Set F = 9, 12, 15, 20, 27 and E = multiples of 3 between 5 and 20. Write down n(F E). Make m the subject of y = (cm - 2b)/t. Simplify (2a+b)/3 - (ab+a+b)/4.

Here are the solutions to your problems. Problem 1: Set F and Set E Given that Set F = \9, 12, 15, 20, 27\ and E = multiples of 3 between 5 and 20. Write down n(F E). Step 1: List the elements of Set E. The multiples of 3 between 5 and 20 are 6, 9, 12, 15, 18. So, E = \6, 9, 12, 15, 18\. Step 2: Find the intersection of Set F and Set E (F E). The elements common to both sets F and E are 9, 12, and 15. So, F E = \9, 12, 15\. Step 3: Determine the number of elements in F E. The number of elements in F E is 3. n(F E) = 3 The number of elements is 3. Problem 2: Make m the subject of the formula Given the formula y = (cm - 2b)/(t). Step 1: Multiply both sides of the equation by t. yt = cm - 2b Step 2: Add 2b to both sides of the equation. yt + 2b = cm Step 3: Divide both sides by c. (yt + 2b)/(c) = m So, m = (yt + 2b)/(c). Problem 3: Simplify (2a+b)/(3) - (ab+a+b)/(4) Step 1: Find a common denominator for the two fractions, which is 12. (4(2a+b))/(12) - (3(ab+a+b))/(12) Step 2: Expand the numerators. (8a+4b)/(12) - (3ab+3a+3b)/(12) Step 3: Combine the fractions over the common denominator. (8a+4b - (3ab+3a+3b))/(12) (8a+4b - 3ab - 3a - 3b)/(12) Step 4: Combine like terms in the numerator. ((8a-3a) + (4b-3b) - 3ab)/(12) (5a + b - 3ab)/(12) The simplified expression is (5a + b - 3ab)/(12). Problem 4: Simplify ((2)/(3x))^-1 × (6)/(x) Step 1: Apply the negative exponent rule (A/B)^-1 = B/A. ((2)/(3x))^-1 = (3x)/(2) Step 2: Multiply the result by (6)/(x). (3x)/(2) × (6)/(x) Step 3: Cancel out common terms (x in the numerator and denominator). (3 × 6)/(2) Step 4: Perform the multiplication and division. (18)/(2) = 9 The simplified expression is 9. Problem 5: Find the first three terms of the sequence with n^th term 3n^2-1. Step 1: Find the first term by substituting n=1. 3(1)^2 - 1 = 3(1) - 1 = 3 - 1 = 2 Step 2: Find the second term by substituting n=2. 3(2)^2 - 1 = 3(4) - 1 = 12 - 1 = 11 Step 3: Find the third term by substituting n=3. 3(3)^2 - 1 = 3(9) - 1 = 27 - 1 = 26 The first three terms are 2, 11, 26. Problem 6: Solve the equation r - 2(1)/(2) = -(1)/(8) Step 1: Convert the mixed number to an improper fraction. 2(1)/(2) = (2 × 2 + 1)/(2) = (5)/(2) The equation becomes r - (5)/(2) = -(1)/(8). Step 2: Add (5)/(2) to both sides of the equation. r = -(1)/(8) + (5)/(2) Step 3: Find a common denominator for the fractions, which is 8. r = -(1)/(8) + (5 × 4)/(2 × 4) r = -(1)/(8) + (20)/(8) Step 4: Add the fractions. r = (-1 + 20)/(8) r = (19)/(8) The solution is r = (19)/(8) or r = 2(3)/(8). That's 2 down. 3 left today — send the next one.