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2 years ago

What is the solution to the system of equations?

Mathematics

2 answers:

nataly862011 [7]2 years ago

8 0

<h2>Steps:</h2>

So with this system of equations, I will be using the elimination method. With the two equations, add them together and you will get:

$2x=6$

Since the y-variable has been eliminated, we can solve for x. With this, divide both sides by 2:

$x=3$

Now that we know the value of x, substitute it into either equation to solve for y:

$3+y=2\\y=-1\\\\3-y=4\\-y=1\\y=-1$

<h2>Answer:</h2>

In (x,y) form, your answer is (3,-1).

zysi [14]2 years ago

7 0

Answer:

x=3, y=-1

Step-by-step explanation:

x+y = 2

x -y =4

I will use elimination to eliminate the variable y. Add the two equations together.

x+y = 2

x -y =4

-------------

2x = 6

Divide each side by 2

2x/2 = 6/2

x = 3

But we still don't know y

x+y =2

Substitute x=3 into the equation

3+y =2

Subtract 3 from each side

3-3 +y =2-3

y =-1

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In which part of the graph is the distance from home constant?

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Answer:

I chose B. 3

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I chose B because the person is either staying still, not moving, or something of the sort.

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2 years ago

A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.

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Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671$

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

$=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)$

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. μ = 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

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3 years ago

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2 years ago

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leva [86]

Answer:

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