the diagram shows a regular decagon please help

where is the table that represents the quadratic function

The mass of the lamina is 6 units.

The center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Here,

To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.

The mass (M) of the lamina is given by the double integral of the density function over the region D:

M = ∬_D ρ(x, y) dA

where dA represents the differential area element.

The center of mass (X,Y) of the lamina can be calculated using the following formulas:

X = (1/M) ∬_D xρ(x, y) dA

Y = (1/M) ∬_D yρ(x, y) dA

Now, let's proceed with the calculations:

The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:

0 ≤ x ≤ 2

0 ≤ y ≤ 3 - (3/2)x

Now, let's calculate the mass (M):

M = ∬_D ρ(x, y) dA

M = ∬_D 2(x + y) dA

We need to set up the double integral over the region D:

M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx

Now, integrate with respect to y first:

M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx

M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx

M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx

Now, integrate with respect to x:

[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]

So, the mass of the lamina is 6 units.

Next, let's calculate the center of mass (X,Y):

X = (1/M) ∬_D xρ(x, y) dA

X = (1/6) ∬_D x * 2(x + y) dA

We need to set up the double integral over the region D:

X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx

Now, integrate with respect to y first:

X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx

X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx

X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx

X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx

Now, integrate with respect to x:

[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]

Next, let's calculate Y:

Y = (1/M) ∬_D yρ(x, y) dA

Y = (1/6) ∬_D y * 2(x + y) dA

We need to set up the double integral over the region D:

Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx

Now, integrate with respect to y first:

Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx

Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx

Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx

Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx

Now, integrate with respect to x:

[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]

So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).

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Answer:

B

Step-by-step explanation:

Answer:

A. 2x

Step-by-step explanation:

Step 1: Factor out a 2

2(2x³ - x² + 4x)

Step 2: Factor out an x

2x(2x² - x + 4)

So our answer is B.

Answer:

1,1/2,1/3,1/4

Step-by-step explanation:

an = 1/n

n is the term number

a1 = 1/1 =1

a2 = 1/2

a3= 1/3

a4 = 1/4

The first 4 terms are 1,1/2,1/3,1/4

Answer:

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 66/132 = 0.50

Number of samples n = 132

Confidence level = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

0.50 +/- 1.645√(0.50(1-0.50)/132)

0.50 +/- 1.645√(0.001893939393)

0.50 +/- 0.071589436011

0.50 +/- 0.072

(0.428, 0.572)

The 90% confidence level estimate of the true population proportion of students who responded "yes" is (0.428, 0.572)

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

Answer:

2009.6

Step-by-step explanation:

As we know, volume of a right cylinder is πr²h.

here, diameter is mentioned, which gives that the radius is half of the diameter.

r= 1/2*16=8 feet

height= 10 feet

π=3.14

volume= 3.14*8²*10

          = 3.14*64*10

            =3.14*640

             = 2009.6

so, that much water is needed to fill the tank

Answer:

2,010.6192982

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ a = 1 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

saying that [tex]x-\sqrt{a}[/tex] is a factor means that [tex]\sqrt{a}[/tex] is a zero which means

[tex]2(\sqrt{a})^4-2a^2(\sqrt{a})^2-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=> 2a^2-2a^3-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=>3-3*\sqrt{a}=0\\\\<=>\sqrt{a}=\dfrac{3}{3}=1\\\\<=> a = 1[/tex]

so the solution is a = 1

Do not hesitate if you have any question

Answer:

It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.

Step-by-step explanation:

I listed all of the possible combinations below

GGGGGGGGG           BGGGGGGGG

BBGGGGGGG           BBBGGGGGG

BBBBGGGGG           BBBBBGGGG

BBBBBBGGG            BBBBBBBGG

BBBBBBBBG             BBBBBBBBB

Total number of combinations with at least one boy is 9/10

This is a very high percentage, which means the couple is very likely to have at least one boy.

Answer:

The equation that shows the profit: P = 2x + 3y

Step-by-step explanation:

The number of sneaker = x

The number of sandals = y

Cost of sneaker = 8 dollars.

Cost of sandals = 14 dollars.

Selling price of sneaker = $10

Selling price of sandals = $17

Total revenue = $10x + $17y

Total cost  = $8x + $14y

Profit (P)  =  Total revenue  - Total cost.

Profit = ($10x + $17y) – ($8x + $14y)

P = 10x +17y – 8x – 14y

P = 2x + 3y

Answer:

Step-by-step explanation:

22x + 1 = 8

Send 1 to the right side of the equation

22x = 8 - 1

22x = 7

Divide both sides by 22

x = 7/22

Hope this helps you

Answer:

Measure of angle 2 = 82°

Step-by-step explanation:

m∠1 = (10 x + 8)°

m∠3 = (12 x - 10)°

2 lines are said to intersect to form 4 angles. And the labelling of the angles was done starting from top left, clockwise: the angles are 1, 2, 3, 4.

Find attached the diagram obtained from the given information.

Vertical angles are angles opposite each other when two lines intersect. As such, they are equal to each other.

Considering our diagram

m∠1 = m∠3

m∠2 = m∠4

Sum of all four angles firmed = 360° (sum of angles at a point)

m∠1 +m∠2 + m∠3 + m∠4 = 360°

m∠1 = m∠3

(10 x + 8)°= (12 x - 10)°

10x-12x = -10-8

-2x = -18

x= 9°

Also m∠2 = m∠4, let each equal to y

(10 x + 8)°+ y + (12 x - 10)° + y = 360

10x + 12x - 10 +8 +2y = 360

Insert value of x

22(9) -2 + 2y = 360

2y = 360-196

2y = 164

y = 82°

m∠2 = m∠4 = y = 82°

Measure of angle 2 = 82°

Answer:

2 = 82°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Factors of 12

2, 3 , 6 , 4, 1, 12

Answer:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Step-by-step explanation:

For this problem we have the following set:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Step-by-step explanation:

O D. F(X) = 3W-3 the answer is D

The function that represents the situation is F(x) = -x² - 3.

