JAMB Mathematics Past Questions & Answers - Page 396

\(x\propto \frac{uv}{u+v}\\x = \frac{kuv}{u+v}\\K = \frac{x(u+v)}{uv}\\\frac{3(3+1)}{3\times1}\\\frac{3\times4}{3}\\k = 4\\x=\frac{4uv}{u+v}\\x=\frac{4\times 3\times3}{3+3}\\x=\frac{36}{6}\\x=6\)

U = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
P = {6,12,18,24,30}
Q = {4,8,12,16,20,24,28}
P∪Q = {4,6,8,12,16,18,20,24,28,30}
(P∪Q)^c = {2,10,14,22,26}

1/6, 1/3, 3/2, 2/3, 8/9 and 4/3
L.C.M of the denominators = 36
The fraction now becomes
6/36, 12/36, 54/36, 24/36, 32/36 and 48/36
Highest fraction = 54/36
Lowest fraction = 6/36
Range = Highest - Lowest
(54/36) - (6/36)
= 48/36
= 4/3

Combination is the number (n) of ways of selecting a number of (m) of objects from n
\(^{12}C_{8}\frac{12!}{8!(12-8)!}\\=\frac{12!}{8!4!}\\\frac{(12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\After\hspace{1mm} cancelling \hspace{1mm}out \hspace{1mm}we\hspace{1mm} have\\11\times 5\times 9 = 495 \)

mean of X = x = (2+6+8+6+2+6)/6 = 30/6 = 5
X → 2,6,8,6,2,6
X - x = -3, 1, 3, 1, 3, 1
(X - x)2 = 9, 1, 9, 1, 9, 1
∑(X-x) = 9+1+9+1+9+1 = 30
Variance = ∑(X-x)2/n = 30/6 = 5