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2 years ago

A system of linear equations contains two equations with negative reciprocal slopes. How many solutions will it have?

Mathematics

2 answers:

pishuonlain [190]2 years ago

5 0

<h2>Answer:</h2>

The number of solutions will be one.

( i.e. the system of equation has a unique solution )

<h2>Step-by-step explanation:</h2>

We are given a system of equations such that:

One of the equation has a negative reciprocal slope as compared to the other.

This means that the two lines are perpendicular.

Hence, the two lines will definitely meet or intersect at just one point and at right angles.

Also we know that the solutions of a system of linear equations are the points where the two lines intersect.

Hence, we will have just one solution.

( since here the two lines will intersect at just one point )

Yanka [14]2 years ago

3 0

Answer:

1 solution

Step-by-step explanation:

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Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

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

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this: