This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve part (a)(i) by listing prime numbers. 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 \2, 3, 5, 7, 11\. Step 2: Solve part (a)(ii) by finding the probability of selecting a non-prime number. 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: 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(not prime) = Number of non-prime numbersTotal number of elements = (6)/(11) The probability is (6)/(11). Step 3: Factorize the expression in part (b). 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) [ (2m-n) - m ] 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 (x+y)(m-n). Step 4: Calculate the amount earned by the typist in part (c). 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: Additional sheets = 35 - 8 = 27 sheets The charge for each additional sheet is GH¢ 11.00. The cost for the additional sheets is: Cost for additional sheets = 27 × GH¢ 11.00 = 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: Total amount earned = GH¢ 68.00 + GH¢ 297.00 = GH¢ 365.00 The total amount earned is GH¢ 365.00. That's 2 down. 3 left today — send the next one.