Question 6 (1 point) Determine which if any, of the three statements are equivalent. You may use DeMorgan's Laws, the other equivalent forms given in your book, or truth tables, but proof must be given. a) If you swim every day, then you lose 5 pounds. b) You do not swim every day or you lose 5 pounds. b) It i false that you swim every day and you do not lose 5 pounds. a and c are equivalent all 3 of these are equivalent none of these are equivalent

Consider the function \( f(x)=2 x^{2}-2 x+5,0 \leq x \leq 10 \). The absolute maximum of \( f(x) \) (on the given interval) is at \( x=\square \) and the absolute minimum of \( f(x) \) (on the given interval) is at \( x=\square \)

Determine which, if any, of the three statements are equivalent. Justify your answer. (HINT: First, put the words in symbolic statements) a) Paul does not like chocolate or he doesn't like fish. b) If Paul likes fish, then he likes chocolate. c) It is not true that Paul likes chocolate and Paul likes fish.

\( f(x)=\left\{\begin{array}{ll}x-2 & \text { para } x \leq 1 \\ x^{2} & \text { para } x>1\end{array}\right. \) cuando \( x \) tiende a 1

224. En un triángulo ABC, se cumple: \( \cot \left(\frac{A}{2}\right)+\cot \left(\frac{B}{2}\right)=3 \cot \left(\frac{C}{2}\right) \) Calcule el valor de: \( \frac{\operatorname{sen}\left(\frac{C}{2}\right)}{\cos \left(\frac{A-B}{2}\right)} \) \( \begin{array}{lll}\text { A) }-3 / 4 & \text { B) }-3 / 5 & \text { C) }-5 / 3 \\ \text { D) } 5 / 3 & \text { E) } 3 / 5 & \end{array} \)

Emily fills \( \square \) racks, \( \square \) basketballs