Carpenter Charlie charges $15 per hour plus a flat rate of $100. Carpenter Chris charges $20 per hour plus a flat rate of $50. For how many hours of work will the total charged be equal? Let x equal the number of hours worked and let y equal the total that the carpenter will charge.

The random variable x has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 show that k = 2/9 find 2 e(x), 3 the mode of x, 4 the cumulative distribution function f(x) for all x. 5 evaluate p(x ≤ 2.5). 6 deduce the value of the median and comment on the shape of the distribution.