Answer:
Hello
Step-by-step explanation:
The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1
and the disk ? (inside of a circle) of center (0,0) and radius 2

SOLUTION
This is a binomial probability. For i, we will apply the Binomial probability formula
i. Exactly 2 are defective
Using the formula, we have

Note that I made the probability of being defective as the probability of success = p
and probability of none defective as probability of failure = q
Exactly 2 are defective becomes the binomial probability

Hence the answer is 0.1157
(ii) None is defective becomes

hence the answer is 0.4823
(iii) All are defective

(iv) At least one is defective
This is 1 - probability that none is defective

Hence the answer is 0.5177
To simplify
![\sqrt[4]{\dfrac{24x^6y}{128x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B24x%5E6y%7D%7B128x%5E4y%5E5%7D%7D)
we need to use the fact that
![\sqrt[4]{x^4}=|x|](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E4%7D%3D%7Cx%7C)
Why the absolute value? It's because
.
We start by rewriting as
![\sqrt[4]{\dfrac{2^23x^6y}{2^6x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E6y%7D%7B2%5E6x%5E4y%5E5%7D%7D)
![\sqrt[4]{\dfrac{2^23x^4x^2y}{2^42^2x^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E4x%5E2y%7D%7B2%5E42%5E2x%5E4y%5E4y%7D%7D)
Since
, we have
, and the above reduces to
![\sqrt[4]{\dfrac{3x^2y}{2^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7B2%5E4y%5E4y%7D%7D)
Then we pull out any 4th powers under the radical, and simplify everything we can:
![\dfrac1{\sqrt[4]{2^4y^4}}\sqrt[4]{\dfrac{3x^2y}{y}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5B4%5D%7B2%5E4y%5E4%7D%7D%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7By%7D%7D)
![\dfrac1{|2y|}\sqrt[4]{3x^2}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%7C2y%7C%7D%5Csqrt%5B4%5D%7B3x%5E2%7D)
where
allows us to write
, and this also means that
. So we end up with
![\dfrac{\sqrt[4]{3x^2}}{2y}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B4%5D%7B3x%5E2%7D%7D%7B2y%7D)
making the last option the correct answer.
I think the answer the answer/question is letter C
1. Do they match? No
How do you know? When substituted y = 3(2) - 4 is 2
y = 3(4) - 4 is 8
y = 3(8) - 4 is 20 not 14. So the table isn’t fully correct.
2. Do they match? No
How do you know? Because it says she walks UP the stairs not down. So -2 doesn’t make sense.
3. Do they match? Yes
How do you know? 0 means that the pile didn’t start with 6 so when you add 3 to 0, it’s 3. (duh lol)
On day 1, it starts with 6, (1)(6) = 6, and then they added 3 rocks, so it’s 9.
Day 2, twice as many rocks, so it starts with 12 now. + 3 is 15.
Day 3 starts with 18 rocks now. + 3 is 21.