Show A and Show B are two of the most popular television shows of all time. The number of episodes of each show are consecutive even integers whose sum is 510. If there are more episodes of Show A, how many episodes of each were there?

Q: Three postal Workers can sort a stack of main in 30 minutes, 20 minutes, and 60 minutes,…

A: See the detailed solution below.

Q: plz solve q4

A:

Q: A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees pläntec…

A: Given 24 trees per row1235 trees to plant

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

A:

Q: pair of these integers with a sum equal to 9.

A: Let us take set under consideration {1,2,3,4,5,6,7,8}Possible pairs {{1,8}, {2,7}, {3,6}, {4,5}}…

Q: A company wants to have 4-digit phone extensions with the first digit not being zero. How many…

A:

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

A:

Q: If the sum of two counting numbers is an even counting number, then the product of the two counting…

A: Suppose the two counting number is 5 and 5

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: 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: In a two-digit number, the tens-digit is greater than the units-digit. The product of these two…

A:

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

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

A:

Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

Q: Write the number 6 as a sum of three natural numbers in several different ways, and, in each sum,…

A: To be solved - Number 6 as a sum of three natural numbers in several different ways, and, in each…

Q: A time traveler can take 5 books with him, and he has 76 books to choose from. How many different…

A:

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: A certain number is doubled and then divided by 8. If after subtracting 4 from this result, one gets…

A: The statements involving algebraic operations and expression namely addition , subtraction ,…

Q: How many digits should be removed from a 1000-digit number 2008... 2008 such that the sum of…

A:

Q: Find a three-digit positive integer such that the sum of all three digits is 14, the tens digit is…

A:

Q: Any n consecutive integers will include a number that is divisible by n.

A:

Q: Suppose a license plate contains two letters followed by three distinct digits with the first digit…

A: Ans#- Given, A license plate contains two letters followed by three distinct digits with the first…

Q: When 32 is divided by an integer, the remainder is 4. When 51 is divided by the same integer, the…

A: We can use concept of HCF to solve the problem

Q: A company wants to have 7-digit phone extensions with the first digit not being zero. .... How many…

A:

Q: Which integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided…

A:

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

A:

Q: how many 6 digit numbers can be formed, if at the place of hundred thousand there are allowed two…

A: Yes your step is right.Hundredth thousand place can be chosen in 2 ways. And hundredth place can be…

Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

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: 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: Prove that the sum of the squares of three consecutive integers cannotbe a square.

A:

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: In a round-robin tennis tournament, every player meets every other player exactly once. How many…

A: let x = number of players Each player plays x-1 matches BUT a vs b is the same as b vs a So the…

Q: How many integers must you pick in order to be sure that at least two of them have the same…

A:

Q: How many distinct integers do we have to pick in order to have two that have the same remainder when…

A: To find - How many distinct integers do we have to pick in order to have two that have the same…

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

A:

Q: Is it possible for two numbers to have the same least common multiple and greatest common devisor?

A: To check whether for two numbers can have the same LCM and HCF.

Q: A time traveler can take 4 books with him, and he has 98 books to choose from. How many different…

A:

Q: In a certain town every telephone number consists of four digits, the first of which cannot be zero.…

A:

Q: The sum of an integer and 4 less than that integer is even.

A:

Q: Find five consecutive odd integers such that when the fifth is subtracted from eigt times the…

A: We're going to solve

Q: If an Iphone password can have 4 or 6 digit passwords how many combination can there be if there has…

A: Iphone password can have 4 or 6 digit passwords. There are 10 digits in the number system,…

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

A:

Q: many even four-digit numbers can be formed from the digits 0, 1, 2, 5, 6, and 9 if each digit can be…

A:

Q: The sum of the four positive integers a, b, c, and d is at most 10. Find the number of possible…

A: Explanation of the answer is as follows

Q: If the sum of n successive odd natural numbers starting from 3 is 48 , Find the value of n

A:

Q: A ball is dropped from a height of 192 feet. If it rebounds 3 4 of the height from which it falls…

A:

Statements and Logic

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