Use base-ten blocks to illustrate 142 + 5. 142 has flat(s), long(s), and unit(s). Starting with the flats, there are set(s) of 5 flats with remaining. Converting the remaining flats to longs gives a total of long(s), which leads to set(s) of 5 longs with remaining. Converting the remaining longs to units gives a total of unit(s), which leads to set(s) of 5 units with remaining. Therefore, the quotient is with a remainder

Q: Let p>5 be the prime number. Prove that the expression p4-10p2+9 is divisible by 1920.

A: Let, p>5 be the prime number. Prove that the expression p4-10p2+9 is divisible by 1920.

Q: 15) n(n*+5) is divisible by for each integer

A:

Q: Use mathematical induction to show that 5? − 1 is divisible by 4. Determine the starting value as…

A:

Q: prove the following statement: Let n be an integer. If a and b are integers such that a is divisible…

A:

Q: Suppose that ? is N(30, 2). What is ?(28 < ? < 34)? *Use the 68-95-99.7% rule.

A:

Q: Determine whether the following statement is true or false. Justify your answer with a proof or a…

A:

Q: By Principle of Mathematical Induction prove 5" -1 is divisible by 2 for all n>1

A: To prove: Proof: Use the first principle of mathematical induction that holds for natural numbers.

Q: 3.) In a statement in Mathematical induction, we may only use positive integers or natural numbers…

A: We have to solve given problem:

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate P(x)

A: Yes we can use mathematical induction for Natural number x.

Q: The fourth term in the expansion (2x – 3) -3 is 270 64x6 O 270 32x6 O 270 64x3 O 540 64x3

A:

Q: person can encode 1000 words in every hour of typing job.which of the number n of hours that the…

A: Number of words the person can encode per hour=1000

Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

A:

Q: The row of Pascal's triangle that corresponds to n = 9 is as follows. 19 36 84 126 126 84 369 1.…

A: The solution is given below

Q: Use mathematical induction to prove that the sum of the squares of the first n natural numbers : Ek?…

A: Let's prove.

Q: Ci) Use the method of Mathematical Induction to show that for all positive integer values n21,…

A: The principle of mathematical induction is a technique of proving a statement or formula which is…

Q: Select all expressions equivalent to (47 4-5)-2. А. 16-2 256 В. 1 С. 45.4-7 O 2019 Nextgenmath.com…

A: Given : ( 4^7.4^-5)^-2

Q: 13. Use mathematical induction to show that 1+4 4-1/344-1).

A:

Q: How many positive integers between 1000 and 9999 inclusive a)are divisible by 9? b)are even?…

A: .

Q: Show by induction that 19"-8" is divisible by 11 for all n >0

A:

Q: 3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all…

A: We have to explain that n!+2, n!+3,…,n!+n-1,n!+n are all composite numbers.

Q: divisible by 3 for

A:

Q: Exercise 6.4 (1) For which natural numbers n is the number 3" + 1 divisible by 10? Find the…

A: (1) We have to find the natural numbers for which the number 3n+1 is divisible by 10. (2) We have to…

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: . Let m be any odd whole number. Then m is a divisor of the sum of any m consecutive whole numbers.…

A: I have supposed that m is any odd whole number and then I have taken another arbitrary whole number…

Q: If n is a natural number, the number 34n+4 – 43n+3 is divisible by: -

A: Given : To find : A positive number which can divide above expression

Q: 5. How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

A: We have the given condition as   Let us consider A be the set of all positive integers whose last…

Q: 9. Find the sum of all'integers between 90 and 190 if each integer Is divisible by 17 (Hint. The…

A:

Q: Find the sum of all four-digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without…

A: Answer: Option b)  666600

Q: How many positive integers greater than 5 and less than 2020 are divisible by 7? are divisible by…

A: 1) Here , 2020/7 = 288.57 So 288 multiples of 7 are there between 5 to 2020 So , 288 integers are…

Q: Let p>5 be the prime number.Prove that the expression p4-10p2+9 is divisible by 1920.

A: Given: Let p&gt;5 be the prime number

Q: A box with a square base and no top is to be made from a square piece of cardboard by cutting 2 in.…

A: Let consider that x be the length of one side of the cardboard When 2 inches are removed from each…

Q: Test each number for divisibility by 11 by alternately adding and subtracting the digits 1 left,…

A:

Q: Consider all numbers between 20000 and 70000. Efficiently determine: A) How many of these numbers…

A: Part A - Let’s represent the number as ABCDE. You have to considere the special cases first, since…

Q: 1. Rehan proved by mathematical induction that for all the positive integers, n + 2n is divisible by…

A: Given that , For all positive integers, n3+2n is divisible by 3. To find an integer counter example:…

Q: P(n): 4" – 1 is divisible by 3.

A:

Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

A:

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in.…

A: Given: A box with a square base and no top is to be made from a square piece of cardboard by cutting…

Q: Let p > 5 be the prime number. Prove that the expression p* - 10p? + 9 is divisible by 1920.

A:

Q: 3. There are seven students who always compare their CS test grades. They discovered that either the…

A: It is given that there are seven students who always compare their CS test grades. They discovered…

Q: n that includes all terms up to

A: The initial value problem is , w''+7xw'-w=0. It is given that w0=6, w'0=0. w''+7xw'-w=0. To find the…

Q: Use base-ten blocks to illustrate 176 +8. 176 has flat(s). long(s), andunit(s). Starting with the…

A: 176 can be written as 1×102+7×101+6×1  so the 1 is called flats 7 is called longs and 6 is the units…

Q: Find the sum of all natural numbers n such that 2021-n/99 is a natural number ?

A:

Q: 74. P is a natural number of at least 6 digits and its left- most digit is 7. When this leftmost…

A: Introductions :

Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: The product of all the natural numbers from 1 to n is written as n! it is read as "n factorial" true…

A:

Q: Given an integer N with an odd number of digits. Let M be the integer formed by reversing the order…

A:

Q: (3) Prove the following by contraposition. If n? is not divisible by 3, then n is not divisible by…

A: Statement:if A then B Contrapositive statement:if not B then not A

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.