Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume th samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1}=\mu_{2} ; \alpha=0.10 \). Assume \( \sigma_{1}^{2}=\sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=35.2, s_{1}=3.5, n_{1}=14 \) and \[ \bar{x}_{2}=37.4, s_{2}=2.2, n_{2}=18 \]

EJERCICIOS PROPUESTOS (1) \( 3 x+2(x-2)=5 x-4 \) (2) \( -2(1-2 x)-(1-2 x)=-x-2 \) (3) \( 2 x+4=3 x+3(x-2)-4 \) (4) \( 5(2 x-2)-4 x=-3(2-x) \) (5) \( 50-[3(2 x-3)-2(2 x-1)]=23 \) (6) \( 8 x+(-5 x-9)=3 x+[-5 x-(x+3)] \) (7) \( 71+[-(3 x+4)-(4 x+3)]=25-[-5 x+(-2 x+3)] \) (8) \( \frac{3 x+1}{3}=\frac{x-3}{6}+\frac{5}{12} \) (9) \( \frac{3 x+1}{8}-\frac{x-1}{6}=\frac{x+3}{4} \) (10) \( \frac{5-x}{4}-\frac{x+3}{6}=\frac{9-x}{4}-\frac{6 x-2}{16} \)

b) Para lavar 5 kg de ropa, se deben usar 60 g de jabón en polvo. ¿Cuánto kilos de ropa se pueden lavar con 288 g de jabón?

prove: \[ \int_{T} \nabla \phi d T=\int_{\partial T} \phi d \partial \text { and } \int_{T} \nabla \times V d T=-\int_{\partial T} v \times d \sigma \] [Hint: Apply Gauss's Theorem \( \int_{T} \nabla \cdot F d T=\int_{\partial T} F \cdot d \sigma \) to \( F=\phi e_{x} \) and \( F=v \times e_{x} \), etc.]

1. Indica en cada coso, la ravon que completa 19 proporoion a \( \frac{3}{8}-\frac{1}{4} \frac{32}{12} ; \frac{12}{32} ; \frac{8}{3} \) \( b \frac{4}{1}=\frac{1}{1} \frac{14}{4} ; \frac{8}{14}: \frac{2}{7} \)

Determine \( \lim _{x-x_{-3}} \frac{x^{2}-x-12}{x+3} \)