Trinity collects rainwater in a cylinder rain barrel. The area of the base of the cylinder is 2x2 – 7x + 3 square feet and the height of the cylinder is x + 5 feet. The
volume of the rain barrel can be found using the equation shown below. Which of the
following represents the volume of the cylinder?
V = (2x2 – 7x + 3 )(x + 5)

A. 2x3 + 17x2 + 38x + 15 ft3 C. 2x3 + 3x2 – 32x + 15 ft3
B. 2x3 – 7x2 + 15 ft3 D. 2x3 + 4x2 – 25x + 8 ft3

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).