Correct Answer: C. Le 3,600,000.00

Explanation

sectoral angle representing food

= 360^o - (80 + 70 + 90)^o

= 120^o

Amount spent on food

= \(\frac{\tect{sectoral angle}}{360^o}\) x Le 10,800,000

= Le 3,600,000

Correct Answer: B. 0.154

Correct Answer: A. perpendicular line to PQ

Explanation

(a) < UST = 100° (exterior angle of a cyclic quad)

< SUT = 36° (angle in alternate segment)

\(\therefore < UST + < SUT + < STU = 180°\) (sum of angles in a triangle)

\(\therefore 100° + 36° + < STU = 180°\)

\(< STU = 180° - 136° = 44°\)

(b)

\(\frac{y}{6} = \frac{2}{5}\)

\(\therefore 5y = 2(6) = 12\)

\(\therefore y = \frac{12}{5} = 2.4 cm\)

\(\therefore XQ + QZ = XZ\)

\(QZ = XZ - XQ\)

= \(6 cm - 2.4 cm = 3.6 cm\)

\(\therefore QZ = 3.6 cm\).

Correct Answer: B. 3

Explanation

Median is \(\frac{n}{2} = \frac{6}{2}\)

= 3

Median = 3

Explanation

(a) \(\frac{0.45 \times 0.91}{0.0117} = \frac{45 \times 91}{117}\)

= \(5 \times 7 = 35\)

(b) Halfway between \(1\frac{6}{7}\) and \(2\frac{11}{28}\)

= \(\frac{1\frac{6}{7} + 2\frac{11}{28}}{2}\)

= \((\frac{13}{7} + \frac{67}{28}) \times \frac{1}{2}\)

= \(\frac{119}{28} \times \frac{1}{2} \)

= \(\frac{119}{56} = 2\frac{7}{56} = 2\frac{1}{8}\)

(c) Let the interior angle = 5x° and the exterior angle = x°.

\(\therefore 5x° + x° = 180°\)

\(6x° = 180° \implies x = 30°\)

Exterior angle = \(\frac{360°}{n} \implies 30° = \frac{360°}{n}\)

\(n = \frac{360°}{30°} = 12\)

The polygon has 12 sides.

(d) Length of pipe = 20 cm

Internal diameter = 6 cm ; radius = 3cm

External diameter = 8 cm ; radius = 4cm

Let the external radius = R and internal radius = r

\(\therefore\) Volume of material used = \(\pi R^{2} l - \pi r^{2} l\)

Where l = length.

\(Volume = \pi l (R^{2} - r^{2}) cm^{3}\)

= \(\frac{22}{7} \times 20 (4^{2} - 3^{2}) = \frac{22}{7} \times 20 \times 7 = 440 cm^{3}\)

Correct Answer: C. −4/7

Explanation

a. The total time taken for the entire journey is the sum of time taken for each journey.

But Average speed = \(\frac { total distance covered}{ time taken}\)

then Time taken = \(\frac { total distance covered}{ time taken}\)

for the first journey(t1), d = 112km and speed = 70km/hr

\(t_1 = \frac{112}{70} = \frac{8}{5}\)hrs

for the second journey(t2), distance = 60km and speed = 50km/hr

\(t_2 = \frac{60}{50} = \frac{6}{5}\)hrs

Therefore, Total time taken = \( t_1 + t_2 = \frac{8}{5} + \frac{6}{5}\) = 2.8hrs.

b. if \(\frac{x}{y}\) = 2 , then x = 2y and if \(\frac{y}{z}\) = 3 then z = \(\frac{y}{3}\),

substituting, the values of x and z into \(\frac{ x + y}{y + z }\)

= \(\frac{2y + y}{y + \frac{y}{3}} = 3y\div\frac{4y}{3} = 3y\times\frac{3}{4y} = \frac{9}{4}\)

Therefore, \(\frac{ x + y}{y + z } = \frac{9}{4}\)

Correct Answer: B. \(\begin{vmatrix} 14 & 8 \\ 7 & 7 \end{vmatrix}\)

Correct Answer: C. 9