12. Alberto figures that the probability of his hockey team winning on Saturday is \( 65 \% \). Alvin figures that the probability of his basketball team winning on Saturday is \( 70 \% \). Assume that the events are independent and that the boys' estimates of the probability are accurate. a. Find the probability that both teams will win on Saturday. b. Find the probability that both teams will lose on Saturday. c. Find the probability that Alberto's team will win, but Alvin's backo team will lose. d. Find the probability that Alberto's team will lose, but Alvin's team will win.

Ejemplos: 3 y \( 5 ; 12 \) y \( 25 ; 3,14 \) y \( 10 ; 1,7,8 \) y 12 . Compruébalo. 16. Usa descomposición simultánea y obtén el mad y el mcm de 117 y 78 . \( \bmod (117,78)= \) \( \operatorname{mom}(117,78)= \)

(1 point) Suppose \( h(x)=\sqrt{f(x)} \) and the equation of the tangent line to \( f(x) \) at \( x=1 \) is \[ y=4+1(x-1) \] Find \( h^{\prime}(1) \) \( h^{\prime}(1)= \) \( \square \)

What is \( (f-g)(x) \) ? \[ \begin{array}{l} f(x)=x^{2}-x-2 \\ g(x)=x^{2}-3 x \end{array} \] Write your answer as a polynomial or a rational function in simplest form. \( \square \)

La concentración de un medicamento en un órgano al instante \( t \) (en segundos) está dada por: \[ x(t)=0,08+0,12 e^{-0,02 t} \] Donde \( x(t) \) son gramos/centimetros cúbicos \( \left(\mathrm{gr} / \mathrm{cm}^{3}\right) \). a) ¿Cuál es la concentración pasado 1 minuto? b) ¿Cuánto tiempo tardará en alcanzar \( 0,18 \mathrm{gr} / \mathrm{cm}^{3} \) de medicamento en el órgano?

La inversa de la función \( y=e^{-5 x+3} \) es