Answer:
lorenzo
Step-by-step explanation:
because he has added more blue shade which will make the icing darker , Mariana's icing will be lighter as she added less blue shade :)
Answer:
First, you add 11 to the other side of the equals sign. So it would be 2x=k+11. Now, you divide 2 from x and do the same on the other side of the equals sign. so x= k+11
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2
Step-by-step explanation:
Answer:
C : 0.167
Step-by-step explanation:
Have a nice day
Answer:
domain: {-12, -8, 0, 1} range: {0, 8, 12}
Step-by-step explanation:
domain are of all the input values shown on the x-axis. The range is the set of possible output shown on the y-axis.
Answer: 27434
Step-by-step explanation:
Given : Total number of vials = 56
Number of vials that do not have hairline cracks = 13
Then, Number of vials that have hairline cracks =56-13=43
Since , order of selection is not mattering here , so we combinations to find the number of ways.
The number of combinations of m thing r things at a time is given by :-
![^nC_r=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
Now, the number of ways to select at least one out of 3 vials have a hairline crack will be :-
![^{13}C_2\cdot ^{43}C_{1}+^{13}C_{1}\cdot ^{43}C_{2}+^{13}C_0\cdot ^{43}C_{3}\\\\=\dfrac{13!}{2!(13-2)!}\cdot\dfrac{43!}{1!(42)!}+\dfrac{13!}{1!(12)!}\cdot\dfrac{43!}{2!(41)!}+\dfrac{13!}{0!(13)!}\cdot\dfrac{43!}{3!(40)!}\\\\=\dfrac{13\times12\times11!}{2\times11!}\cdot (43)+(13)\cdot\dfrac{43\times42\times41!}{2\times41!}+(1)\dfrac{43\times42\times41\times40!}{6\times40!}\\\\=3354+11739+12341=27434](https://tex.z-dn.net/?f=%5E%7B13%7DC_2%5Ccdot%20%5E%7B43%7DC_%7B1%7D%2B%5E%7B13%7DC_%7B1%7D%5Ccdot%20%5E%7B43%7DC_%7B2%7D%2B%5E%7B13%7DC_0%5Ccdot%20%5E%7B43%7DC_%7B3%7D%5C%5C%5C%5C%3D%5Cdfrac%7B13%21%7D%7B2%21%2813-2%29%21%7D%5Ccdot%5Cdfrac%7B43%21%7D%7B1%21%2842%29%21%7D%2B%5Cdfrac%7B13%21%7D%7B1%21%2812%29%21%7D%5Ccdot%5Cdfrac%7B43%21%7D%7B2%21%2841%29%21%7D%2B%5Cdfrac%7B13%21%7D%7B0%21%2813%29%21%7D%5Ccdot%5Cdfrac%7B43%21%7D%7B3%21%2840%29%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B13%5Ctimes12%5Ctimes11%21%7D%7B2%5Ctimes11%21%7D%5Ccdot%20%2843%29%2B%2813%29%5Ccdot%5Cdfrac%7B43%5Ctimes42%5Ctimes41%21%7D%7B2%5Ctimes41%21%7D%2B%281%29%5Cdfrac%7B43%5Ctimes42%5Ctimes41%5Ctimes40%21%7D%7B6%5Ctimes40%21%7D%5C%5C%5C%5C%3D3354%2B11739%2B12341%3D27434)
Hence, the required number of ways =27434