How many trailing zeros are there in (1000+51X5)! In the decimal number system and 96 based number system?

Q: If a number is not divisible by 6, then it is not divisible by 3. true or false

A: If a number is not divisible by 6, then it is not divisible by 3.

Q: How many 3 digit even numbers can be created if repetition of digits is allowed

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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: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

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 four-digit even numbers can you form from the digits 1, 2, 3 and 4?

A: We have to find the number of four-digit even numbers formed from the digits 1, 2, 3 and 4. Then we…

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: Find the number of positive integers not exceeding 1000 that are not divisible by 2 or 3 but…

A: The positive integers not exceeding 1000 that are not divisible by 2 or 3 but divisible by 5 are 5,…

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: Show that 3 + V5 is inational number

A: Let 5^1/3 is a rational numbers. So, we can write it as 5^1/3=p/q ………….(I) according to the…

Q: Suppose 51 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

A: Solution: From the given information, number of cars start at a car race is 51.

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4.

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

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Q: Set C is the set of positive two-digit even numbers less than 56 that are divisible by 5.

A:

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: How to find the last two ditgits of 2^2021 ?

A: Solve the given problem.

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: What two nonnegative real numbers with a sum of 34 have the largest possible product?

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Q: Show that 2 + V5 is imational number

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Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

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: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

A:

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: A hot air balloon descends at a rate of 4ft per minute for 6 minutes, then rises at a rate of 2ft…

A: Given Data: The descending rate of the balloon is: D'=-4 ft per minute The time till the balloon…

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: Suppose 59 cars start at a car race. In how many ways can the top 3 cars finish the race? ... The…

A: There is total 59 cars.

Q: How many positive numbers less than 300 are divisible by 7 but not 5?

A: We need to find positive numbers less than 300 that are divisible by 7 but not by 5. First count the…

Q: What is the sum of the first 100 nonnegative integers?

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Q: What are all of the natural numbers divisible by 8 whose sum of digits is less than 10 and the…

A: Given the requirements

Q: How many 3 digit numbers can be formed from the digits 2, 4, 6, 8 and 9 if repetitions are allowed?

A: Solution: From the given information, the digits are 2, 4, 6, 8 and 9.

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: Determine all natural numbers divisible by 8 whose sum of digits is less than 10 and the product of…

A: Permutation and combination concepts will be used to filter out all the 3 scenarios in getting…

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: Can you think of the smallest number N such that ot can be expressed as a product of the two factors…

A: We have to find out the number N that can be expressed as a product of the two factors which are…

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: How many zeros are there at the end of 1001?

A: This question is related to Number Theory

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

A: .  Symbol of Greatest Integer Function  To Find: Number of positive integers ≤ 1000 that are not…

Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…

Q: The chairs of an auditorium are to be labeled with a letter and a positive integer not exceeding…

A: Given: The chairs of an auditorium are to be labeled with a letter and a positive integer not…

Q: How many zeroes are at the end of 25! (= 25 factorial)?

A: The given number is 25!.  Now, we need to find the number of zeros at the end of 25!.

Q: Number 332 – 1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: We need to find two divisors of 332-1 between 75 and 85.  Now, we can use the identity a2-b2=a-ba+b…

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: What are integers and how can it be easy for me to use them?

A: An integer is a whole number (not a fraction) that can be positive, negative, or zero. Therefore,…

Q: How many three-digit numbers can be formed if only odd numbers are allowed to be re-used?

A: To find three-digit number that can be formed if only odd numbers are allowed to be re-used. Odd…

Q: How many positive integers not exceeding 100 are divisible by 5 or 7?

A:

Q: How many 3-digit numbers with no repeated digits using 4, 5, 6, 7, 8 can be a. less than 520? b.…

A:

Q: What 2 nonnegative numbers with a sum of 23 have the largest possible product?

A: Given information: The two non negative numbers with a sum of 23.  Calculation: Consider x and y are…