11. Higher Order Thinking Why does multiplying numbers by 10 move the decimal point to the right, but multiplying by 0.10 moves the decimal point to the left?

Use identities to simplify the expression. \( \cos x+\frac{\sin ^{2} x}{\cos x} \)

3 Gegeben ist die Gleichung der Funktion \( f \). Ermitteln Sie die Schnittpunkte des Graphen von \( f \) mit den Koordinatenachsen sowie die Extrempunkte mithilfe eines geeigneten digitalen Hilfsmittels. \( \begin{array}{ll}\text { a) } f(x)=\frac{1}{2} x^{3}-x^{2}+\frac{1}{2} x & \text { b) } f(x)=\frac{1}{3} x^{3}-x^{2}+x \\ \text { c) } f(x)=\frac{1}{3} x^{3}-x^{2}+\frac{8}{9} x & \text { d) } f(x)=\frac{1}{4} x^{4}+\frac{3}{2} x^{3}+3 x^{2}+2 x+\frac{1}{2}\end{array} \)

\( f \) a function \( f \) is increasing on the intervals \( [-3,1] \) and \( [9,19] \) and decreasing on the interval \( [1,9] \), determine the interval \( (s) \) on whi \( (x)=-2 f(2 x-7) \) is increasing. The graph \( g(x)=-2 f(2 x-7) \) is increasing on interval (Type your answer in interval notation.)

4. Your 56 -year-old patient, Larry, has recently been admitted to the hospital with cardiovascular disease. He already had been diagnosed with Type 2 diabetes several years earlier. You are in charge of checking on Larry throughout your shift and reporting any changes in his condition. What signs and symptoms of changing patient condition are important to report? Imagine you witness some of these changes in Larry. How would you report any changes in his condition?

There are 72 students sitting on the bleachers and 27 students sitting on the floor. What the ratio of the number of students sitting on the floor to the number of students sitting the bleachers? 27 :