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3 years ago

Can someone help me with this??

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

3 0

Answer:

(-6,-2)

Step-by-step explanation:

Hello! Lets get started!

By looking at this problem, we see that both equations equal 2. This makes this problem much easier!

While there are a few methods you could solve this, I will use substitution. First, I need to find what x is in terms of y!

There are many different ways you could do this, here are two:

-x = 2-2y ==> x = -2+2y

-x + 2y = -3x + 8y ==> 2x = 6y ==> x = 3y

For this problem, I am going to use the second answer, x = 3y, as it is simpler!

We need to substitute 3y in for x in either equation; I am going to use the first equation, -x + 2y = 2.

-3y + 2y = 2

-y = 2

y = -2

Now, lets solve for x!

-x + 2(-2) = 2

-x - 4 = 2

-x = 6

x = -6

After plugging the answers into both equations, we see that they are in fact true!

Therefor, our final answer is (-6, -2)

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3 years ago

1. Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has mater

sladkih [1.3K]

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3 years ago

A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

Helen [10]

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =16$ represent the sample variance

s=4 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.01,19)" "=CHISQ.INV(0.99,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=36.191$

$\chi^2_{1- \alpha/2}=7.633$

And replacing into the formula for the interval we got:

$\frac{(19)(16)}{36.191} \leq \sigma^2 \leq \frac{(19)(16)}{7.633}$

$8.400 \leq \sigma^2 \leq 39.827$

So the 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

7 0

3 years ago

Let v be a vector with initial point (-5, -11) and terminal point (6,2). What is v?

White raven [17]

Answer-The vector is

→

−

→

and the magnitude is

Explanation:

Let the point

(

−

)

and

(

−

)

Then,

−−→

(

−

(

−

)

−

)

(

−

)

The magnitude of

−−→

∣

−−→

∣

√

(

)

(

−

)

Step-by-step explanation:

4 0

3 years ago

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