vendedor de teléfonos celulares tiene dos ofertas de empleos. La compañía A le ofrece un sueldo de \( \$ 200.000 \) nsuales más \( \$ 3.000 \) por cada teléfono vendido. La compañía B le ofrece un sueldo de \( \$ 250.000 \) más \( \$ 2.000 \) por éfono vendido. ¿ Cuántos teléfonos debería vender para recibir el mismo sueldo en ambas compañías? 50 60

Assume the following: \( \bar{x}=42 \) s=6 \( n=25 \) Calculate confidence intervals for a \( 95 \% \) confidence level. Calculate confidence intervals for a \( 99 \% \) confidence level.

Solve for \( x \) : \( 3 x \log 2+\log 2-5 \log 2=x \log 2-1 \log 2 \)

04) Simplifque as fraçŏes algébricas a segurir, considerando que os denominadores não são nulos: a) \( \left(x^{4} z^{5}+x^{3} z^{4}\right): x^{2} z^{2} \) b) \( \left(a^{3} b^{6}+a^{2} b^{5}-a^{3} b^{4}\right): a^{3} b^{4} \) c) \( \left(12 x^{2} y^{3}+8 x^{3} y^{5}\right): 4 x y \)

Volume of a Tank A civil engineering firm is tasked with designing a new water storage tank for a municipal water supply system. The engineers want the tank to have an efficient shape that maximizes storage capacity while minimizing the amount of construction material used. The tank's cross-section will be shaped by revolving the regions bounded by the lines and curves, \( x=\sqrt{2 \sin ^{2} y} \) \( 0 \leq y \leq \frac{\pi}{2}, x=0 \) about the \( y \)-axis. The goal is to determine the volume of the tank that will be created by this revolution around the \( y \)-axis. 4.1 Source: Mafemba, J. (2024) a. Calculate the volume of the solid generated by revolving the regions bounded by the lines and curves mentioned in the scenario above

Montres que \( \frac{\left(9^{n+1}+9^{n}\right)^{8}}{\left(3^{2 n}-3^{8 n+1}\right)^{8}} \in \mathbb{Z} \)