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d1i1m1o1n [39]
3 years ago
15

What is the y-value in the solution to this system of linear equations?

Mathematics
2 answers:
Airida [17]3 years ago
8 0

Answer: The answer is y = -4

Karolina [17]3 years ago
6 0

Answer:

y = -4

Step-by-step explanation:

Solve the following system:

{4 x + 5 y = -12 | (equation 1)

3 y - 2 x = -16 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{4 x + 5 y = -12 | (equation 1)

0 x+(11 y)/2 = -22 | (equation 2)

Multiply equation 2 by 2/11:

{4 x + 5 y = -12 | (equation 1)

0 x+y = -4 | (equation 2)

Subtract 5 × (equation 2) from equation 1:

{4 x+0 y = 8 | (equation 1)

0 x+y = -4 | (equation 2)

Divide equation 1 by 4:

{x+0 y = 2 | (equation 1)

0 x+y = -4 | (equation 2)

Collect results:

Answer:  {x = 2 , y = -4

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Answer:

z=\frac{0.021 -0.012}{\sqrt{\frac{0.012(1-0.012)}{1655}}}=3.363  

p_v =P(z>3.363)=0.00039  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is significantly higher than 0.012 (1.2%)

Step-by-step explanation:

Data given and notation

n=1655 represent the random sample taken

\hat p=0.021 estimated proportion of interest

p_o=0.012 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportions is higher than 0.012.:  

Null hypothesis:p \leq 0.012  

Alternative hypothesis:p > 0.012  

When we conduct a proportion test we need to use the z statisitic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.021 -0.012}{\sqrt{\frac{0.012(1-0.012)}{1655}}}=3.363  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.01. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(z>3.363)=0.00039  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is significantly higher than 0.012 (1.2%)

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