Answer:
7.5 cups of raisins, 10 cups of peanuts and 5 cups of chocolate chips.
Step-by-step explanation:
We are given that,
The amount of ingredients needed for the trail mix are,
Raisins = cup
Peanuts = 1 cup
Chocolate chips = cup
Since, Kiran needs to make 10 cups of the trail mix.
The amount of ingredients needed will be,
Raisins = = = 7.5 cups
Peanuts = 1 × 10 = 10 cups
Chocolate chips = = 5 cups
Hence, the ingredients needed are 7.5 cups of raisins, 10 cups of peanuts and 5 cups of chocolate chips.
Answer:
![(AB)^T = B^T.A^T (Proved)](https://tex.z-dn.net/?f=%28AB%29%5ET%20%3D%20B%5ET.A%5ET%20%20%28Proved%29)
Step-by-step explanation:
Given (AB )^T= B^T. A^T;
To prove this expression, we need to apply multiplication law, power law and division law of indices respectively, as shown below.
![(AB)^T = B^T.A^T\\\\Start, from \ Right \ hand \ side\\\\B^T.A^T = \frac{B^T.A^T}{A^T}.\frac{B^T.A^T}{B^T} (multiply \ through) \\\\ = \frac{A^{2T}.B^{2T}}{A^T.B^T} \\\\=\frac{(AB)^{2T}}{(AB)^T} \ \ (factor \ out \ the power)\\\\= (AB)^{2T-T} \ (apply \ division \ law \ of \ indices; \ \frac{x^a}{x^b} = x^{a-b})\\\\= (AB)^T \ (Proved)](https://tex.z-dn.net/?f=%28AB%29%5ET%20%3D%20B%5ET.A%5ET%5C%5C%5C%5CStart%2C%20from%20%5C%20Right%20%5C%20hand%20%5C%20side%5C%5C%5C%5CB%5ET.A%5ET%20%3D%20%5Cfrac%7BB%5ET.A%5ET%7D%7BA%5ET%7D.%5Cfrac%7BB%5ET.A%5ET%7D%7BB%5ET%7D%20%28multiply%20%5C%20through%29%20%5C%5C%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7BA%5E%7B2T%7D.B%5E%7B2T%7D%7D%7BA%5ET.B%5ET%7D%20%5C%5C%5C%5C%3D%5Cfrac%7B%28AB%29%5E%7B2T%7D%7D%7B%28AB%29%5ET%7D%20%5C%20%5C%20%28factor%20%5C%20out%20%5C%20the%20power%29%5C%5C%5C%5C%3D%20%28AB%29%5E%7B2T-T%7D%20%20%5C%20%28apply%20%5C%20division%20%5C%20law%20%5C%20of%20%5C%20indices%3B%20%5C%20%5Cfrac%7Bx%5Ea%7D%7Bx%5Eb%7D%20%3D%20x%5E%7Ba-b%7D%29%5C%5C%5C%5C%3D%20%28AB%29%5ET%20%5C%20%28Proved%29)
We need an image because of this
The answer is 2 candies per person per month
(1) Find the amount of candy consumed <span>per person per year:
6 700 000 000 </span>÷ 305 000 000 = 21.97 candies per person per year
(2) Find the amount of candy consumed per person per month:
1 year has 12 months.
21.97 candy per person per year ÷ 12 = 1.83 ≈ 2 candies per person per month
Answer:
![12\frac{1}{8}\ yd](https://tex.z-dn.net/?f=12%5Cfrac%7B1%7D%7B8%7D%5C%20yd)
Step-by-step explanation:
we know that
The total fabric that Mrs. Lin needs is equal to
![3(1\frac{2}{3})+2\frac{5}{8}+2(2\frac{1}{4})](https://tex.z-dn.net/?f=3%281%5Cfrac%7B2%7D%7B3%7D%29%2B2%5Cfrac%7B5%7D%7B8%7D%2B2%282%5Cfrac%7B1%7D%7B4%7D%29)
Convert mixed number to an improper fraction
![1\frac{2}{3}=1+\frac{2}{3}=\frac{5}{3}](https://tex.z-dn.net/?f=1%5Cfrac%7B2%7D%7B3%7D%3D1%2B%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B5%7D%7B3%7D)
![2\frac{5}{8}=2+\frac{5}{8}=\frac{21}{8}](https://tex.z-dn.net/?f=2%5Cfrac%7B5%7D%7B8%7D%3D2%2B%5Cfrac%7B5%7D%7B8%7D%3D%5Cfrac%7B21%7D%7B8%7D)
![2\frac{1}{4}=2+\frac{1}{4}=\frac{9}{4}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B4%7D%3D2%2B%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B9%7D%7B4%7D)
substitute
![3(\frac{5}{3})+\frac{21}{8}+2(\frac{9}{4})](https://tex.z-dn.net/?f=3%28%5Cfrac%7B5%7D%7B3%7D%29%2B%5Cfrac%7B21%7D%7B8%7D%2B2%28%5Cfrac%7B9%7D%7B4%7D%29)
![5+\frac{21}{8}+\frac{9}{2}](https://tex.z-dn.net/?f=5%2B%5Cfrac%7B21%7D%7B8%7D%2B%5Cfrac%7B9%7D%7B2%7D)
![\frac{40+21+36}{8}=\frac{97}{8}\ yd](https://tex.z-dn.net/?f=%5Cfrac%7B40%2B21%2B36%7D%7B8%7D%3D%5Cfrac%7B97%7D%7B8%7D%5C%20yd)
Convert to mixed number
![\frac{97}{8}\ yd= \frac{96}{8}+\frac{1}{8}=12\frac{1}{8}\ yd](https://tex.z-dn.net/?f=%5Cfrac%7B97%7D%7B8%7D%5C%20yd%3D%20%5Cfrac%7B96%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B8%7D%3D12%5Cfrac%7B1%7D%7B8%7D%5C%20yd)