(b) Prove that for every n e Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.

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A: TO PROVE:-  There is a positive number z satisfying z5+10z=10 GIVEN :- z5+10z=10

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Q: how did you work out its even in part a?

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A: Given

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A: Prove that  there is no solution for positive integers.Let if for for

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A: In this question, we will compute the matrix.

Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

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Q: Using strong PMI, show that every natural number is a sum of powers of 2. For example, 11 = 23 +2¹…

A: Using strong PMI, we have to show show that every natural number is a sum of powers of 2.

Q: expand 7q(q-2)

A: To expand: 7qq-2 We know that: a(b+c) = ab +ac

Q: c) 2x, +8X2 -Х3 +9х4 =9 X, +3X2 -2х3 +5 Хи 3X, +5Х2 - 12Х3 +17Х4 = 7 че

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Q: Would you be able to help answer the last 3? Those are the ones I am struggling with!

A: X ~Bin(25, .05).

Q: Use matlab to calculate each of these values

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:      MATLAB CODE THAT CAN BE DIRECTLY COPIED TO…