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
Step 1: Classify numbers as odd or even. An even number has a last digit of 0, 2, 4, 6, or 8. An odd number has a last digit of 1, 3, 5, 7, or 9. a) The number is 201,356,479,373,608. The last digit is 8. Therefore, 201,356,479,373,608 is an even number. b) The numbers are 4643, 6592, 9999, 15656, 108791. For 4643, the last digit is 3. It is an odd number. For 6592, the last digit is 2. It is an even number. For 9999, the last digit is 9. It is an odd number. For 15656, the last digit is 6. It is an even number. For 108791, the last digit is 1. It is an odd number. Step 2: Find the ages of the learners. Let the three consecutive ages be x, x+1, and x+2. Their sum is 45. x + (x+1) + (x+2) = 45 3x + 3 = 45 Subtract 3 from both sides: 3x = 45 - 3 3x = 42 Divide by 3: x = (42)/(3) x = 14 The three consecutive ages are: First age: x = 14 Second age: x+1 = 14+1 = 15 Third age: x+2 = 14+2 = 16 The ages are 14, 15, and 16. Step 3: Identify prime numbers and find their sum. Based on the student's work, the numbers to consider are 13 and 43. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For 13: The only divisors are 1 and 13. So, 13 is a prime number*. For 43: The only divisors are 1 and 43. So, 43 is a prime number*. The sum of the prime numbers is: 13 + 43 = 56 The sum of the prime numbers is 56. Step 4: Determine if the hypotenuse is rational or irrational. Let the shorter sides of the right-angled triangle be a = 4 cm and b = 7 cm. Let the hypotenuse be c. Using the Pythagorean theorem, a^2 + b^2 = c^2: c^2 = 4^2 + 7^2 c^2 = 16 + 49 c^2 = 65 c = sqrt(65) To determine if sqrt(65) is rational or irrational, we check if 65 is a perfect square. 8^2 = 64 and 9^2 = 81. Since 65 is not a perfect square, sqrt(65) cannot be expressed as a simple fraction of two integers. Therefore, sqrt(65) is an irrational number. Step 5: Work out the reciprocal of the given numbers. The reciprocal of a number x is (1)/(x). i) For 0.0003528: (1)/(0.0003528) = (1)/(3528)10000000 = (10000000)/(3528) (10000000)/(3528) ≈ 2834.46698 The reciprocal of 0.0003528 is approximately 2834.467. ii) For 3.528 × 10^4: (1)/(3.528 × 10^4) = (1)/(35280) (1)/(35280) ≈ 0.0000283446698 The reciprocal of 3.528 × 10^4 is approximately 0.00002834. Send me the next one 📸