![mnikitha07](/avatars/44305.jpg)
mnikitha07
14.08.2021 •
Mathematics
Find the smallest positive integer n such that the digit sum of n is divisible by 5, and the digit sum of n +1 is also divisible by 5. Note: The digit sum of 1440 is 1+4+4+0 = 9.
Solved
Show answers
More tips
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- L Leisure and Entertainment Carving: History and Techniques for Creating Vegetable and Fruit Decorations...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
- H Health and Medicine What vaccines do children need?...
- H Health and Medicine Reasons for the Appearance of Warts: Everything You Need to Know...
- A Art and Culture How to Learn Screaming: Step-by-Step Guide for Beginners...
- H Health and Medicine Contraceptive Pills After 35: The Importance Of Choosing The Right Medication...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
Answers on questions: Mathematics
- M Mathematics Can someone plz help me...
- M Mathematics All of the following are equivalent except . x - 7. -7 + x. x - (-7). x + (-7)...
- M Mathematics Consumers in Iowa pay a 5% tax on all purchases. If Ted plans to buy a $400 lawn mower, that has a 30% discount, how much money will he need to bring to the store to make his...
- M Mathematics The floor of the school music room being tiled. The room is shaped like a parallelogram. The parallelogram has a base of 25 feet and a height of 11 feet. Each package of tile...
- M Mathematics Michael wants to save money on a new computer. The computer he wants is listed at a regular price of $500.00. This Saturday, the store will be offering the computer at a discount...
- M Mathematics ANSWER THE QUESTION FOR BRAINLIEST...
- M Mathematics At a certain fast food restaurant l,the volume of a large soda is 35% greater than the volume of a small soda.If the volume of the small soda is 150 mL,what is the volume of the...
- M Mathematics Find the value of f(3)...
- M Mathematics I will be back at 2 ppl...
- M Mathematics 2x-y=4 put the following equation of a line into slope intercept form, simplifying all fractions....
Ответ:
Notice that a number is only divisible by 5 if it ends in 5 or 0.
Only using this, we will find that the number is 49,999
Suppose we wanted the sum of the digits to end in 5, then we could have something like:
23
2 + 3 = 5
if we add 1, we get:
23 + 1 = 24
2 + 4 = 6
This will happen always.
instead, if we use a 0 as the last digit of the sum, we get:
For example, the simplest one:
19
we have:
1 + 9 = 10
10 is divisible by 5.
if we add 1, we get:
19 + 1 = 20
2 + 0 = 2
2 is not divisible by 5.
We have a problem again, but this time you can see that the whole structure of the number does change. So we should keep trying with ones and nines.
Now we need to modify our number to the point we get n + 1 to be divisible by 5.
if we add a 9 to the right side of our number, we get:
199
1 + 9 + 9 = 19
clearly, not divisible by 5.
Here we need to add a 1 at the left side to make it divisible by one, so we get:
1199
1 + 9 + 1 + 9 = 20
this is divisible by 5.
now let's add 1:
1,199 + 1 = 1,200
1 + 2 = 3
3 is not divisible by 5.
Now, if you look at the two numbers we used, we can see that:
for 19, the sum of the digits + 1 gave us a 2.
for 1,199, the sum of the digits +1 gave us a 3.
then just let's add two ones and two nines.
We will get:
11,119,999
adding the digits:
1 + 1 + 1 + 1 + 9 +9 +9 +9 = 40
is divisible by 5.
Adding one to our number, we can get:
11,119,999 + 1= 11,120,000
Adding the digits:
1 + 1 + 1 + 2 + 0 + 0+ 0+ 0 = 5
divisible by 5.
Now, we can group the ones together, so instead of the number 11,119,999
we can have 49,999, which is way smaller.
Adding the digits, we get:
4 + 9 + 9 + 9 + 9 = 40
And adding one to our number, we get:
49,999 + 1 = 50,000
Adding the digits:
5 + 0 + 0 +0 + 0 = 5
So we found the smallest number n such that the sum of the digits of n is divisible by 5, and the sum of the digits of n + 1 is also divisible by 5.
If you want to learn more, you can read:
Ответ:
139,999
Step-by-step explanation:
If the digit sum of n is divisible by 5, the digit sum of n+1 can't physically be divisble by 5, unless we utilise 9's at the end, this way whenever we take a number in the tens (i.e. 19), the n+1 will be 1 off being divisble, so if we take a number in the hundreds, (109, remember it must have as many 9's at the end as possible) the n+1 will be 2 off being divisble, so continuing this into the thousands being three, tenthousands being 4, the hundred thousands will be 5 off (or also divisble by 5). So if we stick a 1 in the beginning (for the lowest value), and fill the last digits with 9's, we by process of elimination realise that the tenthousands digit must be 3 such that the digit sum is divisible by 5, therefore we get 139,999
Ответ:
0.872
Step-by-step explanation:
The line is increasing. This means the correlation coefficient will be positive.
This is a fairly good fit; this means we want the larger of the two positive numbers, or 0.872.