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 the questions: 1. Work out: (5)/(7) - (3)/(7) Step 1: Since the denominators are the same, subtract the numerators. (5-3)/(7) Step 2: Simplify the numerator. (2)/(7) The result is (2)/(7). 2. Given that set Q = prime numbers less than 10 and set R = 1, 2, 3, 4, 5. List the elements of set R-Q. Step 1: List the elements of set Q. Prime numbers less than 10 are numbers greater than 1 that are only divisible by 1 and themselves. Q = \2, 3, 5, 7\ Step 2: Identify the elements that are in set R but not in set Q. R = \1, 2, 3, 4, 5\ Comparing R and Q, the elements in R that are not in Q are 1 and 4. R-Q = \1, 4\ The elements of set R-Q are \1, 4\. 3. Solve the inequality: 2x < -6. Step 1: Divide both sides of the inequality by 2. (2x)/(2) < (-6)/(2) Step 2: Simplify both sides. x < -3 The solution to the inequality is x < -3. 4. Anatoli took 1(1)/(2) hours teaching a science lesson that ended at 9:45 a.m. At what time did it start? Step 1: Convert the lesson duration to minutes. 1(1)/(2) hours = 1 hour and 30 minutes = 60 minutes + 30 minutes = 90 minutes. Step 2: Subtract the duration from the end time. End time: 9:45 a.m. Subtract 1 hour from 9:45 a.m. to get 8:45 a.m. Subtract the remaining 30 minutes from 8:45 a.m. to get 8:15 a.m. The lesson started at 8:15 a.m.. 5. Work out the mean of 11, 15, 16 and 18. Step 1: Sum the given numbers. Sum = 11 + 15 + 16 + 18 = 60 Step 2: Count the number of values. There are 4 numbers. Step 3: Calculate the mean by dividing the sum by the count. Mean = SumCount = (60)/(4) = 15 The mean of the numbers is 15. 6. The figure below represents a roundabout in Kumi District. Find its circumference. Step 1: From the figure, the radius of the roundabout is r = 7 m. Step 2: Use the formula for the circumference of a circle, C = 2 r. We will use = (22)/(7). Step 3: Substitute the value of the radius into the formula. C = 2 × (22)/(7) × 7 C = 2 × 22 C = 44 m The circumference of the roundabout is 44 m.