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Use Cramer's Rule to solve the system
6x + 12y=33
4x + 2y=20
1 solutions
Answer 99692 by vleith(2825)   on 2008-04-10 14:51:10 (Show Source):
You can put this solution on YOUR website!Cramer's rule states --> see here http://www.okc.cc.ok.us/maustin/Cramers_Rule/Cramer's%20Rule.htm
So we need to find the determinant first
|6 12|
|4 2 |
12-48 = -36
To find x
|33 12|
|20 2 |
66-240 = -174
x = -174/-36 = 29/6
to find y
|6 33|
|4 20|
120 - 132 = - 12
y = -12/-36 = 1/3
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absolute-value/136140: [2x-5]=[9x+7] Please help
1 solutions
Answer 99691 by vleith(2825) on 2008-04-10 14:34:18 (Show Source):
You can put this solution on YOUR website!For problems in one variable, you need to isolate the variable on one side of the equation.
Given: 
First collect the terms containing the variable on one side and the constant terms on the other side. To do this, subtract 2x from both sides and then subtract (-7) from both sides. Think of the equal sign as a 'balance' point. Whatever you do to one side, you have to do to the other in order to remain in balance.
Now isolate the variable, by dividing both sides by 7
Now check your answer by substituting  for x in the original equation.
Does 
 Check!
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Probability-and-statistics/136133: Given P(A),find P (not A)
Events A and B are dependent.P(A) = 5/12 and P(B given A) = 6/11. Find (A and B)
Thank You for the straightfoward and correct answers you all send me.
1 solutions
Answer 99690 by vleith(2825) on 2008-04-10 14:25:39 (Show Source):
You can put this solution on YOUR website!If the probability of A occurring is x%, then the probability of "not A" is 100-x%.
If the probability of A is 'x out of y', the probability of 'not A', is '(y-x) out of y.
The net result is the sum of the two probabilities must be one (or 100%)
Bayes Theorem states:
P(A and B) = P(B)* P(A|B) = P(A)*P(B|A)
You are given P(A) and P(B|A) - you can do the math :-D
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Conjunction/136137: Can you help me. I need to how to do this logic problem, step by step.
Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.
You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.
You then ask each genius to name the color of his hat (which he cannot see).
The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."
WHAT COLOR IS THE FRONT GENIUS' HAT??????
1 solutions
Answer 99686 by vleith(2825) on 2008-04-10 13:55:30 (Show Source):
You can put this solution on YOUR website!The back genius doesn't know. How can this be? If both the middle and the first people were red, the back would know his was white. He doesn't know. So the options for the two hats he sees are either : 1 red/1 white, or 2 white.
The middle genius doesn't know. He logically decides the first guy saw either 2 whites, or a white and a red. Since he can see the person in front of him, he must be seeing a white hat on the first genius. Because if he saw a red hat on the first genius, he (the second genius) would have to be wearing a white one. And since he is a genius, he would say 'i know'.
The first genius uses the logic above to say "I know". And when they ask what color, she will say "white".
Make sense?
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Probability-and-statistics/135710: jennifer has 8 blue marbles, 12 orange marbles, & 10 red marbles
What is the probability of picking an orange marble.
Predict the number of times out of 120 Jennifer will pick an orange marble.
Please help to explain so we can show the work.
1 solutions
Answer 99457 by vleith(2825) on 2008-04-07 19:52:15 (Show Source):
You can put this solution on YOUR website!How many marbles are the in total?  = 
How many are orange? 
So what are the odds of picking an orange marble?? 12 out of 30 =  = 
If Jen use this same set of marbles over and over again, picking one out, checking the colr and then putting it back. Each time she picked a marble, the odds are 4/10 that it would be an orange one.
Use a ratio
Check your answer. is 48 = 120*0.4?
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Proportions/135636: Hooke's law
The force (f) required to stretch a spring a distance(d) is directly proportional to(d). A force of 5 newtons stretches a spring 0.2 meter.what force will stretch the spring 0.35 meter?
1 solutions
Answer 99455 by vleith(2825) on 2008-04-07 19:47:54 (Show Source):
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Rational-functions/135704: This question is from textbook McDougal Littell Algebra 2
I need help with a homework question,please. It's on solving rational equations.
I am suppose to use Least Common Denominatoe to find the solution, so, I'd really appreciate the help!
1 solutions
Answer 99450 by vleith(2825) on 2008-04-07 19:37:53 (Show Source):
You can put this solution on YOUR website!Given : 
now look in the current denominators and see what unique factors are there.
We have  and  the other solitary x is already covered by the .
So
 = 0
Use the quadratic equation to solve. Then check your answers to make sure that the values of x given do not make  = 0 too
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Exponential-and-logarithmic-functions/135680: In a survey in 2000, the population of two plant species were found to be growing exponentially. Their growth is given by these equations: species A, P=2000e^0.05t and species B, P=5000e^0.02t, where t=0 in the year 2000.
Based on this information, after how many years will the population of species A be equal to the population of species B in the forest?
1 solutions
Answer 99445 by vleith(2825) on 2008-04-07 19:08:15 (Show Source):
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Functions/135693: if f(4)=0 and f(6)=6, which of the following could represent f(x)?
A. 2/3x-4
B. x+2
c. x-4
D. 3x-12
could u show me how to work this out and find the answer?
1 solutions
Answer 99436 by vleith(2825) on 2008-04-07 18:49:18 (Show Source):
You can put this solution on YOUR website!To work this problem, substitute the given values for x into each of the 4 possible answers. Then pick the one(s) that work.
Given: 
2/3x-4
 =  = 0 != 6. A is out
x+2
 =  != 0 . B is out
x-4
 = 0. so far so good.  =  != 6. C is out
3x-12
 =  . so far so good.  =  = . D works
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Quadratic_Equations/135543: Hello, my great Math friend and helper my question is this.
If you are looking at a graph of a quadratic equation, how do you determine where the solutions are? Thanks in advance!
Roosevelt
1 solutions
Answer 99309 by vleith(2825) on 2008-04-06 20:10:20 (Show Source):
You can put this solution on YOUR website!My great math student and friend, when you are asked to solve algebraically for a solution, what does that mean?
It means "find the values of x that make that equation 0". --> y = 0
So when you look at the graph, and the y value is 0, what does that mean in regards to the x -axis?
So, there is a real link between the algebra and the graph. Find "zeroes" graphically isn't a bad way to go is it?
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logarithm/135542: Express Logb r3s/t2 in terms of logarithms of r,s, and t. ( 3 and 2 are exponents and the / is not divide it is a fraction.
1 solutions
Answer 99308 by vleith(2825) on 2008-04-06 20:05:20 (Show Source):
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Linear-equations/135533: This question is from textbook Intro&IntermediateAlgebra
When I move the varible x to the other side and I divide the 12 and -x by negative 6, I am confused. x-6y=12. I get -6y=12-x. I know that to isolate y I need to divide the -6 by all terms. But I don't understand the -x over -6
1 solutions
Answer 99307 by vleith(2825) on 2008-04-06 19:59:20 (Show Source):
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Quadratic_Equations/135306: Michael is growing two strains of yeast in the labratory. Strain A originally had 80 cells and is known to quadruple every 2 hours. Strain B initially had 640 cells and doubles every 5 hours. When will Michael observe the same number of cells in the two yeast cultures.
1 solutions
Answer 99134 by vleith(2825) on 2008-04-04 20:58:05 (Show Source):
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