Solve the equation 1-4x / 3 = (3x-5)/2 and find the mode, median, and mean of the scores from the table.

Here are the solutions to the problems. 1. A. The table shows the scores (m) and their frequencies (f): Scores (m) | Freq. (f) ------------|---------- 1 | 8 2 | 4 3 | 4 4 | 2 5 | 2 The total number of students is the sum of frequencies: N = 8 + 4 + 4 + 2 + 2 = 20 a) Find the mode Step 1: Identify the score with the highest frequency. The highest frequency is 8, which corresponds to a score of 1. The mode is the value that appears most frequently in a data set. Mode = 1 b) Find the median Step 1: Determine the position of the median. Since the total number of data points N=20 (an even number), the median is the average of the ((N)/(2))-th and ((N)/(2)+1)-th values. The positions are the (20)/(2) = 10-th and (20)/(2)+1 = 11-th values. Step 2: Find the values at these positions using cumulative frequencies. • Scores of 1 account for the 1st to 8th values. • Scores of 2 account for the 9th to 12th values (8+4=12). Both the 10th and 11th values are 2. Step 3: Calculate the median. Median = 10th value + 11th value2 = (2+2)/(2) = (4)/(2) = 2 c) Find the mean of the scores Step 1: Calculate the sum of (score × frequency). (m × f) = (1 × 8) + (2 × 4) + (3 × 4) + (4 × 2) + (5 × 2) (m × f) = 8 + 8 + 12 + 8 + 10 = 46 Step 2: Calculate the mean using the formula Mean = ( (m × f))/( f). Mean = (46)/(20) = 2.3 2. A. Solve the equation (3x-5)/(1-4x) = (2)/(3). Step 1: Cross-multiply to eliminate the denominators. 3(3x-5) = 2(1-4x) Step 2: Distribute the numbers on both sides of the equation. 9x - 15 = 2 - 8x Step 3: Collect all terms with x on one side and constant terms on the other side. 9x + 8x = 2 + 15 17x = 17 Step 4: Isolate x by dividing both sides by 17. x = (17)/(17) x = 1 Send me the next one 📸