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: Problem 1: Find the product of 23_5 and 21_5, leaving your answer in base 5. Step 1: Convert the numbers from base 5 to base 10. 23_5 = (2 × 5^1) + (3 × 5^0) = 10 + 3 = 13_10 21_5 = (2 × 5^1) + (1 × 5^0) = 10 + 1 = 11_10 Step 2: Multiply the base 10 numbers. 13_10 × 11_10 = 143_10 Step 3: Convert the product from base 10 back to base 5. Divide 143 by 5 repeatedly and record the remainders: 143 ÷ 5 = 28 remainder 3 28 ÷ 5 = 5 remainder 3 5 ÷ 5 = 1 remainder 0 1 ÷ 5 = 0 remainder 1 Reading the remainders from bottom to top gives 1033_5. The correct option is B. B. 1033_5 Problem 2: Simplify 16^7/4 × 2^-3 × 3^0 Step 1: Simplify each term using exponent rules. 16^7/4 = (2^4)^7/4 = 2^4 × (7)/(4) = 2^7 = 128 2^-3 = (1)/(2^3) = (1)/(8) 3^0 = 1 (Any non-zero number raised to the power of 0 is 1) Step 2: Multiply the simplified terms. 128 × (1)/(8) × 1 Step 3: Calculate the final product. 128 × (1)/(8) × 1 = (128)/(8) = 16 The correct option is C. C. 16 Problem 3: Evaluate (1.44)/((0.12)^2), stating your answer in standard form. Step 1: Calculate the denominator. (0.12)^2 = 0.12 × 0.12 = 0.0144 Step 2: Perform the division. (1.44)/(0.0144) To simplify, multiply the numerator and denominator by 10000 to remove decimals: (1.44 × 10000)/(0.0144 × 10000) = (14400)/(144) = 100 Step 3: Express the answer in standard form. 100 = 1.00 × 10^2 The correct option is C. C. 1.00 × 10^2 Problem 4: Find the rate per annum at which a sum of N52,200.00 gets to N58,000.00 in 1 (1)/(2) years. Step 1: Identify the given values for simple interest. Principal (P) = N52,200.00 Amount (A) = N58,000.00 Time (T) = 1 (1)/(2) years = 1.5 years Step 2: Calculate the simple interest (I). I = A - P = N58,000.00 - N52,200.00 = N5,800.00 Step 3: Use the simple interest formula to find the rate (R). The formula for simple interest is I = (P × R × T)/(100). Rearrange the formula to solve for R: R = (I × 100)/(P × T) Step 4: Substitute the values and calculate R. R = (5800 × 100)/(52200 × 1.5) R = (580000)/(78300) R = (5800)/(783) As a percentage, the rate is approximately: R ≈ 7.4074\% The rate per annum is (5800)/(783)\% or approximately 7.41\%. Send me the next one 📸