Fast food places sometimes advertise that you can buy some number of a particular set of items for a fixed price. The most elaborate one that I can remember was when Arby's offered 5 for \( \$ 5 \) (later \( \$ 5.95, \$ 6.95 \ldots \), It varied how many items were part of the deal, but at the peak, there were 9 options. (I don't recall what they were, but probably something like: soda, curly fries, beef melt, ham melt, turnover, shake, chicken sandwich, mozzarella sticks, potato cakes) 1. How many options are there to order 5 items from 9 choices? Assume that we cannot duplicate any option and that the order is important.

A possible reaction of ethane with chlorine is shown below. \( \mathrm{CH}_{3} \mathrm{CH}_{3}+\mathrm{Cl}_{2} \) This reaction could conceivably occur by the following chain mechanisms [1], [2], and [3]. The chain initiating step(s) is (are) [1] \( \mathrm{Cl}_{2} \) [2] \( \mathrm{Cl}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{CH}_{3} \mathrm{CH}_{3} \xrightarrow{\text { slow }} \mathrm{HCl} \) [3] \( \mathrm{CH}_{3} \mathrm{CH}_{2}^{*}+\mathrm{Cl}_{2} \xrightarrow{\text { fast }} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{CH}_{3} \mathrm{CH}_{2}^{*} \) Only [1] Only [2] Only [3] Only [1] and [2]

Factor the expression completely, or state that the polynomial is prime. \( x^{3}+4 x^{2}-4 x-16 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x^{3}+4 x^{2}-4 x-16= \) B. The polynomial is prime.

2. В параллелограмме \( A B C D \) на стороне \( A B \) отмечена точка \( K \) так, что \( A K: K B=2: 1, O \) - точка пересечения диагоналей. Выразите векторы \( \overline{O C} \) и \( \overline{C K} \) через векторы \( \vec{a}=\overline{A B} ; \vec{b}=\overline{A D} \).

\( \left. \begin{array} { c } { \int \frac { d y } { y \ln ^ { 2 } y } = \int \frac { d y } { y ( \ln y ) ^ { 2 } } } \\ { = \int \frac { 1 } { ( \ln y ) ^ { 2 } } \frac { d y } { y } } \\ { w = \ln y } \\ { d w = \frac { 1 } { y } d y } \\ { d w = \frac { d y } { y } } \\ { = \int \frac { 1 } { w ^ { 2 } } d w } \\ { = \int w ^ { - 2 } d w } \end{array} \right. \)

E área de un rectángulo mide 28 metros Cuadrados. El largo es de 7 metros. metros