<span>First set: 7, 24, 25.
Square 7, 24 and 25.
Add together the squares of 7 and 24.
Compare this sum to the square of 25. </span>
<u>Answer:</u>
A) 720 ways
B) 15 ways
C) 6 ways
<u>Step-by-step explanation:</u>
A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Alicia can arrange her paintings in 720 ways.
B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:
![P(n, r) = \frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=P%28n%2C%20r%29%20%3D%20%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
![= \frac{6!}{4!(6-4)!} = 15](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B6%21%7D%7B4%21%286-4%29%21%7D%20%20%3D%2015)
Therefore, Alicia can choose any 4 of her paintings in 15 ways.
C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways
Answer:
the difference between nine and a number
Step-by-step explanation:
Answer:
16 cups.
Step-by-step explanation:
We have been given that there are 128 fluid ounces of fruit punch in the container. We are asked to find the cups will be in 128 oz.
We know that 1 cup equals 8 fluid oz. To convert 128 oz into cups, we will divide 128 by 8.
![\text{Cups in 128 oz}=\frac{128\text{ oz}}{\frac{8\text{ oz}}{\text{1 cup}}}](https://tex.z-dn.net/?f=%5Ctext%7BCups%20in%20128%20oz%7D%3D%5Cfrac%7B128%5Ctext%7B%20oz%7D%7D%7B%5Cfrac%7B8%5Ctext%7B%20oz%7D%7D%7B%5Ctext%7B1%20cup%7D%7D%7D)
![\text{Cups in 128 oz}=\frac{128\text{ oz}}{8\text{ oz}}\times \text{1 cup}](https://tex.z-dn.net/?f=%5Ctext%7BCups%20in%20128%20oz%7D%3D%5Cfrac%7B128%5Ctext%7B%20oz%7D%7D%7B8%5Ctext%7B%20oz%7D%7D%5Ctimes%20%5Ctext%7B1%20cup%7D)
![\text{Cups in 128 oz}=16\times \text{1 cup}](https://tex.z-dn.net/?f=%5Ctext%7BCups%20in%20128%20oz%7D%3D16%5Ctimes%20%5Ctext%7B1%20cup%7D)
![\text{Cups in 128 oz}=16\text{ cups}](https://tex.z-dn.net/?f=%5Ctext%7BCups%20in%20128%20oz%7D%3D16%5Ctext%7B%20cups%7D)
Therefore, there are 16 cups in the container.