Correct Answer: B. II only

Explanation

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have

\((n - 2) \times 180° = 108n\) ... (1)

\((n - 2) \times 180° = 116n\) ... (2)

\((n - 2) \times 180° = 120n\) ... (3)

Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.

(1): \(180n - 360 = 108n \implies 72n = 360\)

\(n = 5\) (regular pentagon)

(2): \(180n - 360 = 116n \implies 64n = 360\)

\(n = 5.625\)

(3): \(180n - 360 = 120n \implies 60n = 360\)

\(n = 6\) (regular hexagon)

Hence, 116° is not an angle of a regular polygon.

Correct Answer: B. 4√3

Explanation

\(sin \theta = \frac{opp}{hyp}\\

sin 60^o = \frac{|YZ|}{|XZ|}=\frac{6}{P}\\

P sin 60^o = 6\\

P = \frac{6}{sin60^o}\\

=\frac{6}{\sqrt{\frac{3}{2}}}=4\sqrt{3}\)

Explanation

\(p \propto q^2\)

\(q \propto \frac{1}{\sqrt{r}\)

\(p = kq^2\)

\(q = \frac{c}{\sqrt{r}}\)

where c and k are constants.

\(q^2 = \frac{c^2}{r}\)

\(p = \frac{kc^2}{r}\)

If k and c are constants, then kc\(^2\) is also a constant, say z.

\(p = \frac{z}{r}\)

p varies inversely as r.

Correct Answer: C. N700.00

Explanation

15% loss = N595

\(\implies\) (100 - 15)% of CP = N595

85% of CP = N595

CP = \(\frac{595 \times 100}{85}\)

= N700.00

Correct Answer: A. N5.00

Explanation

Represent notebook with x

Represent pen with y

? 3x+y=35 ---- (i)

2x+2y=30 ---- (ii)

Multiply eqn (i) by 2 and eqn (ii) by 1

6x+2y=70 ---- (iii)

2x+2y=30 ---- (iv)

Subtract eqn (iv) from eqn (iii)

4x = 40

X = 10

Substitute x = 10 in eqn (i)

3x+y=35

3(10)+y=35

Y = 5

? The cost of pen is N5.00

Correct Answer: C. 1-(x+y)+xy

Explanation

Prob (passing English) = x

Prob (passing Maths) = Y

Prob (failing English) = 1 - x

Prob (failing Maths) = 1 - y

Prob (failing both test) = Prob(failing English) and Prob(failing Maths) = (1 - x)(1 - y)

=1 - y - x + xy

=1 - (y + x) + xy

Correct Answer: A. 3

Correct Answer: D. 3x²-7x-6=0

Explanation

\(x = -\frac{2}{3} \implies x + \frac{2}{3} = 0\)

\(x = 3 \implies x - 3 = 0\)

\(\implies (x - 3)(x + \frac{2}{3}) = 0\)

\(x^2 - 3x + \frac{2}{3}x - 2 = 0\)

\(x^2 - \frac{7}{3}x - 2 = 0\)

\(3x^2 - 7x - 6 = 0\)

Explanation

(d) /PM/ = 9.7 cm.

Correct Answer: A. \(\frac{3}{5}\)

Explanation

Member that are neither doctors nor lawyers = 60-(15+9)=36

Probability (Not doctors ad not lawyers) \(=\frac{36}{60}\\

=\frac{6}{10}=\frac{3}{5}\)