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: Question 2: Simplify 16^(1)/(4) × 2^-3 × 3^0 Step 1: Evaluate each term in the expression. 16^(1)/(4) = [4]16 = 2 2^-3 = (1)/(2^3) = (1)/(8) 3^0 = 1 Step 2: Multiply the results. 2 × (1)/(8) × 1 = (2)/(8) = (1)/(4) The calculated answer is (1)/(4). However, this is not among the given options (A. 4, B. 8, C. 16, D. 32). Assuming there might be a typo in the question and 2^-3 was intended to be 2^3, let's re-evaluate: 16^(1)/(4) × 2^3 × 3^0 = 2 × 8 × 1 = 16 Based on this assumption, the answer would be 16. The most likely intended answer from the options, assuming a common typo, is C. C. 16 Question 3: If x varies directly as the cube root of y and x=3 when y=64; find x when y=216. Step 1: Write the direct variation equation. If x varies directly as the cube root of y, then x = k [3]y, where k is the constant of proportionality. Step 2: Use the given values (x=3, y=64) to find the constant k. 3 = k [3]64 3 = k × 4 k = (3)/(4) Step 3: Use the constant k and the new value (y=216) to find x. x = (3)/(4) [3]216 x = (3)/(4) × 6 x = (18)/(4) x = 4.5 The final answer is A. 4.5. Question 4: Find the rate per annum at which a sum of N52,200.00 generates a simple interest of N6,525.00 in 2(1)/(2) years. Step 1: Identify the simple interest formula and given values. The simple interest formula is I = PRT. Given: I = N6,525.00 P = N52,200.00 T = 2(1)/(2) years = 2.5 years Step 2: Substitute the values into the formula and solve for R. 6525 = 52200 × R × 2.5 6525 = 130500 × R R = (6525)/(130500) Step 3: Calculate the value of R and convert to a percentage. R = 0.05 To express as a percentage, multiply by 100: R = 0.05 × 100\% = 5\% The final answer is A. 5.0\%. Question 5: Express 0.07552 to two decimal places. Step 1: Identify the digit in the second decimal place. The number is 0.07552. The second decimal place is 7. Step 2: Look at the digit immediately after the second decimal place. The digit after 7 is 5. Step 3: Apply rounding rules. Since the digit (5) is 5 or greater, round up the second decimal place. Rounding 7 up gives 8. So, 0.07552 rounded to two decimal places is 0.08. The final answer is D. 0.08. Question 6: Evaluate (1.44)/((0.12)^2), stating your answer in standard form. Step 1: Calculate the denominator (0.12)^2. (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: (1.44 × 10000)/(0.0144 × 10000) = (14400)/(144) = 100 Step 3: Express the result in standard form (scientific notation). 100 = 1 × 10^2 The final answer is B. 1.00 × 10^2. Question 7: Find the product of 23_5 and 21_5, leaving your answer in base 5. Step 1: Convert the base 5 numbers 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 143_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 final answer is B. 1033_5. Send me the next one 📸