Solve the system using substitution or elimination 2x-y=4 -3x+y=-2

I need to know the answer of that question

vodomira [7]

The answer is about 40 dollars hope this helped you a little

3 0

3 years ago

Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Constr

asambeis [7]

Answer:

a) Null hypothesis: $\rho = 0$

Alternative hypothesis: $\rho \neq 0$

b) The scatter plot is on the figure attached.

c) $t=\frac{0.874}{\sqrt{1-(0.874)^2}} \sqrt{9-2}=4.758$

$p_v = P(t_{7} >4.758) =
0.0010$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that the correlation coefficient is significant.

Step-by-step explanation:

Previous concepts

Pearson correlation coefficient(r), "measures a linear dependence between two variables (x and y). Its a parametric correlation test because it depends to the distribution of the data. And other assumption is that the variables x and y needs to follow a normal distribution".

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

Solution to the problem

In order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

Let X the Court Income and Y= Justice Salary, for this case we have that:

$n=9, \sum X= 3986, \sumY=398. \sumXY=265160, \sum X^2 =4076636, \sumY^2 =22074$

On this case we got that r =0.874

Part a

Null hypothesis: $\rho = 0$

Alternative hypothesis: $\rho \neq 0$

Part b

The scatter plot is on the figure attached.

Part c

In order to test a hypothesis related to the correlation coefficient we need to use the following statistic:

$t=\frac{r}{\sqrt{1-r^2}} \sqrt{n-2}$

Where n represent the sample size and the statistic t follows a t distribution with n-2 degrees of freedom:

$t \sim t_{n-2}$

On this case our value of n = 9 and the statistic is given by:

$t=\frac{0.874}{\sqrt{1-(0.874)^2}} \sqrt{9-2}=4.758$

And the degrees of freedom are given by df=9-2=7

And the p value for this case since we have a bilateral test is given by:

$p_v = P(t_{7} >4.758) =
0.0010$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that the correlation coefficient is significant.

3 0

3 years ago

The graph of y = f(x) is shown below. Determine the value of x when f(x) = -2?

ArbitrLikvidat [17]

Answer:

Great job!

Step-by-step explanation:

4 0

3 years ago

Emily is thinking of a number, which she calls n. She finds 1/4 of the number and then subtracts 3.

Debora [2.8K]

Answer:

n/4 - 3 OR 1/4n - 3

Step-by-step explanation:

First, let's assign a variable to Emily's number. Let is be x.

Now all we have to do is go through the problem step by step.

"She finds 1/4 of the number..."

There are two ways you can do this. You can either multiply n by 1/4 (1/4n), or you can divide by 4 (dividing by four is the same as finding 1/4 of a number). For this example let's divide by four

n/4

"...and then subtracts 3."

All we have to do is subtract 3 from n/4

n/4 - 3

REMEMBER: like I said, there are two possible options. You can either have n/4 or 1/4n. They mean the same thing

6 0

3 years ago

what is the volume of an area? what is a polynomial?

Anon25 [30]

First off, there can't be a volume of an area.
A polynomial is basically a equation that has 2 or more terms that have to be algebraic.

3 0

4 years ago