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.
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Here are the solutions to the questions you sent. Question 3 The total wage, W, earned by a worker in a week is given by the formula W = 15h + 50, where W is the total wage in Ghana cedis and h is the number of hours worked. (i) Find the wage for 20 hours. Step 1: Substitute h = 20 into the formula. W = 15(20) + 50 Step 2: Calculate the wage. W = 300 + 50 W = 350 The wage for 20 hours is GHC 350.00. (ii) If the worker did 35 hours of work, what would be the wage? Step 1: Substitute h = 35 into the formula. W = 15(35) + 50 Step 2: Calculate the wage. W = 525 + 50 W = 575 The wage for 35 hours of work is GHC 575.00. (iii) How long will it take for the wage to reach GHC 500.00? Step 1: Set W = 500 in the formula. 500 = 15h + 50 Step 2: Subtract 50 from both sides. 500 - 50 = 15h 450 = 15h Step 3: Divide by 15 to solve for h. h = (450)/(15) h = 30 It will take 30 hours for the wage to reach GHC 500.00. Vector Problem Given p = 6 \\ -2 and q = -4 \\ 3 , find: (i) 2p - q Step 1: Calculate 2p. 2p = 2 6 \\ -2 = 2 × 6 \\ 2 × -2 = 12 \\ -4 Step 2: Subtract q from 2p. 2p - q = 12 \\ -4 - -4 \\ 3 2p - q = 12 - (-4) \\ -4 - 3 2p - q = 12 + 4 \\ -7 2p - q = 16 \\ -7 (ii) the magnitude of p. Step 1: Use the formula for the magnitude of a vector v = x \\ y , which is ||v|| = sqrt(x^2 + y^2). For p = 6 \\ -2 , x=6 and y=-2. ||p|| = sqrt(6^2 + (-2)^2) Step 2: Calculate the squares. ||p|| = sqrt(36 + 4) Step 3: Add and find the square root. ||p|| = sqrt(40) ||p|| = sqrt(4 × 10) = 2sqrt(10) The magnitude of p is 2sqrt(10). The image also shows a table with "Packages (x)" and "Customers (f)", but the question related to this table is not visible. That's 2 down. 3 left today — send the next one.