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erica [24]
3 years ago
8

Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7, 2), and is parallel to the graph x + 3y = -5.

Pls help ASAP btw, the answer isn’t -12/19 or 12/19
Mathematics
1 answer:
Elena-2011 [213]3 years ago
3 0

Answer:

B - A = -6

Step-by-step explanation:

Given

Point: (-7,2)

x + 3y = -5

Required

Find B- - A in Ax + By = 3

To start with; we need to calculate the slope of x + 3y = -5

x + 3y = -5

Subtract x from both sides

x - x + 3y = -5 - x

3y = -5 - x

Divide both sides by 3

\frac{3y}{3} = -\frac{5}{3} - \frac{x}{3}

y = -\frac{5}{3} - \frac{x}{3}

The slope of the line is the coefficient of x

Slope = - \frac{1}{3}

The question says line Ax + By = 3 is parallel to line x + 3y = -5; This means that they have the same slope of - \frac{1}{3}

Having calculated the slope, next is to calculate the equation of the line using the following formula;

m = \frac{y - y_1}{x - x_1}

Where m is the slope; m = - \frac{1}{3}; (x_1, y_1) = (-7,2)

Substitute these values in the formula above; the formula becomes

-\frac{1}{3} = \frac{y - 2}{x - -7}

-\frac{1}{3} = \frac{y - 2}{x +7}

Cross Multiply

-1(x+7) = 3(y-2)

Open brackets

-x - 7 = 3y - 6

Add x to both sides

x - x - 7 = 3y - 6 + x

-7 = 3y - 6 +x

Add 6 to both sides

-7 + 6 = 3y -6 + 6 + x

-1 = 3y + x

Multipby both sides by -3

-3(-1) = -3(3y + x)

3 = -9y - 3x

-9y - 3x = 3

-3x - 9y = 3

Comparing the above to Ax + By = 3

Ax = -3x\\A = -3

By = -9y\\B = -9

B - A = -9 - (-3)

B - A = -9 + 3

B - A = -6

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Answer:

z=\frac{0.333 -0.3}{\sqrt{\frac{0.3(1-0.3)}{195}}}=1.01  

p_v =P(z>1.01)=0.156  

So the p value obtained was a very low value and using the significance level asumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of women who complain of nausea between the 24th and 28th week of pregnancy is not significantly higher than 0.3 or 30%

Step-by-step explanation:

Data given and notation

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\hat p=\frac{65}{195}=0.333 estimated proportion of women who complain of nausea between the 24th and 28th week of pregnancy

p_o=0.3 is the value that we want to test

\alpha represent the significance level

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 proportion is higher than 0.3.:  

Null hypothesis:p\leq 0.3  

Alternative hypothesis:p > 0.3  

When we conduct a proportion test we need to use the z statisitc, 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{0.333 -0.3}{\sqrt{\frac{0.3(1-0.3)}{195}}}=1.01  

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 assumed is \alpha=0.05. The next step would be calculate the p value for this test.  

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

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