Calculate Mr. Gatua's PAYE (Pay As You Earn) given his salary of Sh. 80,000 and the tax brackets and reliefs provided.

You're on a roll — Step 1: Calculate the tax for each income bracket. Mr. Gatua's annual salary is Sh. 80,000. This is his taxable income. First bracket (Sh. 1 - 1500): Taxable amount = Sh. 1500 Tax = 1500 × 10\% = Sh. 150 Second bracket (Sh. 1501 - 3000): Taxable amount = 3000 - 1500 = Sh. 1500 Tax = 1500 × 15\% = Sh. 225 Third bracket (Sh. 3001 - 4500): Taxable amount = 4500 - 3000 = Sh. 1500 Tax = 1500 × 25\% = Sh. 375 Fourth bracket (Above Sh. 4500): Taxable amount = 80,000 - 4500 = Sh. 75,500 Tax = 75,500 × 35\% = Sh. 26,425 Step 2: Calculate the total annual gross tax. Total Gross Tax = 150 + 225 + 375 + 26,425 = Sh. 27,175 Step 3: Calculate the total annual personal relief. Monthly personal relief = Sh. 1056 Annual personal relief = 1056 × 12 = Sh. 12,672 Step 4: Calculate the PAYE (Pay As You Earn). PAYE = Total Gross Tax - Annual Personal Relief PAYE = 27,175 - 12,672 = Sh. 14,503 Mr. Gatua's PAYE is Sh. 14,503. 12. Step 1: Write down the given terms using the formula for the n-th term of a geometric series, T_n = ar^n-1. The third term (T_3) is 3 (1)/(3) = (10)/(3). T_3 = ar^3-1 = ar^2 = (10)/(3) (Equation 1) The sixth term (T_6) is 11 (1)/(4) = (45)/(4). T_6 = ar^6-1 = ar^5 = (45)/(4) (Equation 2) Step 2: Calculate the common ratio (r) by dividing Equation 2 by Equation 1. (ar^5)/(ar^2) = (45)/(4)(10)/(3) r^3 = (45)/(4) × (3)/(10) r^3 = (135)/(40) Simplify the fraction: r^3 = (27)/(8) Take the cube root of both sides: r = 3/(8) r = (3)/(2) Step 3: Calculate the first term (a) by substituting the value of r into Equation 1. ar^2 = (10)/(3) a ((3)/(2))^2 = (10)/(3) a × (9)/(4) = (10)/(3) a = (10)/(3) × (4)/(9) a = (40)/(27) The common ratio is (3)/(2) and the first term is (40)/(27). 13. Step 1: Identify the given information and the relevant formula. Given triangle RSQ: Angle RSQ (angle S) = 50^ Side SQ = 11.83 cm Side QR = 12 cm We need to find the radius (R) of the circumcircle. The sine rule states that for a triangle with sides a, b, c and opposite angles A, B, C, the radius of the circumcircle R is given by: (a)/( A) = (b)/( B) = (c)/( C) = 2R In this case, we have side QR (opposite angle S) and angle S. So, a = QR = 12 cm and A = angle RSQ = 50^. Step 2: Apply the sine rule to find 2R. (QR)/((angle RSQ)) = 2R (12)/((50^)) = 2R Step 3: Calculate the value of (50^). (50^) ≈ 0.76604 Step 4: Substitute the value and solve for R. (12)/(0.76604) = 2R 15.6649 ≈ 2R R ≈ (15.6649)/(2) R ≈ 7.83245 Rounding to two decimal places: R ≈ 7.83 cm The radius of the circle is 7.83 cm. Mtumie inayofuata 📸