( B = 6 \)[/tex]
2. Known Value of [tex]\( M[5] \)[/tex]:
The value at position [tex]\( M[5] \)[/tex] is given as 50.
- [tex]\( M[5] = 50 \)[/tex]
3. Sum of [tex]\( M[1] + M[3] \)[/tex]:
We are given that the sum of the values at positions [tex]\( M[1] \)[/tex] and [tex]\( M[3] \)[/tex] is 60. While the individual values of [tex]\( M[1] \)[/tex] and [tex]\( M[3] \)[/tex] are not given, we know their sum.
- [tex]\( M[1] + M[3] = 60 \)[/tex]
Based on these given points, the array [tex]\( M \)[/tex] can be represented as having the following properties for a minimum length [tex]\( B = 6 \)[/tex]:
[tex]\[
M = [M[1], M[2], M[3], M[4], M[5], M[6]]
\][/tex]
where:
[tex]\[
M[5] = 50
\][/tex]
[tex]\[
M[1] + M[3] = 60
\][/tex]
### Conclusion:
- The length of array [tex]\( M \)[/tex] is at least 6.
- [tex]\( M[5] = 50 \)[/tex]
- [tex]\( M[1] + M[3] = 60 \)[/tex]
Any of these statements are considered correct:
1. The length of the array [tex]\( M \)[/tex] is 6.
2. The value at [tex]\( M[5] \)[/tex] is 50.
3. The sum of [tex]\( M[1] + M[3] \)[/tex] is 60.
