1. Catalina va al gimnasio 4 do los 7 dias de la semana a realizar su entrenamient personalizado, donde paga \( \$ 32.500 \) por cada uno. Si Catalina ha entrenado Ias úttima 5 semanas, cuanto dinero ha Invertido en Ios entrenamientos personalizados Determina tas proporeiones para crearla regla de tres.

3 En una sucuencia aritmetica la suma de los dos primeros terminos es \( S_{2}=34 \) y la suma de los tres primeros en \( s_{3}=63 \). Encuentra S \( _{8} \), la suma de los primeros ocho terminos

\( \triangle P Q R \cong \triangle X Y Z, P Q=3 a+4 \), and \( X Y=5 a-12 \) . Find \( a \) and \( P Q \). \( a=8 \) and \( P Q=28 \) \( a=2 \) and \( P Q=10 \) \( a=28 \) and \( P Q=8 \) \( a=8 \) and \( P Q=16 \)

1. The radioactive isotope plutonium- 241 decays so as to satisfy the differential equation \[ d Q / d t=-0.0525 Q \text {, } \] where \( Q \) is measured in milligrams and \( t \) in years. (a) Determine the half-life \( \tau \) of plutonium-241. (b) If 50 mg of plutonium are present today, how much will remain in 10 years?

In each of Problems 1 through 4 find the general solution of the given differential equation. x. \( y^{\prime}+(1 / x) y=\sin x, \quad x>0 \)

In a binomial experiment, the number of trials is 10 , and the probability of success is 0.3 . What is the probability of exactly 4 successes?