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
Hey dinmulitawkalu — ready when you are. Find the value of x in the diagram. Step 1: Identify the parallel lines and transversals. The arrows indicate two parallel lines. Step 2: Draw an auxiliary line through the vertex of angle x that is parallel to the two given parallel lines. This divides angle x into two parts, let's call them and . Step 3: Use the property of alternate interior angles. The angle 35^ is an alternate interior angle to the upper part of x. So, = 35^. The angle 130^ is an exterior angle. The interior angle adjacent to it is 180^ - 130^ = 50^. This 50^ angle is an alternate interior angle to the lower part of x. So, = 50^. Step 4: Add the two parts to find x. x = + x = 35^ + 50^ x = 85^ The final answer is C. 85^. 48. Find the median. Step 1: Calculate the total number of students ( f). f = 2 + 1 + 4 + 3 + 8 + 5 + 4 + 3 = 30 Step 2: Determine the position of the median. Since the total number of students is even (N=30), the median is the average of the (N)/(2)-th and ((N)/(2) + 1)-th values. (N)/(2) = (30)/(2) = 15 (N)/(2) + 1 = 15 + 1 = 16 So, we need the 15th and 16th values. Step 3: Create a cumulative frequency table to find the values. • For 1 subject: 2 students (CF = 2) • For 2 subjects: 1 student (CF = 2 + 1 = 3) • For 3 subjects: 4 students (CF = 3 + 4 = 7) • For 4 subjects: 3 students (CF = 7 + 3 = 10) • For 5 subjects: 8 students (CF = 10 + 8 = 18) The 15th and 16th values both fall within the "5 subjects" category, as the cumulative frequency reaches 18 at this point. Step 4: Calculate the median. Median = (5 + 5)/(2) = (10)/(2) = 5 The final answer is B. 5. 49. Calculate the mean of the distribution. Step 1: Calculate the sum of the product of the number of subjects (x) and the number of students (f), i.e., (x · f). (x · f) = (1 × 2) + (2 × 1) + (3 × 4) + (4 × 3) + (5 × 8) + (6 × 5) + (7 × 4) + (8 × 3) (x · f) = 2 + 2 + 12 + 12 + 40 + 30 + 28 + 24 (x · f) = 150 Step 2: Use the formula for the mean of a frequency distribution: Mean = ( (x · f))/( f). We already found f = 30 in question 48. Step 3: Calculate the mean. Mean = (150)/(30) = 5 The final answer is B. 5. Send me the next one 📸