Answer with Step-by-step explanation:
The number of marbles are as under
3 red , 3 green , 1 Lavender total = 7
Now to select five marbles from a total of 7 marbles such that at least 2 marbles are included are the sum of the following cases:
1) We select 2 exactly 2 red marbles from 3 reds and the remaining 3 marbles are selected from 4 of other colours
Thus ![n_{1}=\binom{3}{2}\binom{4}{3}=\frac{3!}{2!}\cdot \frac{4!}{3!}=12](https://tex.z-dn.net/?f=n_%7B1%7D%3D%5Cbinom%7B3%7D%7B2%7D%5Cbinom%7B4%7D%7B3%7D%3D%5Cfrac%7B3%21%7D%7B2%21%7D%5Ccdot%20%5Cfrac%7B4%21%7D%7B3%21%7D%3D12)
2)We select all the 3 red marbles and the remaining 2 are selected from the remaining 4 marbles
![n_2=\binom{4}{2}=\frac{4!}{2!\cdot 2!}=6](https://tex.z-dn.net/?f=n_2%3D%5Cbinom%7B4%7D%7B2%7D%3D%5Cfrac%7B4%21%7D%7B2%21%5Ccdot%202%21%7D%3D6)
Thus the total number of ways are ![n_1+n_2=12+6=18](https://tex.z-dn.net/?f=n_1%2Bn_2%3D12%2B6%3D18)
Answer:
293 seconds
Step-by-step explanation:
60*4=240
240+53=293
Answer:
C. ±4/5
Step-by-step explanation:
25x² = 16
25x² - 16 = 16 - 16
25x² - 16 = 0
25x² + 20x - 20x - 16 = 0
(25x² + 20x) + (- 20x - 16) = 0
5x(5x + 4) - 4(5x + 4) = 0
(5x - 4)(5x + 4) = 0
5x - 4 =0
5x + 4 = 0
![x=-\frac{4}{5}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B4%7D%7B5%7D)
![x=\frac{4}{5}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7B5%7D)
± is a symbol which represents addition and subtraction.
Y7 is your answer! Hope this helps!
Standard form
Coeficients are: a = 3; b = 4; c = 2;
Because
![b^{2} -4ac = -8](https://tex.z-dn.net/?f=%20b%5E%7B2%7D%20-4ac%20%3D%20-8)
<span>is negative we get two </span>Complex<span> solutions;
</span>We can use the special Quadratic Formula
x = (-b + or - i
![\sqrt{ b^{2}-4ac }](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20b%5E%7B2%7D-4ac%20%7D%20)
)/(2a); where i =
![\sqrt{-1} ;](https://tex.z-dn.net/?f=%20%5Csqrt%7B-1%7D%20%3B)
Then, x1 = (-4 + i2
![\sqrt{2} )/6 = 2(-2 + i \sqrt{2} )/6 = (-2+i \sqrt{2} )/3;](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%7D%20%29%2F6%20%3D%202%28-2%20%2B%20i%20%5Csqrt%7B2%7D%20%29%2F6%20%3D%20%28-2%2Bi%20%5Csqrt%7B2%7D%20%29%2F3%3B)
;
In similar way, we obtain x2 = <span> (-2-i \sqrt{2} )/3;[/tex];</span>