Simplify: rac63 parens 5 - rac12 - rac14 parens and Evaluate: 32 div 9 + 40 - 23 imes 32 div 9

The common denominator for 1 (from $5 = \frac{5}{1}$), 2, and 4 is 4.

The simplified expression is $\boxed{\frac{17}{2} \text{ or } 8\frac{1}{2}}$.

1. a) ii. Evaluate: $3^2 \div 9 + 40 - 2^3 \times 3^2 \div 9$

The evaluated expression is $\boxed{33}$.

1. b) A financial analyst calculates a company's revenue as GHC23,365,752.198. How should this value be rounded for presentation in a financial report with:
i. four significant figures.
ii. two decimal places.

i. Rounding to four significant figures:
The first four significant figures are 2, 3, 3, 6. The fifth digit is 5, so we round up the fourth digit.

The revenue rounded to four significant figures is $\boxed{\text{GHC}23,370,000}$.

ii. Rounding to two decimal places:
The first two decimal places are .19. The third decimal place is 8, so we round up the second decimal place.

The revenue rounded to two decimal places is $\boxed{\text{GHC}23,365,752.20}$.

2. a) i. Akua has enough money to buy exercise books at GHC4.50 each. How many pens costing GHC6.00 each can be bought with the same amount of money?

Assumption: The question implies Akua has exactly enough money to buy one exercise book.

Amount of money = GHC4.50.

Since you cannot buy a fraction of a pen, Akua can buy $\boxed{0 \text{ pens}}$.

2. a) ii. On Adwoa's birthday, the father bought her a pack of chocolate containing 250 bars. If Adwoa took 90 bars of the chocolates and gave the rest to her four friends to share equally, how many bars of chocolates did each receive?

Each friend received $\boxed{40 \text{ bars}}$.

2. b) Use the expanded and the box method to solve: $628 \times 39$

Expanded Method:

The product using the expanded method is $\boxed{24492}$.

Box Method (Grid Method):

The product using the box method is $\boxed{24492}$.

2. c) Simplify: $\frac{2x - 1}{3} - \frac{x + 3}{2}$

The least common multiple of 3 and 2 is 6.

Be careful with the subtraction sign.

The simplified expression is $\boxed{\frac{x - 11}{6}}$.

3. a) i. Using a pair of compass and a ruler only, construct triangle ABC such that /AB/ = 8cm, angle BAC = 60° and angle ABC = 45°.
ii. Measure /BC/

i. Construction Steps for Triangle ABC:

1. Draw a straight line and mark a point A.
2. Using a ruler, measure 8 cm from A along the line and mark point B. This forms line segment AB = 8 cm.
3. At point A, construct a 60° angle. Place the compass at A, draw an arc intersecting AB. Without changing the compass width, place the compass at the intersection point on AB and draw another arc to intersect the first arc. Draw a line from A through this intersection. This line forms $\angle BAC = 60^\circ$.
4. At point B, construct a 45° angle. First, construct a 90° angle at B. Then, bisect this 90° angle to get 45°. Draw a line from B along this 45° angle. This line forms $\angle ABC = 45^\circ$.
5. Extend the line from A (for 60°) and the line from B (for 45°) until they intersect. Label this intersection point C. Triangle ABC is now constructed.

ii. Measure /BC/:

• Upon accurate construction and measurement, the length of /BC/ should be approximately $\boxed{7.2 \text{ cm}}$.

3. b) Solve: $5 - 2x > x + 2$

Subtract $x$ from both sides:

Remember to reverse the inequality sign when dividing by a negative number.

The solution is $\boxed{x < 1}$.

3. c) The diameter of a circular lid is 14cm. Find
i. the circumference of the lid
ii. the area of the lid (take $\pi = \frac{22}{7}$)

Given: Diameter $d = 14 \text{ cm}$.
Radius $r = \frac{d}{2} = \frac{14}{2} = 7 \text{ cm}$.
$\pi = \frac{22}{7}$.

i. Circumference of the lid:
The formula for circumference is $C = \pi d$.

The circumference of the lid is $\boxed{44 \text{ cm}}$.

ii. Area of the lid:
The formula for the area of a circle is $A = \pi r^2$.

The area of the lid is $\boxed{154 \text{ cm}^2}$.