Answer:
The sum of all positive integers less than 100, which are not divisible by 3 is 3267.
Step-by-step explanation:
The all positive integers less than 100 has sum, given by
S₁ = 1 + 2 + 3 + 4 + ......... + 99
⇒ S₁ = ![\frac{99 \times (99 + 1)}{2} = 4950](https://tex.z-dn.net/?f=%5Cfrac%7B99%20%5Ctimes%20%2899%20%2B%201%29%7D%7B2%7D%20%3D%204950)
Now, the sum of all positive integers less than 100 which are divisible by 3 is
S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99
⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)
⇒ S₂ = ![3 \times \frac{33 \times (33 + 1)}{2} = 1683](https://tex.z-dn.net/?f=3%20%5Ctimes%20%5Cfrac%7B33%20%5Ctimes%20%2833%20%2B%201%29%7D%7B2%7D%20%3D%201683)
Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)
Note : The sum of n natural numbers S is given by
S = 1 + 2 + 3 + 4 + ....... + n =
.
Answer:
<h2>
![length = \frac{25}{28}](https://tex.z-dn.net/?f=length%20%3D%20%20%5Cfrac%7B25%7D%7B28%7D%20)
</h2>
Step-by-step explanation:
Let the length of the rectangle be l
Area of a rectangle = length × width
From the question
Area = 25/42
width = 5/6
Substitute the values into the above formula and solve for the length
That's
<h3>
![length = \frac{area}{width}](https://tex.z-dn.net/?f=length%20%3D%20%20%5Cfrac%7Barea%7D%7Bwidth%7D%20)
</h3>
So we have
<h3>
![length = \frac{25}{42} \div \frac{4}{6} \\ = \frac{25}{42} \times \frac{6}{4} \\ = \frac{25}{7} \times \frac{1}{4}](https://tex.z-dn.net/?f=length%20%3D%20%20%5Cfrac%7B25%7D%7B42%7D%20%20%5Cdiv%20%20%5Cfrac%7B4%7D%7B6%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B25%7D%7B42%7D%20%20%5Ctimes%20%20%5Cfrac%7B6%7D%7B4%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B25%7D%7B7%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20)
</h3>
We have the final answer as
<h3>
![\frac{25}{28}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%7D%7B28%7D%20)
</h3>
Hope this helps you
linear; y = x – 2 is answer! pls mark me as brainliest i need only 2 more to rank up! Hope I Helped
Http://www.allthetests.com/quiz30/quiz/1379266484/Does-He-Like-you-Back-10-13-year-olds-ONLY
Hi,
Since Fred's part was 56 cm, his sister's was 84-56=28
She cut it into 4 parts, so 28/4=7 cm
Her rope was 7 cm long.
Hope this helps you.