Question

Populations(in hundreds) of 50 towns and villages of a state , taken at random from a census report are: 11, 72, 15, 8, 15, 3, 23, 26, 2, 119, 200, 6, 16, 6, 111, 5,18,140,99,127,3172,18,30,43, 2,1,52,40,3,7,13,5,142,70,86,31,38,70,51,11,52,18,46,89,1,30,25,4,52 Prepare a grouped frequency table for the above data, using class intervals 0-30, 30-60,60-90 and so on. Also find the class with maximum frequency.
please do answer fast​

Answer 1

¹².y⁴ - a⁴.y¹²

you can write a¹² = a⁴.a^8

again, y¹² = y⁴.y^8

now use this,

= a⁴.a^8.y⁴ - a⁴.y⁴.y^8

you see that a⁴.y⁴ are common terms in both so,

= a⁴.y⁴( a^8 - y^8)

[ use,formula , x² - y² = (x - y)(x + y) ]

= a⁴.y⁴(a⁴ - y⁴)(a⁴ + y⁴)

=a⁴.y⁴(a² - y²)(a² + y²)(a⁴+y⁴)

=a⁴.y⁴(a - y)(a+ y)(a²+y²)(a⁴ + y⁴