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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Solve the linear equation: The equation relating the pressure that is denoted by P, to the force, F & the area, A, over which the force is applied is P =F/A. Solve this equat
A wholesaler allows a discount of 20% on the list price to a retailer. The retailer sells at 5% discount on the list price.If a customer paid Rs 114 for an article,what profit is m
briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived
Generate a 1000 vertex graph adding edges randomly one at a time. How many edges are added before all isolated vertices disappear? Try the experiment enough times to determine ho
Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution: There are 10 wa
What is the Vertex Form for a Quadratic Equation ? The vertex form for a quadratic function is as follows: f(x) = a(x - h) 2 + k The graph of this function Is a parabola whos
encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)
Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o
If the side of a square can be expressed as a2b 3 , what is the area of the square in simplified form? Since the formula for the area of a square is A = s 2 , then by substitut
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