The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: Find a positive integer n for which the equality holds = 1 2

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Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

Q: If x is an odd integer then 5x – 7 is an even integer.

A: 5 and x are odd integers. Multiplication of two odd integers is always odd. Hence, 5x is an odd…

Q: The sum of any two integers of the from 4k + 1is always: prime Zero Od Even

A: Given statement, The sum of any two integers of the form 4k + 1 is always……

Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

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Q: Find all the odd positive integers n which satisfy ó(n) = 20. %3D

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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…

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Q: How many integers 2 ≤ n ≤ 65 have no prime divisor less than or equal to ¹/³?

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Q: Find all the odd positive integers n which satisfy 6(n) = 20.

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Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: How many three-digit numbers can be formed under each condition? (a) None of the digits can be 5. X…

A: when there are no condition applied we have 10 choices for each digit : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Q: What two nonnegative real numbers with a sum of 34 have the largest possible product?

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Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The Binomial Theorem is the method of expanding an expression which has been raised to any finite…

Q: If product of two consecutive odd integers is 63, then the integers are: 7, 9 9, 11 7, 11 7, 13

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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: Find the sum of the first 100 positive odd integers.

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

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Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

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Q: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.

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

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Q: Find an integer that leaves a remainder of 2 whan divided by either 3 or 5, but that is divisible by…

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Q: Can you please explain to me why is (k(k+1) ) / 2 is an integer and I know it always even so can you…

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Q: Prove that 4 does not divide n2 +2 for any integer n.

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Q: Show that 2^n &gt;n^2 if n is large enough.

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Q: The sum of the squares of two odd integers is 1) Perfect 2) Prime 3) Not perfect

A: We will find out the required solution.

Q: John found the sum of the first 2021 positive even integers and Bob found the sum of the first 2022…

A: In this question, tne concept of sum of first positive even integers is applied.

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Prove that no number of form 4k+3 (where K is a positive integer) can ever be the sum of two perfect…

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Q: The sum of the digits in the number 56 is 11. (5+6=11) a) Show that the sum of the digits of the…

A: a) Sum of the digits from 15 to 18 1+5=6 1+6=7 1+7=8 1+8=9 Now 6+7+8+9=30

Q: Show that every odd integer is the sum of two consecutive integers

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

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given To evaluate

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The (r+1)th term of the expression (a+b)n is given by Crnan-rbr. Here C represents the combination.…

Q: Find two positive integers such that the four times loo0 and the product large as possible. the .…

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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: True or false, for any integer x, x^2, - x will always result in an even number

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Without expanding completely, find the indicated term(s) in the expansion of the expression.…

Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.