Answer:
![35\ ways](https://tex.z-dn.net/?f=35%5C%20ways)
Step-by-step explanation:
we know that
<u><em>Combinations</em></u> are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
To calculate combinations, we will use the formula
![C(n,r)=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=C%28n%2Cr%29%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
where
n represents the total number of items
r represents the number of items being chosen at a time.
In this problem
![n=7\\r=3](https://tex.z-dn.net/?f=n%3D7%5C%5Cr%3D3)
substitute
![C(7,3)=\frac{7!}{3!(7-3)!}\\\\C(7,3)=\frac{7!}{3!(4)!}](https://tex.z-dn.net/?f=C%287%2C3%29%3D%5Cfrac%7B7%21%7D%7B3%21%287-3%29%21%7D%5C%5C%5C%5CC%287%2C3%29%3D%5Cfrac%7B7%21%7D%7B3%21%284%29%21%7D)
simplify
![C(7,3)=\frac{(7)(6)(5)4!}{3!(4)!}](https://tex.z-dn.net/?f=C%287%2C3%29%3D%5Cfrac%7B%287%29%286%29%285%294%21%7D%7B3%21%284%29%21%7D)
![C(7,3)=\frac{(7)(6)(5)}{3!}](https://tex.z-dn.net/?f=C%287%2C3%29%3D%5Cfrac%7B%287%29%286%29%285%29%7D%7B3%21%7D)
![C(7,3)=\frac{(7)(6)(5)}{(3)(2)(1)}](https://tex.z-dn.net/?f=C%287%2C3%29%3D%5Cfrac%7B%287%29%286%29%285%29%7D%7B%283%29%282%29%281%29%7D)
![C(7,3)=35\ ways](https://tex.z-dn.net/?f=C%287%2C3%29%3D35%5C%20ways)
Answer:
8
Step-by-step explanation:
- You can set up an equation 50=2x+3y where x is the number of carnations and y is the number of roses. Then, you can express x as x=25-3/2y. As x must be positive, you can write 25-3/2y>0, 25>3/2 y. So, y can be 2,4,6,8,10,12,14,16 and the corresponding x's giving u 8 combinations.
Answer:
$38.46
Step-by-step explanation:
Minimum payment = 15% of balance
Balance = $256.38
Therefore
15% of $256.38
Change 15% to decimal
15% /100% x $256.38
0.15 x $256.38
$38.46
Her minimum payment is $38.46
In order from top to bottom.
perpendicular
zero slope
undefined slope
parallel lines
rise
run
positive slope
negative slope
constant rate of change
Given:
Figure of similar triangles.
To find:
The value of x and the measure of NR.
Solution:
In triangle RST and RMN,
(Vertically opposite angles)
(Alternate interior angles)
(By AA property of similarity)
We know that, corresponding sides of similar triangles are proportional.
![\dfrac{RS}{RM}=\dfrac{RT}{RN}](https://tex.z-dn.net/?f=%5Cdfrac%7BRS%7D%7BRM%7D%3D%5Cdfrac%7BRT%7D%7BRN%7D)
![\dfrac{40}{8}=\dfrac{60}{2x-2}](https://tex.z-dn.net/?f=%5Cdfrac%7B40%7D%7B8%7D%3D%5Cdfrac%7B60%7D%7B2x-2%7D)
![5=\dfrac{60}{2x-2}](https://tex.z-dn.net/?f=5%3D%5Cdfrac%7B60%7D%7B2x-2%7D)
![2x-2=\dfrac{60}{5}](https://tex.z-dn.net/?f=2x-2%3D%5Cdfrac%7B60%7D%7B5%7D)
On further simplification, we get
![2x=12+2](https://tex.z-dn.net/?f=2x%3D12%2B2)
![x=\dfrac{14}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B14%7D%7B2%7D)
![x=7](https://tex.z-dn.net/?f=x%3D7)
The value of x is 7.
Now,
![NR=2x-2](https://tex.z-dn.net/?f=NR%3D2x-2)
![NR=2(7)-2](https://tex.z-dn.net/?f=NR%3D2%287%29-2)
![NR=14-2](https://tex.z-dn.net/?f=NR%3D14-2)
![NR=12](https://tex.z-dn.net/?f=NR%3D12)
Therefore, the value of x is 7 and the measure of NR is 12 units.