Am I right? Please help me out

Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is

[tex]\displaystyle \oint_C (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy \\\\ = \iint_{\mathrm{int}(C)}\frac{\partial(4x+y)}{\partial x} - \frac{\partial(\sin(x)+9y)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy[/tex]

(where int(C ) denotes the region interior to the path C )

The remaining double integral is -5 times the area of the trapezoid, which is

[tex]\displaystyle -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy = -\frac52\times(12+4)\times4=-160[/tex]

To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to

[tex]\displaystyle\int_{DA}y\,\mathrm dy = \int_{12}^0y\,\mathrm dy = -\int_0^{12}y\,\mathrm dy = -72[/tex]

Then

[tex]\displaystyle \int_{ABCD} (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy = -160 - (-72) = \boxed{-88}[/tex]

Answer:

If you're asking what cosine 3 is it's 0.9999986292247

Step-by-step explanation:

I don't really understand the question

Answer:

skewness

Step-by-step explanation:

Average.

The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.

Learn more about averages in https://brainly.com/question/22390452

Answer:

A

Step-by-step explanation:

[tex]\sqrt{3-2*\sqrt2}=\sqrt{(\sqrt2)^2-2\sqrt2*1+1^2}=\sqrt{(\sqrt2-1)^2}=\sqrt2-1[/tex]

Answer:

19.65

Step-by-step explanation:

28.9-9.25=19.65

Answer: p >-17/5

Step-by-step explanation:

Answer:

P = [tex]\frac{-17}{5}[/tex]

Step-by-step explanation:

Substract 3P from both sides:

5P  + 2 >  - 15

Subtract 2 from both sides:

5P > -17

Divide both sides by 5:

P = [tex]\frac{-17}{5}[/tex]

Answer:

The man would be 40 years old.

Step-by-step explanation:

Blood pressure as function of age:

Is given by the following equation:

[tex]P = 0.006A^2 - 0.02A + 120[/tex]

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

[tex]129 = 0.006A^2 - 0.02A + 120[/tex]

[tex]0.006A^2 - 0.02A - 9 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So

[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]

[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]

[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

Answer:

[tex]5 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt[]{5} \times \sqrt{2} \\ = 5\sqrt{2} [/tex]

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

Answer:

Hence the confidence interval (2.2, 3.52).

Step-by-step explanation:

Hence,

The point estimate = [tex]\bar x_{1} - \bar x_{2}[/tex]

= 7.9 - 5.04

= 2.86

Given CI level is 0.98, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.326

Margin of Error

ME = tc x sp

ME = 2.326 \ 0.2817

ME = 0.6552

CI = ([tex]\bar x_{1} - \bar x_{2}[/tex] - tc x sp , [tex]\bar x_{1} - \bar x_{2}[/tex] + tc x sp)

CI = (7.9 - 5.04 - 2.326 x 0.2817 , 7.9 - 5.04 - 2.326 x 0.2817

CI = (2.2 , 3.52)

Answer:

7% = .07 = [tex]\frac{7}{100}[/tex]

Step-by-step explanation:

Answer:

The answer is "8.74 and 36.46 years"

Step-by-step explanation:

Mean (life-time)=22.6 years

standard deviation= 3.1 years

We must find out how many standard deviations are 95% of the data.  

[tex]1 - \frac{1}{k^2} = 0.95\\\\1 - 0.95 = \frac{1}{k^2}\\\\\frac{1}{k^2} = 0.05\\\\\frac{1}{0.05} =k^2\\\\k^2 = 20\\\\ k = 4.47[/tex]

Calculating the lower limit and upper limit:

[tex]Lower\ limit = 22.6 - 4.47(3.1) = 22.6 - 13.86 = 8.74\\\\Upper\ limit = 22.6 + 4.47(3.1) = 22.6 + 13.86 = 36.46[/tex]

Limit is 8.74 years to 36.46 years

Answer:

C.I

Step-by-step explanation:

vertex is always the center point if that makes any sense

Answer:

[tex]\boxed{\sf A) ( 1,0) }[/tex]

Step-by-step explanation:

A quadratic function is given to us and we need to find the x Intercept of the graph of the given function . The function is ,

[tex]\sf \implies f(x) = x^2 -2x + 1 [/tex]

For finding the x intercept , equate the given function with 0, we have ;

[tex]\sf \implies x^2 -2x + 1 = 0 [/tex]

Split the middle term ,

[tex]\sf \implies x^2-x-x+1=0[/tex]

Take out common terms ,

[tex]\sf \implies x( x -1) -1( x -1) = 0[/tex]

Take out (x - 1 )as common ,

[tex]\sf \implies (x - 1 )(x-1) = 0[/tex]

Equate with 0 ,

[tex]\sf \implies x = 1,1 [/tex]

Therefore the root of the function is 1. Hence the x Intercept is (1,0)

Hence the x Intercept is (1,0) .

