2. Prove the statement: The sum of the squares of any two consecutive integers is odd.

Q: If P(A) = 0.33%, P(B) = 0.79%, and A and B are mutually exclusive, what is P(A ∩ B)?

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Q: If m and n are integers and m x n = 0, then what is true for the values of m and n?

A: If m and n are integers and m×n=0

Q: Is it true that the rank of [B AB If not, under what condition will it be true? A"-B] equals the…

A:

Q: 9. A string measures 15 inches is cut into two pieces. Let x represent the length of one of the…

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Q: 2. Find NP. M 8

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Q: Based on your answers in (b), show that 12 1 1 2² 3² 4²

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Q: "If a and b are positive integers, a divides b and b divides a, then a = b."

A: To Prove: '' If a and b are positive integers, a divides b and b divides a, then a = b''.

Q: Find the derivatives of all orders of the functions

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: What can you conclude about the numbers m and n if X " = 7 and r is an even number and m and n are…

A: The number that is divisible by 2 is called the even number and the number that is not divisible by…

Q: No two 'a' are adjacent, No two 'b' are adjacent, No two 'c' are adjacent.

A:

Q: 2. Let n be a natural number and let A, B E Mnxn(C). If AB = 0, does it follow that either A = 0 or…

A: Given :  A, B ∈ Mn×n(ℂ)  with  AB = 0. To find : We have to examine whether  A=0 or  B=0.

Q: 8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

A: Given operation is a*b = 3a+b

Q: If m and p are positive integers, which expression must be negative?

A: Let m and p are positive integers ,

Q: Prove : (A-B)n C =(A n C) -B

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Q: r if in reality the company workers have the

A: * Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at…

Q: If both x and ( + + ) are positive integers, what is the least possible value of x? 10 120 90 60 30

A: Given that, x and  x5+x6+x10 are positive integers. To find: Least possible value of x. And, for…

Q: Find a counterexample to show that the following statement is false. The sum of two four-digit…

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Q: If both x and ( ++ ) are positive integers, what is the least possible value of x? 10 120 90 60 30 O…

A: Given : if x and x5+x6+x10 are positive integers. we have to find the least value of x.

Q: If n E N and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Here n  N and n&lt; 2000. So, n= 1,2,3,........,1999.

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: Given that a + bv3 = V151+ 28V3, where a and b are positive integers, calculate the value of a and…

A: To find- Value of a and b.

Q: If the mean of an even number of consecutive integers is 0.5, what is the sum of the two middle…

A: Given The average of an number of consecutive integers is 0.5. We know that that The average of an…

Q: 23 - where a and b are positive integers; How many b values are there for the condition 2a + 3b =…

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Q: O show that ifthe Solution givenbelow fandementalernst! -t -- -22 +3

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Q: Let ab be a two-digit number where a is the tens digit and b is the ones digit. Find the number of…

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Q: If 48 ÷ x is a positive integer and x is an integer, what are the possible values of x?

A: We have to find interger

Q: If k k k = 2, and x = integer, which statement is NEVER true about x? %3D %3! es 4) A) x is 0 B) x…

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Q: What is the value of x?

A: Given, volume of cylinder and radius

Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

Q: Is it true that, if k > n and B is full rank, then rank AB (ii) = rank A? Justify your answer.

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Q: Using the fact that in U39, [4]1 = [10), find [16]–1.

A:

Q: 10. Determine (and explain) if the statement is true or false. (a) |{Ø}| = 0. (b) [0, 1] is…

A: Given sets is

Q: If X~N(10,4) what is P(5<x<8)

A:

Q: Given that a, b, c, d are consecutive positive integers, such that a <b<c<d,which of the following…

A: Consider that a, b, c, d are consecutive positive integers such that a&lt;b&lt;c&lt;d.   Find the…

Q: Show that E(x-a) = E(x; -x) + n(x- a), squares about a = is smallest. other words, show that the sum…

A: The answer is as follows :

Q: Use deductive reasoning to determine the missing numbers in each magic square. | 36 9 4 7 6. 5 10 8…

A: The magic square has  same sum of row elements, sum of column elements  and sum of diagonal elements…

Q: The addition property of equality states that if a b, then a + c =

A: The addition property of equality states that if a = b, then a+c=b+c

Q: 7. How many non-negative integer solutions are there to the equation X1 + X2 + X3 + 4 = 16 such that…

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Q: which

A:

Q: If n E N and n< 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given that, If n∈ℕ and n&lt;2000 then calculate how many numbers n have the property that the sum of…

Q: is ' (3n– 1)? n=1

A:

Q: Use the theorems and given information to show that r | 8. %23 1 2 3 4 87 6/5

A:

Q: b. She gets one of each color other than blue, given that she gets at least one red one.

A: Here use conditional probability and hypergeometric distribution

Q: 6. Find the length of AB in terms of n. 204 B 16 in.

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Q: If P(A) = 0.36%, P(B) = 0.61%, and A and B are mutually exclusive, what is P(A ∩ B)?

A: We have given that,  A and B are Mutually exclusive events and P(A) = 0.36%, P(B) = 0.61% then,  We…

Q: show that given two numbers m and n, if m is even and n is even, then the product is even

A: Solve by using product rule

Q: (d) If x and y are real numbers and x < y, then x² < y*. (e) If æ and y are positive real numbers…

A: We have to find