Suppose A = x ∈ R : -2 ≤ x < 5 and B = (-1, 6]. Draw A and B on two separate number lines. Find A ∪ B and give the answer in interval notation. Write A ∩ B as one set using set builder notation.

Here are the solutions to your questions. Question 1 1.1 Draw A and B on two separate number lines. Set A: A = \x R : -2 x < 5\ This represents an interval starting at -2 (inclusive) and ending at 5 (exclusive). On a number line, you would draw a closed circle at -2, an open circle at 5, and a line connecting them. Set B: B = (-1, 6] This represents an interval starting at -1 (exclusive) and ending at 6 (inclusive). On a number line, you would draw an open circle at -1, a closed circle at 6, and a line connecting them. 1.2 Find A B and give the answer in interval notation. Step 1: Identify the intervals for A and B. A = [-2, 5) B = (-1, 6] Step 2: Determine the union, which includes all elements present in either A or B. The union starts at the smallest value in either set, which is -2 (from A). The union ends at the largest value in either set, which is 6 (from B). Since -2 is included in A, and 6 is included in B, both endpoints are included in the union. A B = [-2, 6] 1.3 Write A B as one set using set builder notation. Step 1: Identify the intervals for A and B. A = [-2, 5) B = (-1, 6] Step 2: Determine the intersection, which includes only elements common to both A and B. The intersection starts at the largest of the lower bounds, which is -1 (since -1 is not included in B, it's not included in the intersection). The intersection ends at the smallest of the upper bounds, which is 5 (since 5 is not included in A, it's not included in the intersection). A B = (-1, 5) Step 3: Write the intersection in set builder notation. A B = \x R : -1 < x < 5\ Question 2 Calculate 5 ÷ (3)/(2) + 2 - ((-4+9)/(4)) without using a calculator. Step 1: Simplify the division and the expression inside the parenthesis. 5 ÷ (3)/(2) = 5 × (2)/(3) = (10)/(3) (-4+9)/(4) = (5)/(4) Step 2: Substitute these simplified values back into the original expression. (10)/(3) + 2 - (5)/(4) Step 3: Find a common denominator for the fractions, which is 12. (10)/(3) + (2)/(1) - (5)/(4) = (10 × 4)/(3 × 4) + (2 × 12)/(1 × 12) - (5 × 3)/(4 × 3) = (40)/(12) + (24)/(12) - (15)/(12) Step 4: Perform the addition and subtraction. = (40 + 24 - 15)/(12) = (64 - 15)/(12) = (49)/(12) a) as an improper fraction (49)/(12) b) as a mixed fraction Divide 49 by 12: 49 ÷ 12 = 4 with a remainder of 1. 4 (1)/(12) c) as a decimal fraction correct to two decimal places. Convert the improper fraction to a decimal. (49)/(12) ≈ 4.0833... Rounding to two decimal places: 4.08 Question 3 *a) A certain bank offers an interest rate of 12.5\% on a one-year fixed deposit and the interest is compounded at the end of the year.