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german
3 years ago
6

The length of a rectangle is (x^2- 4x+2) feet and the width is (x+4) feet

Mathematics
1 answer:
erastovalidia [21]3 years ago
4 0

Answer:

A=x^3-14x+8

Step-by-step explanation:

Given that,

Length of a rectangle, l=(x^2- 4x+2)

Width of a rectangle, b=(x+4)

We need to find the area of the rectangle.

We know that,

Area of a rectangle = l × b

Substituting all the values,

A=(x^2- 4x+2)\times (x+4)\\\\=x^3+4x^2-4x^2-16x+2x+8\\\\=x^3-14x+8

Hence, the area of the rectangle is x^3-14x+8.

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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) =&#10;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
(24+3)+3+3 use order of operations to solve
Stella [2.4K]

Answer:

33

Step-by-step explanation:

(24 + 3) + 3 + 3

(27) + 3 + 3              First solve what's in the parenthesis

30 + 3                     Then work left to right

33

6 0
3 years ago
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I need help will give a lot of credit and brainly if you tell me the right boxes and if it is correct FYI this is zearn
kicyunya [14]

Answer:

Step-by-step explanation:

3 0
3 years ago
A parabola with vertex (h, k) and a vertical axis of symmetry is modeled by the equation y - k = a(x - h)2. Determine the vertex
Inessa05 [86]
<span>y - k = a(x - h)²

</span><span>y = (x − 5)² + 8 -------> y-8 = (x-5)²

</span>y - k = a(x - h)²
y - 8 =   (x - 5)²
Compare these formulas we can see that k=8, h =5.

Vertex (5,8).
5 0
4 years ago
Maya painted 3/4 of her art project in the morning and 1/8 of her project in the evening which equation can Maya use c to find h
Tatiana [17]

Answer:

Maya painted 3/4 of her art project in the morning and 1/8 of her project in the evening which equation can Maya use c to find how much of the project she painted dtrdtrdtrdtrdrt9945 is waiting for your help.

Step-by-step explanation:

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3 years ago
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