Step-by-step explanation:

x² - 2x + 1 = 0

x² - (x + x) + 1 = 0

x² - x - x + 1 = 0

x(x - 1) - 1(x - 1) = 0

(x - 1)(x - 1) = 0

x = 1

Hence,

Option A

Answer:

no solutions

Step-by-step explanation:

y = - 2x + 5

y = -2x + 20

Set the two equations equal

- 2x + 5  = -2x + 20

Add 2x to each side

- 2x+2x + 5  = -2x+2x + 20

5 = 20

This is never true so there are no solutions

Answer:

no solution

Step-by-step explanation:

Hi there!

We are given this system of equations:

y=-2x+5

y=-2x+20

and we want to find the solution (the point in which the lines intersect)

There are 3 ways to solve a system, but let's use substitution in this case

Both equations are set to y, so they should be equal to each other via a property known as transitivity (if a=b and b=c, then a=c)

-2x+5=-2x+20 (the same as y=y)

Now let's solve for x

add 2x to both sides

5=20

In this case, we got an untrue statement. If this happens, then the lines won't intersect.

If they won't intersect, there's no solution

Hope this helps!

Answer:

2538

2.5%

Step-by-step explanation:

The population equayio since year 2000 can be modeled mathematically as :

P = 2538(1.025)^t

This is an exponential growth function which is represented by the general formula :

y = a(b)^t

Where, a is the initial population ;

b = growth factor ; b = (1 + r) where r = growth rate

Comparing the equations, the population in year 2000 represents the initial population, a = 2538

The percentage Rate of increase in population is :

(1 + r) = 1.025

r = 1.025 - 1

r = 0.025 ; 0.025 * 100% = 2.5%

Answer: d=7 inches

r=7/2

r=3.5

A=πr²

A=3.14(3.5inch)²

A=3.14×12.25inch²

A=38.465inch²

A≈38.47inch²

=================================================

Work Shown:

ED/DF = AB/AC

x/24 = 12/16

16x = 24*12

16x = 288

x = 288/16

x = 18

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

Explanation:

Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.

So for instance, another proportion you could solve is ED/AB = DF/AC.

The key is to keep up the same pattern when forming the ratios.

What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.

Answer:

2/12 = 1/6

Step-by-step explanation:

To find the probability of something with an equal chance of each outcome, we can apply the formula (number of favorable outcomes)/(number of total outcomes). Because there is an equal chance for each side of the die to be landed on, we can apply this.

On a 12 sided die, there are 12 sides. Two of those sides are 3 and 9. Therefore, there are two favorable outcomes (3 and 9). There are 12 sides to choose from, so there are 12 total outcomes, making the probability 2/12 = 1/6

Answer:

17/16 =x

Step-by-step explanation:

The triangle is a right triangle so we can use Pythagorean theorem

a^2+b^2 = c^2

x^2 + 9^2 = (x+8)^2

FOIL

x^2+81=x^2+16x+64

Subtract x^2 from each side

81 = 16x+64

Subtract 64 from each side

81 -64 = 16x+64-64

17 =16x

Divide by 16

17/16 =x

Answer:

The critical value used is T = 3.747.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{127+174+157+120+161}{5} = 147.8[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188[/tex]

Confidence interval:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 5 - 1 = 4

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.747, which is the critical value used.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944  

The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Answer:  option C is correct

Step-by-step explanation:[tex]s=( \alpha +\beta +c)/2\\2s=\alpha +\beta +c\\2s-\beta -c=\alpha \\\alpha =2s-\beta -c[/tex]

Answer:

The polygons are not similar..

Step-by-step explanation:

We have given the two polygons which are parallelogram with the opposite sides 10.4 units, 3.74 units, 4 units and 1.7 units

For the polygons to be similar, ratios of both the polygons must be equal.

Lets check whether the two polygons are equal or not.

10.4/3.74 = 2.78

4/1.7 = 2.35

Therefore it is proved that both the polygons are not similar because both these ratios are not equal....

Answer:

It multiplies

Step-by-step explanation:

if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours

Answer:

2.5 x 2.5 = 6.25cm^2 (area of one side)

6.25 * 6 = 37.25cm^2 (area of all sides)

Step-by-step explanation:

Answer:

V = 192 m^3

Step-by-step explanation:

The volume of a cuboid is given by

V = l*w*h

V = 4m * 6m *8m

V = 192 m^3

Answer:

Small (11.5) is 37 cents per ounce.

Large (27.8) is 36 cents per ounce.

27.8 ounces is the better buy.