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chubhunter [2.5K]
2 years ago
14

To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry d

ecided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
(20pt)
because the system of equations actually has only one solution
because the system of equations actually has no solution
because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist
Mathematics
1 answer:
Oksanka [162]2 years ago
6 0

Answer:

"because the graphs of the two equations overlap each other"

Step-by-step explanation:

If he graphs both equations on the graphing calculator and it shows only one line this can mean only one thing:

<em>Both linear equations are the same</em>

An example of this is

x+y=2

2x+2x=4

If you simplify the second equation by dividing everything by 2 you get the same equation as the first one

This means the answer would be "because the graphs of the two equations overlap each other"

<em />

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Step-by-step explanation:

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Events A and B are independent. find the missing probability<br> P(A)= 1/4 , P(B)= 3/5, P(B I A) =?
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Answer:

hello : P(A and B) = 3/20

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Varvara68 [4.7K]

Answer:

X \sim Binom(n=10, p=0.3)

And for this case we want to find this probability:

P(X =2)

And we can use the probability mass function and we got:

P(X=2)=(10C2)(0.3)^2 (1-0.3)^{10-2}=0.233

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.3)

And for this case we want to find this probability:

P(X =2)

And we can use the probability mass function and we got:

P(X=2)=(10C2)(0.3)^2 (1-0.3)^{10-2}=0.233

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