Solution:
We know, g(x) = f(x) + k --------(1)
It is given that f(x) =
(x+2)
and g(x) =
(x+5)
Substituting f(x) and g(x) into equation (1):
→
(x+5) =
(x+2) + k
→
= k
→ k = 
Thus, the value of k is 1.
Response: (0.8115, 0.8645)
Step-by-step outline:
Define p as the proportion of individuals who leave one space after a sentence.
Provided: Sample size: n= 525
Number of respondents indicating they leave one space: 440
Thus, the sample proportion is: 
The z-score for a 90% confidence interval is: 1.645
The formula for determining the confidence interval:


Consequently, a 90% confidence interval for the proportion of people who leave one space after a period is: (0.8115, 0.8645)