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Alecsey [184]
3 years ago
7

Solve by substitution. 3x-y=5 -2x+y=0

Mathematics
2 answers:
Jobisdone [24]3 years ago
7 0
First, rewrite the equation -2x+y=0 into y-mx+b format. This is y=2x+0. We can then substitute this into our first equation.
3x-y=5
turns into
3x-2x=5
x=5
We can then plug in our value for x to find y.
3(5)-y=0
simplifies into
15-y=0
Simplify this to get that y=15
You can then plug these into the other equation ot make sure it's right.
-2(5)+15=5
-10+15=5
which is 5=5 (true)

So your answers are x=5 and y=15.

:)
Citrus2011 [14]3 years ago
3 0
In order to use substitution, you need to isolate a variable on one of the equations:

-2x+y=0
y=2x

Then you plug that equation into the other equation. Since we isolated y, we plug in 2x for y in the other equation:

3x-(2x)=5
x=5

Then plug the value you found into any equation to solve for the other variable:

3(5)-y=5
15-y=5
-y=-10
y=10

So your answers are x=5, y=10
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Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636​, the central limit theorem appl
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Answer:

a) \bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1

b) P(\bar X >101)=1-P(\bar X

c) P(\bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".  

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: P(A)+P(A') =1

Let X the random variable that represent the variable of interest on this case, and for this case we know the distribution for X is given by:  

X \sim N(\mu=100,\sigma=6)  

And let \bar X represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:  

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})  

a. What are the mean and variance of the sampling distribution for the sample​ means?

\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)

\mu_{\bar X}=100 \sigma^2_{\bar X}=1.2^2=1.44

b. What is the probability that x overbarxgreater than>101

First we can to find the z score for the value of 101. And in order to do this we need to apply the formula for the z score given by:  

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

If we apply this formula to our probability we got this:  

z=\frac{101-100}{\frac{6}{\sqrt{25}}}=0.833  

And we want to find this probability:

P(\bar X >101)=1-P(\bar X

On this last step we use the complement rule.  

c. What is the probability that x bar 98less than

First we can to find the z score for the value of 98.

z=\frac{98-100}{\frac{6}{\sqrt{25}}}=-1.67  

And we want to find this probability:

P(\bar X

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