Cocoa farming in Ghana is supported by specific agricultural practices. What method is most commonly used for drying cocoa beans after fermentation? a. Sun drying combined with artificial heating b. Employing large-scale solar drying panels c. Using mechanized dryers for rapid drying d. Spreading beans in the open air for six days

A historian is exploring the demographic patterns in West Africa's high forest zone. Which historical factor best explains the hig population density in this area? a. Absence of significant slave raids b. Consistent low temperatures c. Frequent and devastating wars d. Lack of fertile soils for agriculture

5. A psychologist is interested in exploring the effect of utorial suppot on students' academic performance and assign students into two groups. Students in group one the tutorial support and those in groupltwo do not. In this example, what is the a) Dependent variable b) Independent variable c) Control group d) Experimental group

4. ¿Cuál de estas igualdades es correcta? (A) \( \log _{3} 8=2 \) (B) \( \log _{3} 2=8 \) (C) \( \log _{2} 8=3 \) (D) \( \log _{2} 3=8 \) (D)

12. Find a standard basis vector for \( R^{3} \) that can be added to the set \( \left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\} \) to produce a basis for \( R^{3} \). (a) \( \mathbf{v}_{1}=(-1,2,3), \mathbf{v}_{2}=(1,-2,-2) \) (b) \( \mathbf{v}_{1}=(1,-1,0), \mathbf{v}_{2}=(3,1,-2) \)

(b) Show that the relation R on the set \( \mathrm{A}=\{1 \), \( 2,3,4,5\} \) given by \( \mathrm{R}=\{(\mathrm{a}, \mathrm{b}):|\mathrm{a}-\mathrm{b}| \) is even \( \} \) is an equivalence relation.