Which of these years was a leap year: 2020, 2021, 2022?

Here are the solutions for questions one to twelve: 1) Numbers can either be written in figures, words or Roman numerals. Write in figures: One and a half million Step 1: One million is 1,000,000. Step 2: Half a million is 500,000. Step 3: Add these values. 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 To express a percentage as a decimal, divide the percentage value by 100. For example, X\% 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 = 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: A leap year is generally divisible by 4. Step 2: Check each year: • 2020 ÷ 4 = 505. 2020 is divisible by 4, so it is a leap year. • 2021 ÷ 4 = 505 with a remainder of 1. Not a leap year. • 2022 ÷ 4 = 505 with a remainder of 2. 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. 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: 1, 6, 5, 3. Step 2: Look at the fifth significant figure, which is 6. Step 3: Since 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 x=5 and y=4 into the first part of the expression. (x+y)^2 = (5+4)^2 = 9^2 = 81 Step 2: Substitute x=5 and y=4 into the second part of the expression. (2x-y)^2 = (2 × 5 - 4)^2 = (10 - 4)^2 = 6^2 = 36 Step 3: Perform the division. (x+y)^2 ÷ (2x-y)^2 = 81 ÷ 36 (81)/(36) = (9 × 9)/(4 × 9) = (9)/(4) As a decimal, (9)/(4) = 2.25. The value of the expression is (9)/(4) or 2.25. 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 other number be N. Step 2: Set up the equation. 128 + N = 502 Step 3: Solve for N. N = 502 - 128 N = 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 2 So, 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. Rate of loss = 2 minutes3 hours Step 2: Multiply the rate by the total hours. Total loss = (2)/(3) minutes/hour × 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, which is 12. (1)/(4) = (3)/(12) (1)/(3) = (4)/(12) Step 3: Add the fractions. Total spent = (3)/(12) + (4)/(12) = (7)/(12) Step 4: Subtract the spent fraction from the total (1, or (12)/(12)). Fraction left = 1 - (7)/(12) = (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: List the universal set . = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10\ Step 2: Find the intersection of sets A and B (A B), which are the elements common to both sets. A = \1, 3, 6, 9, 10\ B = \2, 4, 6, 8, 10\ A B = \6, 10\ Step 3: Find the complement of (A B), denoted as (A B)'. This includes all elements in that are not in (A B). (A B)' = \1, 2, 3, 4, 5, 7, 8, 9\ (A B)' = \1, 2, 3, 4, 5, 7, 8, 9\. 3 done, 2 left today. You're making progress.