Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7
(a) are divisible by 5 and by 7.
(b) have distinct digits.
(c) are not divisible by either 5 or 7.
Homework Answers
We can find out that
35*286=10010 and 35*29=1015
Therefore the number divisible by 35, n35
= 286-29=257
(b) distinct digits
First digit has 9 choices (1-9)
second and subsequent digits 9,8,7 choices each
Numbers with distinct digits
= 9*9*8*7
= 4536
(c) not divisible by either 5 or 7
Divisible by 5, n5= (10000-1000)/5=1800
Divisisble by 7, n7 = (10003-1001)/7=1286
Divisible by 5 or 7 or both
=n5+n7-n35
=1800+1286-257
=2829
Numbers NOT divisible by either 5 or 7
=(10000-1000)-2829
=6171
Add Answer to:
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7
an urn contains 12 red How many positive integers between 100 and 500 inclusive, a. are...
an urn contains 12 red
How many positive integers between 100 and 500 inclusive, a. are divisible by 7? b. are odd? c. have the same three decimal digits? (e.g. 333) d. have distinct digits? (e.g. 123, 234, etc.) How many bit strings of length 8 contain a. exactly three 1s? b. at most three 1s? c. at least three 1s? d. an equal number of Os and 1s?
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How...
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How many positive integers between 1000 and 4999, inclusive: 1. have no repeated digit? 2. have at least one repeated digit? 3. have at most two repeated digits? Note that by 'one repeated digit' we mean that there is a digit that appears at least twice (eg, 1123 has one repeated digit). Similarly, by two repeated digits we mean a digit that appears at least...
How many integers from 1 to 1000 are divisible by either 5 or 7 (or both)?
How many integers from 1 to 1000 are divisible by either 5 or 7 (or both)?
In C program #include<stdio.h> The first 11 prime integers are 2, 3, 5, 7, 11, 13,...
In C program #include<stdio.h> The first 11 prime integers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. A positive integer between 1 and 1000 (inclusive), other than the first 11 prime integers, is prime if it is not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. Write a program that prompts the user to enter a positive integer between 1 and 1000 (inclusive) and that outputs whether the number...
Eight consecutive three digit positive integers have the following property: each of them is divisible by...
Eight consecutive three digit positive integers have the following property: each of them is divisible by its last digit. What is the sum of the digits of the smallest of the eight integers? A 10 B 11 С 12 D 13 E 14
8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5...
8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5 are there? (ii) What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using t...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc
How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.) (a) have exactly three digits which are 9s?
Hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C,...
Hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. (Please explain briefly) How many hexadecimal strings of length ten have at least three E’s? How many hexadecimal strings of length ten have exactly two A’s and at most two B’s? How many hexadecimal strings of length ten have six digits from the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and four digits from the set...
Counting and Pigeonhole Principle (a). A set of four different integers is chosen at random between...
Counting and Pigeonhole Principle (a). A set of four different integers is chosen at random between 1 and 200 (inclusive). How many different outcomes are possible? (b). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least 3 of them are even? (c). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least 2 of them add up to 20? (d). How many different...
an urn contains 12 red
How many positive integers between 100 and 500 inclusive, a. are divisible by 7? b. are odd? c. have the same three decimal digits? (e.g. 333) d. have distinct digits? (e.g. 123, 234, etc.) How many bit strings of length 8 contain a. exactly three 1s? b. at most three 1s? c. at least three 1s? d. an equal number of Os and 1s?
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How many positive integers between 1000 and 4999, inclusive: 1. have no repeated digit? 2. have at least one repeated digit? 3. have at most two repeated digits? Note that by 'one repeated digit' we mean that there is a digit that appears at least twice (eg, 1123 has one repeated digit). Similarly, by two repeated digits we mean a digit that appears at least...
Eight consecutive three digit positive integers have the following property: each of them is divisible by its last digit. What is the sum of the digits of the smallest of the eight integers? A 10 B 11 С 12 D 13 E 14
8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5 are there? (ii) What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
Counting and Pigeonhole Principle (a). A set of four different integers is chosen at random between 1 and 200 (inclusive). How many different outcomes are possible? (b). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least 3 of them are even? (c). How many different integers between 1 and 200 (inclusive) must be chosen to be sure that at least 2 of them add up to 20? (d). How many different...
Most questions answered within 3 hours.
-
1.
A hemophiliac male mates with a healthy female. what are the
possible genotypes for the...
asked 2 minutes ago -
After reading the Primary Care scenario in the Allied Health
Community, what could have been implemented...
asked 10 minutes ago -
Calculate the change in the Gibbs energy of the system for the
following processes: a) 6.0...
asked 6 minutes ago -
A solution is prepared by dissolving 11.60 g of a mixture of
sodium carbonate and sodium...
asked 15 minutes ago -
1. Mini Case Study: Suppose that, in the future, most jobs will
be bid upon by...
asked 17 minutes ago -
Plantinga argues for the view that there is no solution to the
problem of moral evil....
asked 13 minutes ago -
For this Discussion, you examine a case study of
hearing-impaired children who developed their own language...
asked 18 minutes ago -
At the beginning of the year, Palermo Brothers, Inc., purchased
a new plastic water bottle making...
asked 16 minutes ago -
You could argue that even though Rockefeller clearly had
enormous market power (90% of the market)...
asked 17 minutes ago -
The moment of inertia of a disk rotating about its axis of
symmetry is Icm=1/2MR^2
The...
asked 24 minutes ago -
When using a relational database what makes data
formatting so important and critical to the functions...
asked 35 minutes ago -
The following temperatures show the (fictional) daily low
measured at O'Hare airport every January 1st from...
asked 55 minutes ago