Answer:
8 I belive is C and 9 I think is D :)
Example:
If I give u a ratio of the number of teachers to students is 2:1 would mean that for every 2 teachers there is 1 student.
In question 10(a) the ratio of grey to black is 3:1 which means that the percentage would be 33%
In 10 (B) the ratio would be 6:4
There are 2 answers: Choice 1, Choice 4
=======================================
Why is this? Because we use the rule
P(A & B) = P(A) * P(B)
which only works if events A and B are independent
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For the first answer choice,
P(A) * P(B) = 0.6*0.4 = 0.24 = P(A & B)
so that matches.
The same applies to the fourth answer choice as well
P(A) * P(B) = 0.3*0.2= 0.06 = P(A & B)
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The other answer choices don't match up.
The second answer choice has
P(A) * P(B) = 0.3*0.4 = 0.12 but that doesn't match with the 0.70 given
Similarly for the third answer choice,
P(A) * P(B) = 0.5*0.1 = 0.05 which doesn't match with the 0.60
![\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\ -----------------------------\\\\ 2cos(A)=3tan(A)\implies 2cos(A)=3\cfrac{sin(A)}{cos(A)} \\\\\\ 2cos^2(A)=3sin(A)\implies 2[1-sin^2(A)]=3sin(A) \\\\\\ 2-2sin^2(A)=3sin(A)\implies 2sin^2(A)+3sin(A)-2](https://tex.z-dn.net/?f=%5Cbf%20sin%5E2%28%5Ctheta%29%2Bcos%5E2%28%5Ctheta%29%3D1%5Cimplies%20cos%5E2%28%5Ctheta%29%3D1-sin%5E2%28%5Ctheta%29%0A%5C%5C%5C%5C%5C%5C%0Atan%28%5Ctheta%29%3D%5Ccfrac%7Bsin%28%5Ctheta%29%7D%7Bcos%28%5Ctheta%29%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%0A2cos%28A%29%3D3tan%28A%29%5Cimplies%202cos%28A%29%3D3%5Ccfrac%7Bsin%28A%29%7D%7Bcos%28A%29%7D%0A%5C%5C%5C%5C%5C%5C%0A2cos%5E2%28A%29%3D3sin%28A%29%5Cimplies%202%5B1-sin%5E2%28A%29%5D%3D3sin%28A%29%0A%5C%5C%5C%5C%5C%5C%0A2-2sin%5E2%28A%29%3D3sin%28A%29%5Cimplies%202sin%5E2%28A%29%2B3sin%28A%29-2)
![\bf \\\\\\ 0=[2sin(A)-1][sin(A)+2]\implies \begin{cases} 0=2sin(A)-1\\ 1=2sin(A)\\ \frac{1}{2}=sin(A)\\\\ sin^{-1}\left( \frac{1}{2} \right)=\measuredangle A\\\\ \frac{\pi }{6},\frac{5\pi }{6}\\ ----------\\ 0=sin(A)+2\\ -2=sin(A) \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5C%5C%5C%5C%5C%5C%0A0%3D%5B2sin%28A%29-1%5D%5Bsin%28A%29%2B2%5D%5Cimplies%20%0A%5Cbegin%7Bcases%7D%0A0%3D2sin%28A%29-1%5C%5C%0A1%3D2sin%28A%29%5C%5C%0A%5Cfrac%7B1%7D%7B2%7D%3Dsin%28A%29%5C%5C%5C%5C%0Asin%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%3D%5Cmeasuredangle%20A%5C%5C%5C%5C%0A%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2C%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5C%5C%0A----------%5C%5C%0A0%3Dsin%28A%29%2B2%5C%5C%0A-2%3Dsin%28A%29%0A%5Cend%7Bcases%7D)
now, as far as the second case....well, sine of anything is within the range of -1 or 1, so -1 < sin(A) < 1
now, we have -2 = sin(A), which simply is out of range for a valid sine, so there's no angle with such sine
so, only the first case are the valid angles for A
Answer:
Step-by-step explanation:
The hardware store has 200 paintbrushes. They order 9 boxes with 12 paintbrushes each. This means that the total number of paintbrushes that was ordered is
12 × 9 = 108
Therefore, the total number of paintbrushes that the store has would be
200 + 108 = 308
They sell 11 boxes that have 6 paintbrushes each. This means that the total number of paintbrushes that they sold is
11 × 6 = 66
Therefore, the number of paintbrushes left would be
308 - 66 = 242
The manager's estimate is reasonable. They ordered about 120 paintbrushes and sold about 60 of them so they should have about 60 more paintbrushes than they started with.
