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
Here are the answers to your questions: 1. Classification of 15 The number 15 is an odd number because it is not divisible by 2. It is also a composite number because it has factors other than 1 and itself (its factors are 1, 3, 5, and 15). 2. Reciprocal of production rate Step 1: Identify the production rate. The production rate is 8 units per hour. Step 2: Find the reciprocal. The reciprocal of a number a is (1)/(a). The reciprocal of 8 is (1)/(8). (1)/(8) 3. Rational or irrational numbers a) sqrt(49) Step 1: Evaluate the square root. sqrt(49) = 7 Step 2: Determine if it's rational or irrational. Since 7 can be expressed as a fraction (7)/(1), it is a rational number. b) sqrt(2) Step 1: Evaluate the square root. sqrt(2) ≈ 1.41421356... Step 2: Determine if it's rational or irrational. Since sqrt(2) cannot be expressed as a simple fraction of two integers and its decimal representation is non-terminating and non-repeating, it is an irrational number. 4. Reciprocal of 0.25 Step 1: Convert 0.25 to a fraction. 0.25 = (25)/(100) = (1)/(4) Step 2: Find the reciprocal of the fraction. The reciprocal of (1)/(4) is (4)/(1) = 4. 4 5. Express 5^3 × 5^4 as a single power of 5 Step 1: Apply the law of indices a^m × a^n = a^m+n. 5^3 × 5^4 = 5^3+4 Step 2: Simplify the exponent. 5^3+4 = 5^7 5^7 6. Simplify (2^5 × 2^3)/(2^4) Step 1: Simplify the numerator using a^m × a^n = a^m+n. 2^5 × 2^3 = 2^5+3 = 2^8 Step 2: Substitute the simplified numerator back into the expression. (2^8)/(2^4) Step 3: Apply the law of indices (a^m)/(a^n) = a^m-n. (2^8)/(2^4) = 2^8-4 = 2^4 2^4 7. Find log250 to 4 decimal places Step 1: Use a calculator or logarithm tables to find the value of _10(250). _10(250) ≈ 2.39794000867... Step 2: Round the value to 4 decimal places. 2.3979 2.3979 8. Simplify log100 + log0.1 Step 1: Evaluate each logarithm. _10(100) = _10(10^2) = 2 _10(0.1) = _10(10^-1) = -1 Step 2: Add the values. 2 + (-1) = 1 Alternatively, using the logarithm law a + b = (ab): _10(100) + _10(0.1) = _10(100 × 0.1) _10(10) = 1 1 9. Evaluate (27)^(2)/(3) Step 1: Rewrite the expression using the property a^(m)/(n) = ([n]a)^m. (27)^(2)/(3) = ([3]27)^2 Step 2: Calculate the cube root of 27. [3]27 = 3