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: Q.8 Step 1: Determine the total time available. The time available is from 8 pm to 10 pm, which is 2 hours. 2 hours = 2 × 60 minutes = 120 minutes Step 2: Calculate the height one monkey can climb in the available time. The problem states that a monkey takes 5 minutes to climb "a wall". Assuming "a wall" refers to a unit of height, for example, 1 foot, then: Rate of one monkey = 1 ft5 min Height climbed by one monkey in 120 minutes = 1 ft5 min × 120 min = 24 ft Step 3: Calculate the number of monkeys needed. The total height to be climbed is 2016 ft. Number of monkeys = Total height to climbHeight climbed by one monkey in available time Number of monkeys = 2016 ft24 ft/monkey = 84 monkeys The correct option is (A). A) 84 Q.9 To round 7.887 to the nearest hundredth, we look at the digit in the thousandths place. The number is 7.887. The hundredths digit is 8. The digit to its right (in the thousandths place) is 7. Since 7 is 5 or greater, we round up the hundredths digit. Rounding 7.887 to the nearest hundredth gives 7.89. The correct option is (B). B) 7.89 Q.10 Step 1: Set up the equations. Let the two numbers be x and y. "Twice the sum of two numbers is 484": 2(x + y) = 484 x + y = (484)/(2) x + y = 242 (Equation 1) "twice the difference is 52": 2(x - y) = 52 x - y = (52)/(2) x - y = 26 (Equation 2) Step 2: Solve the system of equations. Add Equation 1 and Equation 2: (x + y) + (x - y) = 242 + 26 2x = 268 x = (268)/(2) x = 134 Substitute x = 134 into Equation 1: 134 + y = 242 y = 242 - 134 y = 108 The two numbers are 134 and 108. The smaller number is 108. Step 3: Calculate the value of the smaller number divided by 2. (108)/(2) = 54 The correct option is (D).