How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?

Q: The number 6 has four divisors -- namely: 1, 2, 3, and 6. List all of the numbers less than 20 that…

A: Given that: Divisors of number 6 = 1, 2, 3, 6

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: How many zeros does 25! end with?

A: A number will have trailing zeros when 5 and at least one even number are factors of it.   Also, the…

Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: Suppose a license plate number in this state can only contain capital letters and digits and can…

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

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Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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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: Use the binary exponentiation algorithm to compute the remainder when 385 is divided by 53.

A: Remainder (385 / 53) 385 = 77 * 5 77 / 53 leaves remainder 24 So  24 * 5 = 120  When 120 / 53 leaves…

Q: How many 10-bit strings are there if the string must have exactly one 1 in the first half and…

A: The string must contain exactly one 1 in the first half and exactly one 1 in the second half. So…

Q: In one case a byte is defined as a sequence of 8 bits. Each bit can be either zero or one. How many…

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Q: Find x and a21 if 5x - 3, X+2, and 3x - 11 form an arithmetic scquence

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Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

A: Conditional probability : Conditional probability is a measure  of the probability of an event…

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: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

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

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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: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: = 5 Find a3, a4, and as for the recursive formula an = an-1 +3an-2 if a1 = 2 and a2

A: given   recursive formula is an= an-1+3an-2and   a1=2   ,  a2=5then we have to find  a3 , a4  , a5…

Q: How many hexadecimal numbers from 1 through FFFF do not have any repeated digits?

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Q: Find the sum of the first 20 positive even integers.

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Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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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 zeroes does 188! end with?

A: count number of five's in 188, 5*2=10 . Divide 188 and write quotient again divide quotient again by…

Q: Select each expression that has a sum of 4 4/12 3 1/5 + 1 3/7 1 11/12 + 2 1/4 1 3/6 + 1 1/2 + 1…

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Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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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: the minimum and maximum numbers that can be represented in two’s complement in 6 bits?

A: We have to find the minimum and maximum numbers that can be represented in two’s complement in 6…

Q: A password must have 2 letters from the school acronym SSPU and 3 digits from 1 to 9. How many…

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

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