A. show that {a : 15a ≡ 18 (mod 24)} is not a subgroup of the group z24 (with operation +)
b. let g = zm (the operation is addition) and let b be some number with 1 ≤ b < m. show that the cyclic subgroup h generated by b is all of g if and only if the least common multiple of b and m is bm, if and only if (b, m) = 1.
c. show that the subgroup of z consisting of all solutions x in z of ax ≡ 0 (mod m) is the cyclic subgroup rz where r = m/(a, m).

1. what expression would be the same as 6x+x+0 2. find the prime factorization of 60 3. write the expression for 6 + x in words.

Una caja de galletas contiene 16 paquetes y cada una de estas tiene 12 galletas y se quieren repartir entre 6 niños ¿de cuantas galletas le toca a cada niño?

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.