For what values of m and n is 16 + mx"+9 a perfect square for all integer values of x?

Q: 7 8. The sum of two consecutive even integers is of their product. Find these integers. 24

A: Topic- basic maths

Q: 1. Identify the necessary condition in each of the following pairs: It has four sides. Seeing…

A: Solution is here

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: Is the statement true or false? If an odd number is less than 15, then it is prime. False Give a…

A: We have to check

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

A:

Q: Use Polya’s Four Steps to solve the problem: How many perfect squares are between 1,000,000 and…

A: Find the number of perfect square between 1,000,000 to 9,000,000.   The four step of Polya’s is…

Q: How many integer solutions are there to the equation x1+x2+x3+ x4 25 subject to x; > i? Let y. X,-\,…

A:

Q: E Show that the sum of the squares of the first n Fibonacci numbers is given by the formula u + už +…

A: I have proved the result by using given hint

Q: a) The square of any integer is either of the form 3k or 3k + 1.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose, and no are the smallest of two positive integers so that 300x is a perfect square and 300y…

A: The given problem is to find the values of x and y and sum of value of x+y for which smallest…

Q: A student has scores of 78, 77.25, and 81.75 on his first three tests. He needs an average of at…

A:

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: If k is a positive integer, find the (n!)k + 6 Σ ((k + 6)n)! n = 0 R =

A:

Q: In the diagram below, ABCD is a rectangle with side lengths AB = 3 and BC = 11, and AECF is a…

A: Properties of rectangle Opposite sides are parallel and equal. Each interior angle has measure of…

Q: Find formulas for the entries of M", where n is a positive integer. M"

A: First find the Eigen Value and Eigen vector

Q: Find the least positive integer n for which 2" + 5" - n is a multiple of 1000.

A: To find the value of n substitute n=1,2,3... multiple of 1000 is a certain number divided by 1000…

Q: 2. Find the area of the regular polygon. 3 12 -6 -5 -4 -3 -2 -1 n= 4 B

A:

Q: The sum of the nth row of Pascal's triangle equals 2". O True O False

A: Given that the nth row of Pascal's triangle equal to 2n

Q: How many integer solutions to x1 + x2 + x3 + x4 = 32 are there for which x1≥6, x2 ≥5, x3 ≥3 and x4…

A:

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…

A:

Q: All perfect squares are divisible by 2. A.) True B.) False, counterexample of 16 C.) False,…

A: Numbers that are divisible by 2 are {0,2,4,6,8 ,10 } Perfect sq 1X1=1 2X2=4 3X3=9  4X4=16 5X5=15…

Q: Given 0≤θ<2π , solve 2tan⁡ θ−6=0

A: 2tan(θ) - 6=0 2tan(θ)=6 tan(θ)=3 θ=arctan(3) + n*π  θ=1.10714+n*π  (in the interval [0,2π])…

Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: 2. How many positive integer solutions are there to Xị + x2 + x3+ x4 < 100

A:

Q: If m is a positive integer, does 6 divide (2m)(m+2)(3m+3)? True False

A: Here, the given number is: (2m)(m+2)(3m+3)=2(m(m+2))3(m+1)=6m(m+1)(m+2) because multiplication is…

Q: Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

A: We have to show that the sum of the squares of the first n natural numbers is given by S=nn+12n+16…

Q: 3. Determine the nth-term formula for the number of square tiles in the nth figure. а. a2 a4 as b.…

A:

Q: Determine all prime numbers a, b and c for which the expression a² + b° + c° - 1 is a perfect…

A: We have to find the prime numbers a, b and c such that the expression a2+b2+c2-1 is a perfect…

Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 &amp; x4≥6.

Q: 2. A toy company sells 3-packs of sphere-shaped bouncy balls. If the company ships the three bouncy…

A: Finding the empty space in the given figure.

Q: 7. How many integer solutions are there to 2r, + 2tz + 2rz + Xg +X5 = 9 with x; 2 0? (Hint: break…

A: Solutions to the equation are the set of values for which equations returns the same value on both…

Q: Any integer of the form 8k + 7 is also of the form а) Зт + 1 b) 5m + 2 4m + 3 d) 6m + 1

A: given the integer of the form                                                               8k+7 it…

Q: For which positive integers $n$ greater than or equal to 2 is $\sqrt[n]{a^{n}}=a$ always a true…

A: We need to check for all the values to get the result

Q: Which of the following sequeces in GP will have common ratio 3, where n is an Integer? a) gn = 2n2…

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Q: Show that every odd integer is the difference between two consecutive perfect squares.

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Q: 6. If x is any positive integer, which one of the following terms could be added to the sum of 2x +…

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Q: Suppose that r1, 12, · · · ,x13 are natural numbers, and consider all solutions of the equation…

A: Given - Suppose that x1, x2, ....., x13 are natural numbers , and consider all solutions of the…

Q: 10. Which of the following is the cube of ( 2x - 1)? a. 8x + 12x + 6x +1 b. 8x + 12x2 + 6x -1 c. 8x°…

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Q: How many multiplicity of - 1 are there in the roots of x +3x2 + 3x+1 0? O 1 O 2 3 O 4

A: Given equation  x3+3x2+3x+1=0

Q: How many integer solutions are there to 1 +X2+X3+X4+Xs=31 with

A: Given, x1+x2+x3+x4+x5=31 Number of Solutions when xi≥0 and xi&gt;0.

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

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Q: 2.4 Find all the integer points on the following lines, or show that none exist. (a) 16x – 33y = 2.…

A: Note "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: How many solutions are there to the equation x1 + x2 +3 + x4 + x5 = 39, where each x; is an integer…

A: Solution

Q: the acdjainbaf square of As of 2.

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Q: Abby notices that for the first twenty perfect squares, each square is either a multiple of 5, one…

A: If n is a natural number, then n2 can be written as 5k- 1,5k, or 5k +1, where k is a whole number.…

Q: 4. The area of a parallelogram is 198 square units. If the base and the height of the parallelogram…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.