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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Here are the solutions to the problems: 13. Write 0.55 as a fraction in its lowest terms. Step 1: Convert the decimal to a fraction. 0.55 = (55)/(100) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (55 ÷ 5)/(100 ÷ 5) = (11)/(20) The correct option is A. A. (11)/(20) 14. Express 0.68 as a fraction in its lowest term. Step 1: Convert the decimal to a fraction. 0.68 = (68)/(100) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. (68 ÷ 4)/(100 ÷ 4) = (17)/(25) The correct option is B. B. (17)/(25) 15. Subtract 125.47 from 203.90. Step 1: Perform the subtraction. 203.90 - 125.47 Step 2: Calculate the result. 203.90 - 125.47 = 78.43 The correct option is B. B. 78.43 16. Factorize xy + 5x + 2y + 10. Step 1: Group the terms and factor out common factors from each group. xy + 5x + 2y + 10 = (xy + 5x) + (2y + 10) = x(y + 5) + 2(y + 5) Step 2: Factor out the common binomial factor (y+5). = (x + 2)(y + 5) The correct option is C. C. (x+5)(y+2) 17. Expand (a-2b)(a-2b). Step 1: Recognize the expression as the square of a binomial: (a-2b)^2. Step 2: Use the formula (A-B)^2 = A^2 - 2AB + B^2, where A=a and B=2b. (a-2b)^2 = a^2 - 2(a)(2b) + (2b)^2 Step 3: Simplify the expression. = a^2 - 4ab + 4b^2 The correct option is B. B. a^2 - 4ab + 4b^2 18. Ashim is N years old now. How old will he be in 10 years? Step 1: To find Ashim's age in 10 years, add 10 to his current age. Current age = N years. Age in 10 years = N + 10 years. The correct option is B. B. (N+10) years 19. Solve for x if 2x+5 = 3x-7. Step 1: Subtract 2x from both sides of the equation. 5 = 3x - 2x - 7 5 = x - 7 Step 2: Add 7 to both sides of the equation to isolate x. 5 + 7 = x x = 12 The correct option is A. A. 12 20. If: 27 = 6:18, find a. Assuming the question implies a proportion of the form 27:18 = 6:a. Step 1: Write the proportion as an equation of fractions. (27)/(18) = (6)/(a) Step 2: Simplify the fraction on the left side. (27)/(18) = (3 × 9)/(2 × 9) = (3)/(2) Step 3: Set up the simplified equation and solve for a. (3)/(2) = (6)/(a) Cross-multiply: 3a = 2 × 6 3a = 12 a = (12)/(3) a = 4 The correct option is A. A. 4 That's 2 down. 3 left today — send the next one.