Mathematics Questions and Answers

Two word mathematics is first rewritten as mathematics, since every letter of mathematics appears once in the english alphabet.

Hence the probability that letter selected is from the word mathematics is prob. (matheics) = \(\frac{8}{26}\)

= \(\frac{4}{13}\)

The diagram given simple illustrates that a pentagon contains three \(\Delta\)s.

Two angles which are in the ratio 2:3 will have actual values 2x^o, 3x^o respectively. Thus 2x^o + 3x^o + 3 x 60 = 3x sum of angles of \(\Delta\)a

i.e. 5x^o + 180^o = 3 x 180^o

5x^o + 180^o = 540^o

5x^o = 540^o - 180^o

5x^o = 360^o

x^o = \(\frac{360^o}{5}\)

= 72^o

Hence, the smaller of the two angles is

2 x 72^o = 144^o

Area of floor = 3.5m x 2.2m = 7.7m²

Area of carpet = (3.5 - 0.5 - 0.5)m x (2.2 - 0.5 - 0.5)m

2.5m x 1.2m = 3m²

hence, area of margine

= area of floor - area of carpet

= (7.7 - 3)m²

= 4.7m²

mean = \(\bar{x}\) = \(\frac{\sum x}{n}\)

= \(\frac{5 + 3 + 0 + 7 + 2 + 1}{6}\)

\(\frac{18}{6}\) = 3

\(\begin{array}{c|c}
x & x - \bar{x} & |x - \bar{x}|\\ \hline 5 & -2 & 2 \\ \hline 3 & 0 & 0 \\ \hline 0 & -3 & 3 \\ \hline 7 & 4 & 4 \\ \hline 2 & -1 & 1 \\ \hline 1 & -2 & 2 \\ \hline & & & \sum|x - \bar{x}| \\ \hline & & & 12
\end{array}\)

hence, MD = \(\frac{\sum|x - \bar{x}}{n}|\)

\(\frac{12}{6}\)

= 2

\(\frac{1}{4}\)p + 3p = 10...(1)

2p - \(\frac{1}{3}\)q = 7...(2)

Multiply equation (2) by 3 to clear fraction

3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7

6p - q = 21

6p - 21 = q....(3)

substituting 6p - 21 for q in (1)

\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)

Multiply equation (4) by 4 to clear fraction

4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10

p + 12(6p - 21) = 40

p + 72p - 252

73p = 292

p = \(\frac{292}{73}\)

= 4