Answer:
4.5 gallons
Step-by-step explanation:
1.5 x 3 = 4.5
(5 x 3 = 15 minutes to stop the leak)
The answer is five 5 hope it helps you out :)
Just multiply each ingredient by 2/3.
2 * 2/3 = 1 1/3 cups of melted butter
24 * 2/3 = 16 cups of marshmallows
13 * 2/3 = 8 2/3 cups of cereal
Please consider marking this answer as Brainliest to help me advance.
Answer:
Let be
the i-th odd positive integer number, ![\sum_{i=1}^{k}{n_i}=k^2](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5E%7Bk%7D%7Bn_i%7D%3Dk%5E2)
Step-by-step explanation:
Let be
the i-th odd positive integer number
![k=1\\n_1=1\\S_1=n_1=1\\\\k=2\\n_1=1, n_2=3\\S_2=n_1+n_2=1+3=4\\\\ k=3\\n_1=1, n_2=3, n_3=5\\S_3=n_1+n_2+n_3=1+3+5=9\\\\\\k=4\\n_1=1, n_2=3, n_3=5, n_4=7\\S_4=n_1+n_2+n_3+n_4=1+3+5+7=16\\\\](https://tex.z-dn.net/?f=k%3D1%5C%5Cn_1%3D1%5C%5CS_1%3Dn_1%3D1%5C%5C%5C%5Ck%3D2%5C%5Cn_1%3D1%2C%20n_2%3D3%5C%5CS_2%3Dn_1%2Bn_2%3D1%2B3%3D4%5C%5C%5C%5C%20k%3D3%5C%5Cn_1%3D1%2C%20n_2%3D3%2C%20n_3%3D5%5C%5CS_3%3Dn_1%2Bn_2%2Bn_3%3D1%2B3%2B5%3D9%5C%5C%5C%5C%5C%5Ck%3D4%5C%5Cn_1%3D1%2C%20n_2%3D3%2C%20n_3%3D5%2C%20n_4%3D7%5C%5CS_4%3Dn_1%2Bn_2%2Bn_3%2Bn_4%3D1%2B3%2B5%2B7%3D16%5C%5C%5C%5C)
It seems that the sum of the first k odd positives integers is ![k ^ 2](https://tex.z-dn.net/?f=k%20%5E%202)
Note that,
![n_1=1=1+2\times 0\\n_2=3=1+2\times 1\\n_3=5=1+2\times 2\\n_4=7=1+2\times 3\\n_5=9=1+2\times 4\\.\\.\\.\\n_k=2k-1=1+2\times (k-1)\\](https://tex.z-dn.net/?f=n_1%3D1%3D1%2B2%5Ctimes%200%5C%5Cn_2%3D3%3D1%2B2%5Ctimes%201%5C%5Cn_3%3D5%3D1%2B2%5Ctimes%202%5C%5Cn_4%3D7%3D1%2B2%5Ctimes%203%5C%5Cn_5%3D9%3D1%2B2%5Ctimes%204%5C%5C.%5C%5C.%5C%5C.%5C%5Cn_k%3D2k-1%3D1%2B2%5Ctimes%20%28k-1%29%5C%5C)
thus,
![\sum_{i=1}^{k}{n_i}=\sum_{i=1}^{k}{(2i-1)}=2\sum_{i=1}^{k}i-\sum_{i=1}^{k}1\\\\\sum_{i=1}^{k}{n_i}=2\frac{k(k+1)}{2}-k=k^2](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5E%7Bk%7D%7Bn_i%7D%3D%5Csum_%7Bi%3D1%7D%5E%7Bk%7D%7B%282i-1%29%7D%3D2%5Csum_%7Bi%3D1%7D%5E%7Bk%7Di-%5Csum_%7Bi%3D1%7D%5E%7Bk%7D1%5C%5C%5C%5C%5Csum_%7Bi%3D1%7D%5E%7Bk%7D%7Bn_i%7D%3D2%5Cfrac%7Bk%28k%2B1%29%7D%7B2%7D-k%3Dk%5E2)
I’m guessing zombie by bad wolves, it’s my favorite metal song