1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ollegr [7]
3 years ago
10

Sum of all natural numbers from100to300 which are divisible by 4and 5 is​

Mathematics
1 answer:
My name is Ann [436]3 years ago
4 0

If x is a number that is both divisible by 4 and 5, then

\begin{cases}x\equiv0\pmod4\\x\equiv0\pmod5\end{cases}

4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that x=20n is a solution to the system, where n is any integer. Simply put, any multiple of 20 fits the bill.

Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have 20n=100 when n=5, so the sum we want to compute is

\displaystyle\sum_{n=5}^{15}20n=\boxed{2200}

You might be interested in
Three times the sum of a number and seven is negative thirty-six. What is the number?
Katarina [22]

Answer:

n =-19

Step-by-step explanation:

3* (n+7) = -36

Distribute

3n+21 = -36

Subtract 21 from each side

3n+21-21 = -36-21

3n = -57

Divide by 3

3n/3 = -57/3

n =-19

7 0
3 years ago
Read 2 more answers
A minimum temperature of -4.44°C was recorded at a lake. A minimum temprature of 23.3°C was recorded later on the same day. Dete
GuDViN [60]

Answer:

27.74 is the difference

Step-by-step explanation:

23.3° C - (-4.44° C)

23.3 + 4.44

27.74

5 0
2 years ago
Pipe A can fill a swimming pool in 12 h.  Working with another Pipe B, it only takes 3h How long would it take Pipe B working al
MatroZZZ [7]
My guess is 9 hours, because since pipe a takes 12 hours and with pipe b it takes 9, it's 12-9=3 I think.
5 0
3 years ago
Who was the best president in history
vova2212 [387]

Answer:

<em>Abraham Lincoln </em>

Step-by-step explanation:

<u><em>Abraham Lincoln was the 16th president of the United States and is regarded as one of America's greatest heroes due to his role as savior of the Union and emancipator of enslaved people. Lincoln's distinctively humane personality and incredible impact on the nation have endowed him with an enduring legacy. With his ability to command a room, give a powerful speech and negotiate, he is regarded as one of the best presidents in American history. As a leader, Lincoln was determined to hold together a nation that was falling apart at the seams. </em></u><u><em>Abraham Lincoln was voted the best US president in a survey where nearly 100 historians and biographers rated past commanders in chief on 10 leadership qualities</em></u>

3 0
2 years ago
Cool Scoops ice cream shop offers 60 different one-topping sundaes. If there are 5 flavors of ice cream, how many toppings are t
Alona [7]
How you would solve this problem is: 

60 divided by 5 = 12 

So there will be 12 toppings. 
5 0
3 years ago
Read 2 more answers
Other questions:
  • Toilets come in a pack of 4 and 9 the 4 pack is priced 2.04 and the 9 pack i sold at 4.68 by calculating the price per roll whic
    10·1 answer
  • 18 tens 20 ones equal what hundreds
    9·1 answer
  • A tank can hold 50 liters of water. At present, it is only 30% full. How many liters of water shall I put in the tank, so that i
    11·1 answer
  • Is it equilateral or equiangular or regular?
    5·1 answer
  • While participating in a blood drive at school, Keona learns that blood has a density of 1.06 g/mL. She donates one pint of bloo
    8·2 answers
  • The Barnes family has a coupon for 10% off their dinner. If their bill comes to $82.50 and they wish to tip 15%, what will they
    10·2 answers
  • Lin wants to save 75$ for a trip to the city. If she has saved $37.50 so far, what percentage of her goal has she saved? What pe
    7·2 answers
  • Evolution requires at molecules and atoms<br> assemble themselves into what order​
    6·1 answer
  • Help me please help pleaseeeeeeeeeeeee
    14·1 answer
  • What is the queuing theory and how to use it?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!