Se realizó una encuesta a 20 estudiantes de grado sexto acerca de la cantidad de pan que consumen durante la semana, y estos fueron los resultados obtenidos: \[ 3,1,6,3,2,4,5,3,4,3 \] \[ 2,8,1,3,5,8,6,5,4,4 \] La cantidad promedio de panes que cada uno de los 20 estudiantes consume a la semana es:

Perform the following additions and/or subtractions: \( r^{2}+6 r+5 r+30= \)

PN \( =\mathbf{n R T} \) \( \frac{V_{1} \times P_{1}}{T_{1}}=\frac{V_{2} \times P_{2}}{T_{2}} \quad \) Formula de la ley combinada de las gases: \( \frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}} \quad \)

The points \( A(2,3), B(-11,8) \) and \( C(-4,-5) \) are vertices of a parallelogram \( A B C D \) which has \( A C \) as a diagonal. Find the coordinates of vertex \( D \).

6. Solve for \( b \). \( \frac{b h}{2}=A \)

Answer any five questions from this section \[ \text { All questions carry equal marks. } \] (a) Prove that if \( \frac{z-6 i}{z+8} \) is real, then the locus of the point representing the complex number \( Z \) is a straight line. Hence state the gradient of the line. (06 marks) (b) If \( Z_{1}=\frac{2 i}{1+3 i} \) and \( Z_{2}=\frac{3+2 i}{5} \); (i) Represent \( Z_{1} \) on an Argand diagram (ii) Find \( \left|Z_{1}-Z_{2}\right| \)