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
enangachantal873, let's knock this out. 1) Numbers can either be written in figures, words or Roman numerals. Write in figures: One and a half million Step 1: Understand "one million". One million is 1,000,000. Step 2: Understand "half million". Half a million is (1)/(2) × 1,000,000 = 500,000. Step 3: Combine "one million" and "half million". 1,000,000 + 500,000 = 1,500,000. In figures, one and a half million is 1,500,000. 2) Fractions can be expressed as decimals. Express % as a decimal This question asks how to express a percentage as a decimal in general. Step 1: Understand that "percent" means "per hundred" or "out of 100". Step 2: To convert a percentage to a decimal, divide the percentage value by 100. For example, if you have X\%, it is equivalent to (X)/(100) as a decimal. So, to express a percentage as a decimal, you divide the number by 100. For example, 25\% = (25)/(100) = 0.25. 3) Numbers written in index form can be expanded. Expand 7^2 × 5^3 Step 1: Expand 7^2. 7^2 = 7 × 7 = 49. Step 2: Expand 5^3. 5^3 = 5 × 5 × 5 = 25 × 5 = 125. Step 3: Multiply the expanded values. 49 × 125 = 6125. The expanded form is 49 × 125 = 6125. 4) Some years are called leap years. Which of these years was a leap year: 2020, 2021, 2022? Step 1: Recall the rules for a leap year. A year is a leap year if it is divisible by 4, unless it is a century year (like 1900) which must be divisible by 400. Step 2: Check each given year. • For 2020: 2020 ÷ 4 = 505. Since 2020 is divisible by 4, it is a leap year. • For 2021: 2021 ÷ 4 = 505 with a remainder of 1. So, 2021 is not a leap year. • For 2022: 2022 ÷ 4 = 505 with a remainder of 2. So, 2022 is not a leap year. The leap year among the given years is 2020. 5) A mixed fraction can be converted to an improper fraction. Convert 14 (1)/(2) to an improper fraction. Step 1: Multiply the whole number by the denominator. 14 × 2 = 28. Step 2: Add the numerator to the result from Step 1. 28 + 1 = 29. Step 3: Place this sum over the original denominator. The improper fraction is (29)/(2). 6) Write 16.53675 correct to 4 significant figures. Step 1: Identify the first four significant figures. These are 1, 6, 5, 3. Step 2: Look at the fifth significant figure, which is 6. Step 3: Since the fifth significant figure (6) is 5 or greater, round up the fourth significant figure (3). The number becomes 16.54. 16.53675 correct to 4 significant figures is 16.54. 7) Given that x = 5 and y = 4, calculate (x+y)^2 + (2x-y)^2 Step 1: Substitute the values of x and y into the expression. (5+4)^2 + (2 × 5 - 4)^2 Step 2: Calculate the values inside the parentheses. (9)^2 + (10 - 4)^2 (9)^2 + (6)^2 Step 3: Square the numbers. 81 + 36 Step 4: Add the results. 81 + 36 = 117 The value of the expression is 117. 8) The sum of two numbers is 502. If one of the numbers is 128, what is the value of the other number? Step 1: Let the two numbers be a and b. Given a + b = 502. Step 2: Let one number be a = 128. Substitute this into the equation. 128 + b = 502. Step 3: Solve for b. b = 502 - 128. b = 374. The value of the other number is 374. 9) Modular arithmetic deals with the remainder. What is 3 + 7 4? Step 1: Perform the addition. 3 + 7 = 10. Step 2: Find the remainder when 10 is divided by 4. 10 ÷ 4 = 2 with a remainder of 10 - (4 × 2) = 10 - 8 = 2. So, 10 2 4. 3 + 7 4 is 2. 10) A clock loses 2 minutes in every 3 hours. How many minutes does it lose in 15 hours? Step 1: Determine the rate of loss per hour. Loss rate = 2 minutes3 hours. Step 2: Calculate the total loss for 15 hours. Total loss = Loss rate × Total hours Total loss = 2 minutes3 hours × 15 hours Total loss = (2 × 15)/(3) minutes Total loss = (30)/(3) minutes Total loss = 10 minutes The clock loses 10 minutes in 15 hours. 11) After spending (1)/(4) of my money on bread and (1)/(3) on eggs, what fraction have I left? Step 1: Find the total fraction of money spent. Total spent = (1)/(4) + (1)/(3). Step 2: Find a common denominator for the fractions, which is 12. (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) (1)/(3) = (1 × 4)/(3 × 4) = (4)/(12) Step 3: Add the fractions. Total spent = (3)/(12) + (4)/(12) = (3+4)/(12) = (7)/(12) Step 4: The total money is represented by 1 (or (12)/(12)). Subtract the spent fraction from 1 to find the fraction left. Fraction left = 1 - (7)/(12) = (12)/(12) - (7)/(12) = (12-7)/(12) = (5)/(12) The fraction of money left is (5)/(12). 12) If = \1, 2, 3, 4, 5, 6, ..., 10\, A = \1, 3, 6, 9, 10\ and B = \2, 4, 6, 8, 10\, Find (A B)' Step 1: Identify the universal set . = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10\. Step 2: Find the intersection of Set A and Set B (A B). This includes elements common to both A and B. A = \1, 3, 6, 9, 10\ B = \2, 4, 6, 8, 10\ The common elements are 6 and 10. A B = \6, 10\. Step 3: Find the complement of (A B), denoted as (A B)'. This includes all elements in the universal set that are not in (A B). Elements in : \1, 2, 3, 4, 5, 6, 7, 8, 9, 10\ Elements in A B: \6, 10\ Remove \6, 10\ from : (A B)' = \1, 2, 3, 4, 5, 7, 8, 9\. (A B)' = \1, 2, 3, 4, 5, 7, 8, 9\. Got more? Send 'em!