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
Here are the solutions to your questions: 2.2.1 To calculate the new bus fare, we first find the increase amount and then add it to the original fare. Step 1: Calculate the increase amount. Increase = 20\% × R15.00 = 0.20 × R15.00 = R3.00 Step 2: Calculate the new bus fare. New Fare = Original Fare + Increase = R15.00 + R3.00 = R18.00 The new bus fare that Mr Mabuza pays for a single trip is R18.00. 2.2.2 To calculate how much more Mr Mabuza will pay, we first find the total cost before and after the increase for 20 return trips. Step 1: Determine the total number of single trips per month. Total Single Trips = 20 return trips × 2 trips/return = 40 trips Step 2: Calculate the total cost per month before the increase. Cost Before = 40 trips × R15.00/trip = R600.00 Step 3: Calculate the total cost per month after the increase. Cost After = 40 trips × R18.00/trip = R720.00 Step 4: Calculate the difference in cost. Difference = Cost After - Cost Before = R720.00 - R600.00 = R120.00 Mr Mabuza will pay R120.00 more per month for the return trips after the increase. 3.1 The data set is: 48; 51; 59; 63; 69; 36; 54; 60; 63; 71; 68; 48; 37; 48; 53; 50. To find the mode, we identify the value that appears most frequently. • 48 appears 3 times. • 63 appears 2 times. • All other values appear once. The mode of the data set is 48 kg. This value is referred to as the mode because it is the mass that occurs most often among the learners. 3.2 In the context of the given data set, the median is the middle value of the learners' masses when they are arranged in ascending or descending order. It divides the data set into two equal halves. 3.3 To determine the median value, we first arrange the data set in ascending order: 36, 37, 48, 48, 48, 50, 51, 53, 54, 59, 60, 63, 63, 68, 69, 71 There are 16 data points. Since the number of data points is even, the median is the average of the two middle values (the 8th and 9th values). The 8th value is 53. The 9th value is 54. Median = (53 + 54)/(2) = (107)/(2) = 53.5 The median value is 53.5 kg. 3.4 To verify Lebohang's statement about the range, we calculate the difference between the maximum and minimum values in the data set. The ordered data set is: 36, 37, 48, 48, 48, 50, 51, 53, 54, 59, 60, 63, 63, 68, 69, 71. Maximum Value = 71 kg Minimum Value = 36 kg Range = Maximum Value - Minimum Value = 71 kg - 36 kg = 35 kg Lebohang's statement that the range of the above data set is 35 kg is valid. 3.5 To calculate the average mass (mean), we sum all the masses and divide by the number of learners. Sum of Masses = 48+51+59+63+69+36+54+60+63+71+68+48+37+48+53+50 = 918 kg Number of Learners = 16 Average Mass = Sum of MassesNumber of Learners = 918 kg16 = 57.375 kg The average mass of the data set is 57.375 kg. 3.6 The above data is continuous. This is because mass can take any value within a given range (e.g., a learner could weigh 50.1 kg, 50.15 kg, etc.), rather than being restricted to specific, distinct values. 3.7 To determine the probability of having a learner that weighs less than 50 kg, we count the number of learners whose mass is less than 50 kg and divide by the total number of learners. Learners weighing less than 50 kg are: 36, 37, 48, 48, 48. There are 5 learners with a mass less than 50 kg. Total number of learners = 16. Probability = Number of learners weighing less than 50 kgTotal number of learners = (5)/(16) Probability = 0.3125 The probability (as a decimal) of having a learner that weighs less than 50 kg is 0.3125. 3 done, 2 left today. You're making progress.