Final answer:
To find the sum of all single-digit replacements for n that make the number divisible by 3, add all the single-digit numbers together.
Step-by-step explanation:
To determine the sum of all single-digit replacements for n such that the number 42,789,n37 is divisible by 3, we need to find the values of n that make the sum of the digits of the given number divisible by 3.
Since the sum of the digits 4+2+7+8+9+3+7 = 40, which is divisible by 3, any single-digit replacement for n will maintain the divisibility by 3.
Therefore, the sum of all single-digit replacements for n is 0+1+2+3+4+5+6+7+8+9 = 45.