Mathematics Questions and Answers

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

No explanation has been provided for this answer.