Correct Answer: D. 11/15

Explanation

P(X \(\cup\) Y) = \(\frac{1}{3} + \frac{2}{5}\)

= \(\frac{11}{15}\)

Explanation

(a) \(/QY/ = 2cm; /RS/ = 3cm\)

\(\therefore /YZ/ = /RS/ = /PQ/ = 3cm\) (opp sides of a parallelogram)

But \(/PZ/ = /PQ/ + /QY/ + /YZ/\)

\(\therefore /PZ/ = 3cm + 2cm + 3cm = 8cm\)

(b) Difference in longitude = 95° - 25° = 70°

Distance PQ = \(\frac{70}{360} \times 2\pi R \cos \theta\)

= \(\frac{70}{360} \times 2 \times \frac{22}{7} \times 6400 \cos 56\)

= \(\frac{7}{36} \times 2 \times \frac{22}{7} \times 6400 \times 0.5592\)

= \(4374.19 km \approxeq 4374 km\) (to the nearest km)

Explanation

P = (\(\frac{rk}{Q} - ms\))\(^{\frac{2}{3}}\)

P\(^{\frac{3}{2}}\) = \(\frac{rk}{Q}\) - ms

P\(^{\frac{3}{2}}\) + ms = \(\frac{rk}{Q}\)

Q = \(\frac{rk}{p^{\frac{3}{2}}ms}\)

(a)(ii)

Q = \(\frac{10 \times 4}{3\frac{3}{2} + 15 (0.2)}\)

Q = \(\frac{40}{5.1958 + 3}\)

Q = \(\frac{40}{8.1958}\)

= 4.88 to 2 d.p

(b) \(\frac{x + 2y}{5} = x - 2y\)

x + 2y = 5(x - 2y)

x + 2y = 5x - 10y

x - 5x = -10y - 2y

-4x = -12y

\(\frac{x}{y} = \frac{12}{4}\)

x : y = 3 : 1

Correct Answer: C. 510.2

Explanation

q = 10\(^{2.7078}\)

Antilog of 2.7078 = 510.2

Correct Answer: A. 5005 ft

Explanation

The first thing to do is figure out which stalk is in the middle. Since there are an even number of stalks, there is no exact middle; there are 500 on one side and 500 on the other. This means that the 500th and the 501st are the median. These will have to be averaged. Now, we need to determine the height of these two stalks. Consider the pattern given: 1st stalk: 10 feet 2nd stalk: 20 feet 3rd stalk: 30 feet 4th stalk: 40 feet You should see the pattern that emerges for this problem. Each stalk is 10 times that stalk's place in the row. This means that the 500th stalk will be: 500?10=5000 The 501st stalk will be: 501?10=5010 The average of these two numbers is: 5000+5010/2= 10010/2=5005 5005 feet is the median.

Correct Answer: A. 3%

Explanation

(a) 20 kg at N5.00 each = N100.00

10 kg at N3.00 each = N30.00

5 kg at N2.00 each = N10.00

5 kg at 50k each = N2.50

Total = N 142.50.

(b) Selling price = N142.50

Cost price = N120.00

\(\therefore\) Profit = N(142.50 - 120.00) = N22.50.

(c) \(% profit = \frac{22.5}{120} \times 100%\)

= \(\frac{45}{240} \times 100% = 18.75%\)

Explanation

(a)

Momentum before collision = \((20 \times 80) + (30 \times 50) = 1600 + 1500\)

= \(3100 kgm/s\)

Momentum after collision = 50v kgm/s

Momentum before collision = Momentum after collision

\(3100 = 50v\)

\(v = \frac{3100}{50} = 62m/s\)

(b)

Momentum before collision = \((20 \times 80) - (30 \times 50) = 1600 - 1500\)

= \(100 kgm/s\)

Momentum after collision = \(50v kgm/s\)

\(\therefore 100 = 50v\)

\(v = 2m/s\)

Correct Answer: B. 240°

Correct Answer: A. 20°

Explanation

< QOR = 50° x 2 = 100°

Reflex < QOR = 360° - 100° = 260°

\(\therefore\) 30° + 50° + 260° + m = (4 - 2) x 180°

340° + m = 360°

m = 360° - 340° = 20°