Why is Mexico and parts of Central America prone to earthquakes? There is no clear reason why the area is prone to earthquakes. The building codes are old and outdated. The soil is soft and easily moved. The region lies on the border of two tectonic plates.

circunferencia: \( (x-1)^{2}+(y-1)^{2}=25 \quad \) en el punto \( \quad P_{1}(5,4) \)

Graph the quadratic equation. What is the vertex of the quadratic equation? The vertex is (Simplify your answer. Type an ordered pair.) What is(are) the \( y \)-intercept(s), if they exist? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept(s) is(are) \( \square \). (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) B. There are no \( y \)-intercepts.

83. Da una scatola che contiene 3 dischetti gialli e 1 dischetto nero si estrae un dischetto e, dopo averlo rimesso nella scatola, se ne estrae un altro. Calcola la probabilità di ciascuno dei seguenti eventi. a. \( E_{1}: \) "estrarre due dischetti entrambi gialli" \( \rightarrow \) b. \( E_{2}: \) "estrarre due dischetti entrambi neri" \( \rightarrow \) c. \( E_{3}: \) "estrarre due dischetti di colore diverso" \( \rightarrow \)

Use the Gauss-Jordan method to solve the following system of equations. \[ \begin{array}{l}2 x+7 y-z=0 \\ 5 x-4 y+2 z=1 \\ 7 x+3 y+z=1\end{array} \]

Sketch the area bounded between the two curves \( 2 x+y^{2}=8 \) and \( x=y \). For credit, you must include calculations for intersection points, zeros of parabola, etc. - exactly the way I showed how to do it in lecture.