Develop a divisibility test that will work for 45. Then prove your divisibility test for the four-digit number 1000a3+ 100a2+ 10a1+ a0. This should be a mathematical proof, not a word or paragraph proof.

Q: If you want to check that 613 is a prime number using the test for primality, what is the minimum…

A: Given number is : 613 To find what is the minimum amount of number must divide into 613 to check…

Q: How many different three-digit numbers can be formed using the digits 3,4,8,5,7,1, and 6 without…

A: Given problem:- How many different three-digit numbers can be formed using the digits 3,4,8,5,7,1,…

Q: How many phone numbers are there of the form 962-xxxx? repeated is possible Answer:

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Q: Determine the number of natural numbers less than 700 that can be written using the digtits 5,6,7,9?

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Q: Briefly explain the differences between proof by contradiction and proof by mathematical induction.

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Q: Determine whether the statement, 'I used the permutations formula to determine the number of ways…

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Q: A number N is divisible by 4 iff the number formed by the last 2 digits of N is divisible by 4. For…

A: We can find number divisible by 4  by using the concept given in the question

Q: Outside a home, there is an 8-key keypad numbered 1 through 8. The correct five-digit code will open…

A: There are totally 8-key keypad numbers. The correct five-digit code will open the garage door. The…

Q: How many ways can you get we get a 2 digit passcode if zeros are not allowed?

A: If zero is not allowed, The number of available digits is 9 (1,2,3,4,5,6,7,8,9)

Q: Two-digit numbers are formed, with replacement, from the digits 0-9. How many numbers are divisible…

A: Assume that the two-digit numbers are formed, with replacement, from the digits 0-9. From that, find…

Q: Determine whether the statement is true or false. Modify each false statement to make it a true…

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Q: Marshall had d dogs that he put into 4 different areas. How do you write this as a divison sentence?

A: Consider the provided question, Given, Marshall had d dogs that he put into 4 different areas. We…

Q: Given the characters A,B,C,H,I,T,U,V,1,2,3,and 4, how many seven character passwords can be made? (…

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Q: Using the digits 2, 4, 6, 7 and 9, how many five-digit numbers can be formed if the number is…

A: Given Information: Digits = 2, 4, 6, 7 and 9 To find how many five-digit numbers can be formed if…

Q: Determine the formula and (largest) domain for the following expression and then prove it using…

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Q: How many positive integers between 5 and 31 (a) are divisible by 3? (b) are divisible by 4? (C) are…

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Q: To use an automated teller machine at a certain bank, you must enter a 3-digit code, using the…

A:

Q: A contest consists of finding all code words that can be formed from the letters in the word…

A: A). The number of ways to form 5-letter words is, Thus, the number of ways to form 5-letter words…

Q: i Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g. '924 VXA' or 4…

A: We have to use sum and product rule to solve given questions- (I) Concept: Since total number of…

Q: Is the statement, "If a number is divisible by 2 and 3, then the number is divisible by 6" true or…

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

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Q: 3.) Using matiematical induction, prove tiat lo" + 3 ·4*7+5 n+ 2 is divisible by 9 for n ?0

A: To prove the given statement by induction.

Q: In how many possible ways can you arrange the numbers 123456 such that: A) There is one block of…

A: Consecutive and ascending numbers : 1,2,3 2,3,4 3,4,5 4,5,6 Number of arrangements =?

Q: Lizzie came up with a divisibility test for a certain number : Break a positive integer  into…

A: Introduction: The divisibility is the base of number theory. There are different rules of…

Q: Which divisibility test can you use to find out if any number is even? O Divisibility test for 3…

A: Given, the divisibility test for 2, 3, 4 and 5.

Q: what are ALL the six-digit numbers of the form 47_8_6 that are divisible by 24?

A: The six-digit number has form 47__8__6

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: 千 -9 -8 -7 -6· -5 -4 -3 -2 -1 0 1 2 3 egment on the number line?

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Q: Find the number of distinguishable permutations of the digits of the number 228,434.

A: Write the number in frequency format: Numbers Frequency fi 2 2 8 1 4 2 3 1 Total…

Q: Find the number of different 7-digit numbers which can be formed from the seven digits 4, 4, 7, 9,…

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Q: A certain website wants you to build a 6-character password from the letters a through i, the…

A: Given: The letters will be selected from a through i. Thus, there are a total of 9 letters from a…

Q: Without using a calculator, test for 60,330 for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11 Is…

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Q: I want to make a password using 3 consonants followed by 3 vowels. Given that I do not want…

A: password : 3 consonants followed by 3 vowels   out of 26 letters there are 5 vowels {a,e,i,o,u} so…

Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

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Q: To use an automated teller machine at a certain bank, you must enter a 6-digit code, using the…

A: To determine the number of 3-digit codes.

Q: An employee in the Department of Motor Vehicles for this state believes that it is easier for people…

A: There are 26 upper case letter, and 10 numerical digits (0 - 9). The first letter have 26 possible…

Q: (a) Suppose we want to test whether or not the number 217 is prime. List the minimum amount of…

A: A prime number is a number that is divisible only by 1 or itself. So, to test whether the number 217…

Q: Find the number of possible call letters of a radio station (5 letters long) if the first letter…

A: Note: Hi there! Thank you for posting the question. As there are several independent questions,…

Q: How many three-digit code can be made where the order of digits is not important? The possible…

A: Three digits code is to be prepared by  0,1,2,3,4,5,6,7,8,9. That is with the help of the 10 digits…

Q: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits…

A: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits (don’t…

Q: What is the first common multiple of 5 and 7 that is even num

A: Multiple of an integer d:For an integer d, if there exists a  such that n = kd, where n and k are…

Q: How many different five-digit numbers can be formed using only the digits of the number 75, 226,…

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Q: A palindrome is a number that reads the same forward and backward, such as 2,743,472. (a) Give a…

A: Solve the following

Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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

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Q: Japanese license plates in each state consist of 8 characters. The first two characters can be any…

A: From 0-9 there are 10 digits  First character can occur in 10 ways  The second character can occur…

Q: Answer the following question. Each positive integer can be written as a sum or difference of…

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Q: ônsider the set of whole numbers from 3 to 30, inclusive. List the numbers that meet the condition:…

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Q: Use inductive reasoning to predict the next three numbers in the pattern. 4, – 12, 36, – 108, ..…

A: Given numbers are  4, -12, 36 , -108..

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.