A television set is sold at GHC 1,517.50 inclusive of 12.5% VAT and 2.5% NHIL. Calculate the original cost, VAT, and NHIL.

$$P = \frac{1517.50}{1.15}$$ $$P = 1319.5652...$$

Rounding to two decimal places for currency:

$$P = \boxed{\text{GHC } 1319.57}$$

b) The NHIL charged.

$$\text{NHIL} = 0.025 \times 1319.5652...$$ $$\text{NHIL} = 32.9891...$$

Rounding to two decimal places:

$$\text{NHIL} = \boxed{\text{GHC } 32.99}$$

c) The VAT charged.

$$\text{VAT} = 0.125 \times 1319.5652...$$ $$\text{VAT} = 164.9456...$$

Rounding to two decimal places:

$$\text{VAT} = \boxed{\text{GHC } 164.95}$$

2.
The electrical resistance $R$ varies directly as its length $L$ and inversely as the square of its radius $r$. This can be written as $R = k \frac{L}{r^2}$, where $k$ is the constant of proportionality.
Given: $L_1 = 500$ m, $r_1 = 0.2$ cm, $R_1 = 30$ ohms.
Convert $r_1$ to meters: $0.2 \text{ cm} = 0.002 \text{ m}$.

i) Find the rule connecting $R, L$ and $r$.

$$30 = k \frac{500}{(0.002)^2}$$ $$30 = k \frac{500}{0.000004}$$ $$30 = k \times 125,000,000$$

$$k = \frac{30}{125,000,000} = \frac{3}{12,500,000} = 0.00000024$$

The rule connecting $R, L$ and $r$ is $\boxed{R = 0.00000024 \frac{L}{r^2}}$.

ii) Evaluate the resistance of the same type of copper wire 750m long and radius 0.25cm.
Given: $L_2 = 750$ m, $r_2 = 0.25$ cm.
Convert $r_2$ to meters: $0.25 \text{ cm} = 0.0025 \text{ m}$.

$$R_2 = 0.00000024 \frac{750}{(0.0025)^2}$$ $$R_2 = 0.00000024 \frac{750}{0.00000625}$$

$$R_2 = 0.00000024 \times 120,000,000$$ $$R_2 = \boxed{28.8 \text{ ohms}}$$

3.

a) Copy and complete the multiplication table for modulo 6 on the set $\{2,3,4,5\}$.
The operation $a \otimes b$ means $(a \times b