Answer:
4%
Step-by-step explanation:
310
/7759 x 100% = 4%
Answer: 1 in 18
This is the same as writing the fraction 1/18
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Explanation:
Since she has 36 marbles total, and the probability of picking green is 1 in 2, this means (1/2)*36 = 18 marbles are green.
Then she also has (1/3)*36 = 12 red marbles and (1/9)*36 = 4 blue marbles.
So far, that accounts for 18+12+4 = 34 marbles in all. That leaves 36-4 = 2 marbles left over that must be black, as it's the only color left.
From that, the probability of choosing a black marble is 2/36 = 1/18.
There's a 1 in 18 chance of Maddy picking a black marble.
1/18 = 0.0556 = 5.56% approximately
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
Answer:
The answer is "9 and 7".
Step-by-step explanation:
Given:
![A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D)
Using formula:
![\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\](https://tex.z-dn.net/?f=%5Cto%20%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D-%5Clambda%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%7C%3D0%5C%5C%5C%5C%5C%5C%20%5Cto%20%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%20%7C%3D0%5C%5C%5C%5C%5C%5C%5Cto%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7-%5Clambda%20%269%5C%5C0%269-%5Clambda%5Cend%7Barray%7D%5Cright%5D%7C%3D0%5C%5C%5C%5C%5C%5C%5Cto%7C%287-%5Clambda%29%289-%5Clambda%29%7C%3D0%5C%5C%5C%5C%5Cto%20%287-%5Clambda%29%289-%5Clambda%29%3D0%5C%5C%5C%5C%5Cto%207-%5Clambda%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%209-%5Clambda%3D0%5C%5C%5C%5C)
The answer is actually choice A
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If we add up the equations straight down we will have 0a+2b = 6
Note how adding the 'a' terms gives us 3a + (-3a) = 3a-3a = 0a. The 0a term is really 0 since 0 times anything is 0. So the 'a' terms will go away
The equation 0a+2b = 6 turns into 0+2b = 6 and that simplifies to 2b = 6
To isolate b, we divide both sides by 2
2b = 6
2b/2 = 6/2
b = 3
We can stop here since only one answer choice has b = 3, which is choice A. However, let's keep going to find the value of 'a'
Plug b = 3 into any equation with 'a' and 'b', then solve for 'a'
3a+4b = 9
3a+4*3 = 9
3a+12 = 9
3a+12-12 = 9-12
3a = -3
3a/3 = -3/3
a = -1
So a = -1 and b = 3 pair up to form (a,b) = (-1,3)
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To check, plug this ordered pair back into both equations
Equation 1:
3a+4b = 9
3*(-1)+4*3 = 9
-3+12 = 9
9 = 9
Equation 1 has been checked out
Equation 2:
-3a-2b = -3
-3(-1)-2(3) = -3
3 - 6 = -3
-3 = -3
this is true as well
So this confirms that the final answer is choice A
