Mathematics Questions and Answers

1m = 1.1 yard, length(L)= 50m

= (50 x 1.1)yards

= 55 yards

Area(A) = length(L) y width (W)

1815 = 55y width (W)

width (w) = \(\frac{1815}{55}\)

= 33 yards

But 33 yards = 30 meters

The least length is \(\frac{40}{48}\) = \(\frac{5}{8}\)

for the rod to be cut in exactly equal trips

Ratio \(\frac{5}{6}\) : \(\frac{48}{40}\)

\(\frac{\frac{5}{6}}{\frac{40}{48}}\) = 1

\(\frac{5}{6}\) x \(\frac{48}{40}\) = \(\frac{240}{240}\) = 1

The least length = 240cm

241₅ = 2 x 5² + 4 x 5 + 1 x 5 + 1 x 5^o

50 + 20 + 1 = 71₁₀

Convert 71₁₀ to base 8
\(\begin{array}{c|c} 8 & 71 \\ 8 & 8 R 7\\8 & 1 R 0\\8 & 0 R 1\end{array}\)

= 107₈

The total sample space when two dice are thrown together is 6 x 6 = 36

\(\begin{array}{c|c} & 1 & 2 & 3 & 4 & 5 & 6\\ 1. & 1.1 & 1.2 & 1.3 & 1.4 & 1.5 & 1.6\\ 2 & 2.1 & 2.2 & 2.3 & 2.4 & 2.5 & 2.6\\3 & 3.1 & 3.2 & 3.3 & 3.4 & 3.5 & 3.6\\ 4 & 4.1 & 4.2 & 4.3 & 4.4 & 4.5 & 4.6\\ 5 & 5.1 & 5.2 & 5.3 & 5.4 & 5.5 & 5.6\\6 & 6.1 & 6.2 & 6.3 & 6.4 & 6.5 & 6.6 \end{array}\)

At least 10 means 10 and above

P(at least 10) = \(\frac{6}{36}\)

= \(\frac{1}{6}\)

Mean \(\bar{x}\) = \(\frac{156}{10}\) = 15.6

Median = \(\bar{y}\) = \(\frac{15 + 16}{2}\)

\(\frac{31}{2}\) = 15.5

\(\frac{x}{y}\) = \(\frac{15.6}{15.5}\) = 1.0065

1.0(1 d.p)