he district attorney informed the assistant DA that she had no choice but to Deve forward with the prosecution's domestic assault case, regardless of the Precharge diversion EST exemplity? Deferred prosecution diversion No-drop prosecution

\( n \) désignant un entier naturel non nul, on considère l'ensemble \( E_{n} \) des mots de \( n \) lettres que l'on peut former à l'aide des lettres a, b et c uniquement et ne contenant pas deux lettres consécutives identiques. On note \( F_{n} \) la partie de \( E_{n} \) constituée par les mots qui commencent et se terminent par deux lettres différentes. On pose \( \alpha_{n}=\operatorname{card}\left(E_{n}\right) \) et \( \beta_{n}=\operatorname{card}\left(F_{n}\right) \). 1. Déterminer \( \alpha_{n} \) en fonction de \( n \).

The marketing manager for a newspaper has commissioned a study of the advertisements in the classified section. The results for the Wednesday edition showed that 187 are help-wanted ads, 498 are real estate ads, and 330 are other ads. a. If the newspaper plans to select an ad at random each week to be published free, what is the probability that the ad for a specific week will be a help-wanted ad? b. What method of probability assessment is used to determine the probability in part a? c. Are the events that a help-wanted ad is chosen and that an ad for other types of products or services is chosen for this promotion in a specific week mutually exclusive? Explain.

Hallar la ecuación de la circunferencia con centro en el punto \( (7,1) \) y radio \( r=2 \) a. \( X^{2}+Y^{2}-7 X-2 Y+44=0 \) b. \( X^{2}+Y^{2}-14 X-2 Y+4=0 \)

Find the least common denominator of \( \frac{5 x}{x-6} \) and \( \frac{9 x}{x-7} \)

5. Für \( k>0 \) ist die Funktion \( f_{k} \) gegeben durch \( f_{k}(x)=x^{3}-k^{2} x \). Berechnen Sie \( k \) so, dass der Graph von \( f_{k} \) mit der \( x \)-Achse eine Fläche mit dem Inhalt 8 einschließt.