The correct option is A.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.

here, we have,

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The value of k can find the direction of shift:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given that ,

the parent function is g(x) = x².

To find the transformed function F(x):

The function's diagram is in the opposite direction.

That means the function is -x².

And the function is shifted 3 units down vertically.

From the definition the required function is,

F(x) = -x² - 3.

Therefore, F(x) = -x² - 3.

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complete question:

The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?

A.

F(x) = –x2 – 3

B.

F(x) = x2 – 3

C.

F(x) = –(x + 3)2

D.

F(x) = –(x – 3)2

Step-by-step explanation:

[tex] \frac{2}{ \sqrt{9} } [/tex]

[tex] \frac{2 \times \sqrt{9} }{ \sqrt{9} \times \sqrt{9} } [/tex]

[tex] \frac{2 \sqrt{9} }{9} [/tex]

Answer:

[tex]\frac{2\sqrt{9} }{9}[/tex]

Step-by-step explanation:

[tex]\frac{2}{\sqrt{9} } \\[/tex]

[tex]\frac{2}{\sqrt{9} } * \frac{\sqrt{9} }{\sqrt{9} }[/tex]

[tex]\frac{\sqrt{9} }{\sqrt{9} }[/tex]  is equal to 1, so it doesn't change the value, just helps us simplify.

[tex]\frac{2\sqrt{9} }{9}[/tex]

There are no common factors between 2 and root 9, so we are done

Answer:

B.

Step-by-step explanation:

The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that  gets to a point at the middle of the height.

Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.

Answer:

B.

Step-by-step explanation:

answer: B. one triangle tip on top and invert above it with the top touching

Answer:

20% probability that a box weighs more than 32.2 ounces

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X higher than x is given by the following formula.

[tex]P(X > x) = \frac{b-x}{b-a}[/tex]

Uniform distribution ranging from 31 to 32.5 ounces.

This means that [tex]a = 31, b = 32.5[/tex]

What is the probability that a box weighs more than 32.2 ounces?

[tex]P(X > 32.2) = \frac{32.5 - 32.2}{32.5 - 31} = 0.2[/tex]

20% probability that a box weighs more than 32.2 ounces

Answer:

The required sample size increases.

Step-by-step explanation:

The margin of error of a confidence interval is given by:

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

The confidence level decreases, so z decreases.

For the margin of error to stay the same, the sample size also has to decrease.

The required sample size increases.

Answer:

Function

Step-by-step explanation:

A function is a relation where each x-value has only one y-value. In this problem, all the x-values have a y-value of 3. It is a function because even though they all share the same y-value, they don't have more than one y-value. It would be a relation but not a function if one x-value had two y-values.

Hope this helps. :)

Answer:

for us to be able to ascertain whether a function has no limit we approach from two points which are from zero and infinity.

Step-by-step explanation:

the two best path to approach a function is to approach from zero and approach from infinity, literary what we are trying to do is approach from the smallest to the greatest and it each point we can conclude with certainty whether the function has a limit or not.

Answer:

Step-by-step explanation:

Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

Step-by-step explanation:

Net $103.92 [$25.98 ÷ 20%]

List. $129.90 [ $103.92 + $25.98]

Answer:

Where is the table because I dont see it up here?

━━━━━━━☆☆━━━━━━━

▹ Answer

#3. 1.89/100

▹ Step-by-Step Explanation

1.89 → hundreths place so..

1.89/100 is the correct answer

Hope this helps!

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Brainliest is greatly appreciated!

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Answer:

The following combination describes a regression line that is a good fit for the data

a. Larger R-sq and small Se

Step-by-step explanation:

In regression analysis, we measure the goodness of fit in terms of two parameters.

1. R² ( R-squared or also called the coefficient of determination)

2. SE ( Standard Error)

1. R-squared

The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.

R-squared is measured in percentage so it doesn't have any unit.

The greater the R-squared percentage, the better is the goodness of fit.

2. Standard Error

The SE basically indicates that on average how far the data points are from the regression line.

The unit of the standard error is the same as the dependent variable.

The lower the SE, the better is the goodness of fit.

Therefore, the correct option is (a)

a. Larger R-sq and small Se

Answer:

9π or 28.3 units²

Step-by-step explanation:

A = πr²

A = π(3)²

A = 9π

or

A= 28.3 units²

Hope this helps. :)

Answer:

f(x) = - 9x² + 9

g(x) = 8x² + 9x

To find (f+g)(x) add g(x) to f(x)

That's

(f+g)(x) = -9x² + 9 + 8x² + 9x

Group like terms

(f+g)(x) = - 9x² + 8x² + 9x + 9

To find (f + g)(- 1) substitute - 1 into (f+g)(x)

That's

(f + g)(- 1) = -(-1)² + 9(-1) + 9

= - 1 - 9 + 9

Hope this helps you

Answer:

Cannot be factored

Step-by-step explanation:

Answer:

Step-by-step explanation:

First we must first find the LCM

The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is

x² + 3x + 2

So we have

[tex] \frac{x}{ {x}^{2} + 3x + 2 } - \frac{1}{(x + 2)(x + 1)} \\ \\ = \frac{x - 1}{ {x}^{2} + 3x + 2 } [/tex]

Hope this helps you

Answer:

The answer is OPTION D!

Step-by-step explanation:

HoPe ThIs HeLpS!