Mathematics Questions and Answers

$\theta = 115° , radius = 3.4cm^2$

Area of a sector = $\frac{\theta}{360} \times \pi r^2$

= $\frac{115}{360} \times \frac{22}{7} \times 3.4\times 3.4$

= $\frac{29246.4}{2520}$

= $11.6cm^2$

$1 + \sqrt [3]{x-3} = 4$

= $\sqrt[3]{x - 3} = 4 - 1$

$\sqrt[3]{x - 3} = 3$

take the cube of both sides

= x - 3 = 27
 x = 27 + 3
∴ x = 30

∠SOR = 2 × 28° = 56° (angle at the centre is twice the angle at the circumference)
From ∆SOR
|OS| = |OR| (radii)
So, ∆SOR is isosceles.

∠ORS = $\frac{180^0 -  56^0}{2} = \frac{124^0}{2}$    ( base angles of isosceles triangle are equal)

∴ ∠ORS = 62°

12 men working 8 hours a day can complete the work in 4 days

12 men working 1 hour a day will complete the same work in (8 x 4) days [working less hours a day means they have to work for more days]


1 man working 1 hour a day will complete same work in (8 x 4 x 12) days [fewer number of men working means the remaining ones will have to work for more days ]

So, it will take 1 man working 1 hour a day to complete a piece of work in (8 x 4 x 12) days = 384 days

Now,

1 man working 16 hours a day will complete the piece of work in (384/16) days = 24 days [working more hours a day means less days to complete the work]

∴ 4 men working 16 hours a day will complete the piece of work in (24/4) days = 6 days [more men working means fewer days to complete the work]

ALTERNATIVELY

12 x 8 x 4 = 4 x 16 x d

⇒ d = $\frac{12 \times 8 \times 4}{4 \times 16}$

⇒ d = $\frac{384}{64}$

⇒ d = 6

∴ 4 men working 16 hours a day will complete the piece of work in 6 days

Let $x$ = number of VIP tickets sold and

$y$ = number of regular tickets sold

Total number of tickets sold = 200

⇒ $x$ + $y$ = 200 ---- (i)

If it costs ₦1,200 for a VIP ticket, then it costs ₦1200x for $x$ number of VIP tickets sold and

If it costs ₦700 for a regular ticket, then it costs ₦700$y$ for $y$ number of VIP tickets sold

The total amount realised from the sale of tickets = ₦180,000

⇒ 1200$x$ + 700$y$ = 180000 ----- (ii)

From equation (i)

$x$ = 200 - $y$ ----- (iii)

Substitute (200 - $y$) for $x$ in equation (ii)

⇒ 1200(200 - $y$) + 700$y$ = 180000

⇒ 240000 - 1200$y$ + 700$y$ = 180000

⇒ 240000 - 500$y$ = 180000

Collect like terms

⇒ 240000 - 180000 = 500$y$

⇒ 60000 = 500$y$

⇒ $y = \frac{60000}{500} = 120$

Substitute 120 for $y$ in equation (iii)

⇒ $x = 200 - 120$

⇒ $x = 80$

∴ The total number of VIP tickets sold is 80 and regular is 120