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
a) Step 1: List all elements in set K. The set K = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\. a)(i) Step 2: Identify prime numbers in K. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers in K are 2, 3, 5, 7, 11. The list of prime numbers in K is: \2, 3, 5, 7, 11\ a)(ii) Step 3: Determine the total number of elements and the number of non-prime numbers in K. Total number of elements in K is 11. Number of prime numbers in K is 5. Number of non-prime numbers = Total elements - Number of prime numbers = 11 - 5 = 6. The non-prime numbers are \1, 4, 6, 8, 9, 10\. Step 4: Calculate the probability that a number selected at random from K is not a prime number. Probability (not prime) = Number of non-prime numbersTotal number of elements P(not prime) = (6)/(11) The probability is: (6)/(11) b) Step 1: Write the expression to be factorized. (x+y)(2m-n) - m(x+y) Step 2: Identify the common factor and factor it out. The common factor is (x+y). (x+y)[(2m-n) - m] Step 3: Simplify the expression inside the square brackets. (x+y)[2m - n - m] (x+y)[m - n] The completely factorized expression is: (x+y)(m-n) c) Step 1: Calculate the number of additional sheets typed. Total sheets typed = 35. First 8 sheets. Additional sheets = Total sheets - First 8 sheets = 35 - 8 = 27 sheets. Step 2: Calculate the cost for the additional sheets. Charge per additional sheet = GH¢ 11.00. Cost for additional sheets = 27 sheets × GH¢ 11.00/sheet = GH¢ 297.00. Step 3: Calculate the total amount earned. Charge for the first 8 sheets = GH¢ 68.00. Total amount earned = Charge for first 8 sheets + Cost for 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.