Suppose we are given a set S of 50 distinct ordered pairs of integers (ai , bi). Does there exist two ordered pairs (aj , bj ) and (ak, bk) in S such that both (aj mod 7 ≡ ak mod 7) and (bj mod 7 ≡ bk mod 7)? Prove your answer.

Organisms that live in the alpine and taiga biomes have developed unique adaptations that aid in their survival. the douglas-fir is a conifer tree that grows in the taiga biome. it has an average height of about 70 feet, and its wood is an important source of lumber.

In the triangles, tr = ge and sr = fe. if = 3.2 ft, which is a possible measure of ? 1.6 ft 3.0 ft 3.2 ft 4.0 ft

Find the distance between (0,5) & (-4,2)