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.
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Step 1: Solve Question 26. The sequence is 36, 12, 4, . This is a geometric sequence with first term a = 36. The common ratio r = (12)/(36) = (1)/(3). Since |r| < 1, the sum to infinity exists and is given by the formula S_ = (a)/(1-r). S_ = (36)/(1 - 1)3 = (36)/(2)3 = 36 × (3)/(2) = 18 × 3 = 54 The correct option is B. The sum to infinity is 54. Step 2: Solve Question 27. A computer prints 2100 words in 5 minutes. The printing rate is 2100 words5 minutes = 420 words/minute. We need to find the number of words printed in 6(1)/(2) minutes. 6(1)/(2) minutes = 6.5 minutes. Number of words = Rate × Time Number of words = 420 words/minute × 6.5 minutes = 2730 words The correct option is B. The number of words is 2730. Step 3: Solve Question 28. We need to express 51.0596 correct to 3 decimal places. The third decimal place is 9. The digit immediately after it is 6. Since 6 5, we round up the third decimal place. Rounding 9 up results in 10, so we write 0 in the third decimal place and carry over 1 to the second decimal place. The second decimal place is 5. Adding the carried-over 1 makes it 6. So, 51.0596 rounded to 3 decimal places is 51.060. The correct option is C. The number is 51.060. Step 4: Solve Question 29. We need to find the value of the digit 3 in 4.035. In the number 4.035, the digit 3 is in the hundredths place. Its value is 3 × (1)/(100) = (3)/(100) = 0.03. The correct option is A. The value of the digit 3 is 0.03. Step 5: Solve Question 30. The symbol means "less than or equal to". The correct option is D. The symbol means Less than or equal to. Step 6: Solve Question 31. From the graph, point T is located at x = -2 and y = -4. The coordinates of T are (-2, -4). The correct option is B. The point T is (-2, -4). Step 7: Solve Question 32. We need to evaluate 16 - 2 × 3. Following the order of operations (BODMAS/PEMDAS), multiplication is performed before subtraction. 16 - 2 × 3 = 16 - 6 = 10 The correct option is B. The value is 10. Step 8: Solve Question 33. We need to find which point lies on the line 2y = 4x. The equation can be simplified to y = 2x. Let's test each option: A) (4, 2): 2 = 2(4) 2 = 8 (False) B) (1, 2): 2 = 2(1) 2 = 2 (True) C) (2, 1): 1 = 2(2) 1 = 4 (False) D) (1, 1): 1 = 2(1) 1 = 2 (False) The point (1, 2) lies on the line. The correct option is B. The point on the line is (1, 2). Step 9: Solve Question 34. We need to find the coefficient of x in the expansion of (2x - 1)(3x + 5). Expand the expression: (2x - 1)(3x + 5) = (2x)(3x) + (2x)(5) + (-1)(3x) + (-1)(5) = 6x^2 + 10x - 3x - 5 = 6x^2 + (10 - 3)x - 5 = 6x^2 + 7x - 5 The coefficient of x is 7. The correct option is A. The coefficient of x is 7. Step 10: Solve Question 35. The question is incomplete, but based on the pie chart, it likely asks for the angle of the third item, "Oats". A full circle has 360^. The angle for Corn is 130^. The angle for Beans is 60^. The sum of the known angles is 130^ + 60^ = 190^. The angle for Oats is 360^ - 190^ = 170^. The angle for Oats is 170^.