If n EN and n < 2000, how many numbersn have the property that the sum of the digits of n and the sum of digits of n +1 are odd numbers?

Q: how many four digit numbers can be formed if all the digits are odd numbers and each digit can be…

A: Using the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, here 4 digit numbers are formed in which all…

Q: How many three numbers with no repeated digits, can be formed by the use of the digits 0, 2, 3, 4,…

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Q: How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be…

A: It is given that the first three digits cannot be 800 or 900 or all the numbers from 000 to 099.…

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: How many 5 digit even numbers are there, a. Given that the first digit cannot be zero. b. Given…

A: In five digit following digit can be filled in following ways: First digit can be filled by…

Q: How many numbers of four different digits each greater than 5000 can be formed from the digits 1, 2,…

A: Answer - How many numbers of four different digits each greater than 5000 can be formed from the…

Q: How many six-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: From the given information,Sample space = {0,1,2,3,4,5,6,7,8,9}It has been given that the leftmost…

Q: A Certain bacteria culture triples in a number every day. If there were 100 bacteria at the end of…

A: Let in general there are n0 bacteria after 1 day.  Then after second day, no of bacteria will be 3a0…

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

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Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each…

A: Given:     The sequence is:     1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,... To get this number, we have to…

Q: How many 6-places license plates are possible if he first 3 places re to be occupied by letters and…

A: Given data: How many 6-places license plates are possible if he first 3 places are to be occupied by…

Q: How many three digit numbers have the property that the sum of that number and the three digit…

A: How many three digit numbers have the property that the sum of that number and the three digit…

Q: How many five​-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: To count the number of 5 digit integers satisfying the given conditions

Q: A company wants to have 6-digit phone extensions with the first digit not being zero. How many…

A: Given, No. of digit in phone extension = 6 First no- cannot be  0 Therefore no. of ways it can be…

Q: How many positive integers less than 1,000,000 have a digit sum of 5?

A: We have to find the number of positive integers 1,000,000 have a digit sum of 5. The number less…

Q: Prove that the sum of any three consecutive numbers is divisible by 3

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Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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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: How many 4-digit odd numbers can be made from the digits 0; 2; 4; 5; 8; 9 if the number has no…

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Q: How many mombers between 50 and 200 can be expressed as 4k-1, where k is an integer?

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Q: Among all the numbers between 40000 and 90000, including the numbers 40000 and 90000, how many each…

A: The total number of numbers between 40,000 and 90,000 is 90,000-40,000+1=50,001. First calculate the…

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: How many 2 – digit numbers can be formed from the four integers 1, 2, 3, and 4 if repetition is…

A: Given2-digit numbers to be formedNo.of integers =4           (1,2,3,4)

Q: How many 5 digit even numbers can you form using all of the digits 1, 2, 3, 3, 5?

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Q: How many odd 4-digit numbers greater than 3000 can be formed from the digits 1, 5, 6, 7, 8 if no…

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Q: Show A and Show B are two of the most popular television shows of all time. The number of episodes…

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Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: In a large math conference with 2022 participants, each person shakes hands with some number of…

A: For 'n' number of participants the maximum number of handshakes is n(n-1)/2.

Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

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Q: The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is…

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repetition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

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

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

A: 22-5n&gt;-3

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

Q: How many four-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: Among all the numbers between 20000 and 70000, including the numbers 20000 and 70000, how many each…

A: The total number of numbers between 20,000 and 70,000 is 70,000−20,000+1=50,001. First calculate the…

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

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Q: How many three-digit odd numbers are possible if the leftmost digit cannot be zero?

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

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Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

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Q: How many even three digits numbers can be formed from the digits 3,2,5,6 and 9if each digit can be…

A: We have to make three digit even number which means that last digit should be even number. Here,…

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

A: Given: n∈ℕ And n&lt;2000

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

A:

Q: How many even number more than 10 but less than 800 can be formed from the digits 1, 4, 5, 6, 8 and…

A: even number more than 10 but less than 800 can be formed from the digits 1, 4, 5, 6, 8 and 9

Q: How many four-digit positive integers both start and end in even digits:

A: We need to find the number of positive integers both start and end in even digits.