The set is K = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\. (a) List the prime numbers in K. (b) Calculate the probability of selecting a non-prime number from K. (c) Factorize (x+y)(2m-n) - m(x+y).

The set $K = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The prime numbers in set $K$ are:

• 2 (divisors: 1, 2)
• 3 (divisors: 1, 3)
• 5 (divisors: 1, 5)
• 7 (divisors: 1, 7)
• 11 (divisors: 1, 11)

The list of prime numbers in $K$ is $\boxed{\{2, 3, 5, 7, 11\}}$.

Total number of elements in set $K$ is 11.
From part (a)(i), the number of prime numbers in $K$ is 5.
The number of non-prime numbers in $K$ is the total number of elements minus the number of prime numbers:

$$\text{Number of non-prime numbers} = 11 - 5 = 6$$

The probability of selecting a non-prime number is the ratio of the number of non-prime numbers to the total number of elements:

$$P(\text{not prime}) = \frac{\text{Number of non-prime numbers}}{\text{Total number of elements}} = \frac{6}{11}$$

The probability is $\boxed{\frac{6}{11}}$.

The expression is $(x+y)(2m-n) - m(x+y)$.
Notice that $(x+y)$ is a common factor in both terms. We can factor it out:

$$(x+y)(2m-n) - m(x+y) = (x+y) \left[ (2m-n) - m \right]$$

Now, simplify the terms inside the square brackets:

$$(x+y) (2m - n - m)$$

Combine the $m$ terms:

$$(x+y) (m - n)$$

The completely factorized expression is $\boxed{(x+y)(m-n)}$.

The typist typed a total of 35 sheets.
The charge for the first 8 sheets is GH¢ 68.00.
The number of additional sheets is the total sheets minus the first 8 sheets:

$$\text{Additional sheets} = 35 - 8 = 27 \text{ sheets}$$

The charge for each additional sheet is GH¢ 11.00.
The cost for the additional sheets is:

$$\text{Cost for additional sheets} = 27 \times \text{GH¢ } 11.00 = \text{GH¢ } 297.00$$

The total amount earned is the sum of the charge for the first 8 sheets and the charge for the additional sheets:

$$\text{Total amount earned} = \text{GH¢ } 68.00 + \text{GH¢ } 297.00 = \text{GH¢ } 365.00$$

The total amount earned is $\boxed{\text{GH¢ } 365.00}$.