A species of fish was added to a lake. The population size \( P(t) \) of this species can be modeled by the following function, where \( t \) is the number of years from the time the species was added to the lake. \[ P(t)=\frac{2200}{1+7 e^{-0.42 t}} \] Find the population size of the species after 2 years and the population size after 7 years. Round your answers to the nearest whole number as necessary. Population size after 2 years: חi] fish Population size after 7 years: \( \square \) fish

\( \frac{2}{3}\left(\frac{3}{5}-\frac{3}{4}\right)+\frac{1}{2} \div \frac{1}{4} \) Step \( 1 \div \frac{2}{3}\left(-\frac{3}{20}\right)+\frac{1}{2} \div \frac{1}{4} \) Step \( 2:-\frac{1}{10}+\frac{1}{2} \div \frac{1}{4} \) Step \( 3:-\frac{1}{10}+\frac{1}{8} \) Step \( 4: \frac{1}{40} \)

(c) \( x^{4 / 3}=-64 \) \( x=\square \) (d) \( x^{3 / 2}=_{=} \) \( x=\square \) (e) \( x^{3 / 4}=-16 \) \( x=\square \)

3.3 ข้อมูลชุดหนึ่งเรียงจากมากไปน้อย ดังนี้ \( 17,14,14,11,6,4, x \) พิสัยเท่ากับ 13 ค่าเฉลี่ยเลขคณิตของข้อมูลชุดนี้เป็นเท่าไร

Solve the simultaneous equations. You must show all your working. \[ \begin{array}{c}3 x+10 y=106 \\ 5 x-4 y=1\end{array} \]

Es sei \( \rho(x) \) eine Wahrscheinlichkeitsdichtefunktion (WD), die im Intervall \( [0 ; 2] \) gegeben ist durch \( \rho(x)=N_{0}(1 /(x+1)-1 / 3) \) und Null auBerhalb des Intervalls, \[ \rho(x)=\left\{\begin{array}{ll}N_{0}\left(\frac{1}{x+1}-\frac{1}{3}\right) & \text { fulr } x \in[0,2], \\ 0 & \text { sonst. }\end{array}\right. \] Bestimmen Sie die Konstante \( N_{0} \), so dass \( \rho(x) \) korrekt normiert ist.