I need help with this please y’all

Explain how the quotient of powers was used to simplify this expression.

If 0° ≤ θ ≤ 90° and cosθ = 11 15 , what is the value of sin (90° - θ)? a) 11 /15 b) 15/ 11 c) 15 /4 d) 4/15

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) ).