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ycow [4]
3 years ago
13

X+2y=5

Mathematics
1 answer:
Vilka [71]3 years ago
3 0

Answer:

A)1,-3

Step-by-step explanation:

X+2y=5

X-3y=7

To write a determinant we take the coefficient of the variables

To get first row we take the coefficients of x and y from the equation x+2y = 5

x or 1x  are same

1x+2y = 5

The coefficient of x  is 1  and coefficient of y is 2

So first row is 1 , 2

We do the same for second row

To get second row we take the coefficients of x and y from the equation x-3y = 7

1x - 3y = 7

The coefficient of x  is 1  and coefficient of y is -3

So second row is 1, -3

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Which point on the graph below is included in the solution to the following system of equations?
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Answer:

D(-7,-2)

Step-by-step explanation:

A(-4,3)  B(5,-1)  C(-2,-6)    D(-7,-2)

A: 5×(-4) + 6×3 = -2 ≥ -30 ..... No

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C:  -6 ≤ 2/3×-2 +1 ....No

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3 years ago
A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w
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Answer:

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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".  

p_A represent the real population proportion for business  

\hat p_A =\frac{75}{400}=0.1875 represent the estimated proportion for Business

n_A=400 is the sample size required for Business

p_B represent the real population proportion for non Business

\hat p_B =\frac{137}{500}=0.274 represent the estimated proportion for non Business

n_B=500 is the sample size required for non Business

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

And replacing into the confidence interval formula we got:  

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

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2 years ago
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