answer:b. The people honored the spirits of their ancestors. Explanation: In many African village cultures, honoring the spirits of ancestors was a significant characteristic. Ancestor veneration is a common practice in various African cultures, where people believe that the spirits of their deceased ancestors continue to play an important role in their lives. They often seek guidance, protection, and blessings from their ancestors through rituals, prayers, and offerings. This practice reflects the strong sense of community and interconnectedness within African village cultures, where the past, present, and future are intertwined.

answer:We know that the volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. We also know that the rate of change of volume with respect to time is given by dV/dt = -2/3 cm³/min. We can use the chain rule to find the rate of change of the radius with respect to time: dV/dt = (dV/dr)(dr/dt) Substituting the given values, we get: -2/3 = (4πr²)(dr/dt) Solving for dr/dt, we get: dr/dt = -(2/3) / (4πr²) When the diameter of the snowball is 10 cm, the radius is 5 cm. Substituting this value into the equation, we get: dr/dt = -(2/3) / (4π(5)²) dr/dt = -0.0021 cm/min Therefore, the radius is decreasing at a rate of 0.0021 cm/min. The radius is decreasing at a rate of 0.0021 cm/min.

answer:We can state that for every n in mathbb{N} left|operatorname{Hom}(mathbb{Z}_n,mathbb{Z})right| = 1 which result to be the trivial homomorphism, since from the First Homomorphism Theorem mathbb{Z}_n / operatorname{Ker}(varphi) cong operatorname{Im}(varphi) < mathbb{Z}, but all the subgroup of mathbb{Z} are of the form dmathbb{Z} which of course are infinite, and since |mathbb{Z}_n / operatorname{Ker}(varphi)| < +infty we have d = 0 hence operatorname{Ker}(varphi) = mathbb{Z}_n Conversely to count left|operatorname{Hom}(mathbb{Z},mathbb{Z}_6)right| we know they are determined once assigned the image of a generator since mathbb{Z} is a cyclic group. Because we can choose phi(1) in |mathbb{Z_{6}}| = 6 ways there are 6 such homomorphisms.

answer:The Euclidean distance d between the two vectors is calculated as follows: [ d = sqrt{left(frac{38}{5} - frac{41}{5}right)^2 + left(frac{3}{5} - 7right)^2 + left(frac{39}{5} - left(-frac{16}{5}right)right)^2 + cdots + left(frac{8}{5} - left(-frac{29}{5}right)right)^2} ] [ d = sqrt{left(-frac{3}{5}right)^2 + left(-frac{32}{5}right)^2 + left(frac{55}{5}right)^2 + cdots + left(frac{57}{5}right)^2} ] [ d = sqrt{frac{9}{25} + frac{1024}{25} + frac{3025}{25} + cdots + frac{3249}{25}} ] [ d = sqrt{frac{9 + 1024 + 3025 + cdots + 3249}{25}} ] [ d = sqrt{frac{7072}{25}} ] [ d = frac{4 sqrt{707}}{5} ] Thus, the distance between the two vectors is frac{4 sqrt{707}}{5}.