Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = 1 2A x2 dy C y = ? 1 2A y2 dx C where A is the area of D. Find the centroid of a quarter-circular region of radius a.

Answer:

-7

Step-by-step explanation:

(-4)2 | -7 - (-5)| -23

-4*2=-8

-7- -5=-2

|-2|=2

-8*2=16

16-23=-7

If there is a problem with this answer please feel free to tell me, thanks :)

The mean and standard deviation of the sample data in the table is 182 and 508 respectively.

To calculate the mean and standard deviation,

mean= E(x)

=  ∑x*f(x)

= 1(2) + 2(13) + 3(15)+4(11) + 5(13)

=2+26+45+44+65

=182

Standard deviation = E(x²)

=  ∑x²*f(x)) - E(x)

=1(2) + 4(13) + 9(15)+16(11) +25(13)  - E(x)

= 2 +52+135+176+325  - E(x)

=690 - 182   - E(x)

=508

The mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The three most frequently employed measures of central tendency are the mean, median, and mode.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. 

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The points that make both equations true are, (0,3) and (-3,3).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the equations is attached with the answer below. The points are (0,3) and (-3,3).

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The thing that the horizontal line signifies in the confidence interval plot is D. These horizontal lines are placed to help you visually locate the dot.

A confidence interval is a range of values that contains the value of an unknown population parameter. Given the characteristics of your sample data, these intervals represent a plausible domain for the parameter.

Confidence intervals are calculated using a specified confidence level and are derived from sample statistics. Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. These horizontal lines are placed to assist you in visualizing the dot.

In conclusion, the correct option is D.

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Step-by-step explanation:

based on the geometric mean theorem

h² = pq

h = height of the main right-angled triangle.

p and q are the segments of the baseline of the main right-angled triangle.

12² = 36x

144 = 36x

x = 144/36 = 4

so, DC is 4 units long.

The equation of a line into slope is 1/2x+1

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

Y equals mx plus b is actually the slope intercept form. Because it provides both a slope and an intercept, the form is known as a slope intercept form.

A line's slope and y-intercept are expressed in the following formula: y=mx+b. The y-intercept, which is usually represented in coordinate form as (0,b), is the point where the line crosses the y-axis.

y=1/2x+1

8y-4x=8

Add 4x to both sides.

8y=4x+8

Divide 8 (the one with y) by both sides.

y=1/2x+1

Therefore the equation of a line into slope is 1/2x+1

The complete question is : 8y−4x=8 Put the following equation of a line into slope-intercept form, simplifying all fractions.

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The  first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.

When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.

In this question, when we perform long division, we compare;

64 vs 1 . . . no quotient digit

64 vs 15 . . . no quotient digit

64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.

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Answer:

4.67 (nearest hundredth)

Step-by-step explanation:

In 3 weeks, Landscape Elementary uses 14 reams of paper.

In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...

The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.

4.66666... = 4.67 (nearest hundredth)

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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As per binomial distribution the probability of the following conditions are as follow:

a. probability for out of 5 none is concerned is 0.09924.

b. probability for out of 5 all are concerned is 0.02825

c. probability for out of 5 three are concerned is 0.4669.

As given in the question,

Percent of adults are concerned = 37%

p = 0.37

Percent of adults are not concerned = (100 -37)%

                                                         = 63%

1 - p = 0.63

Total number of adults 'n' = 5

Probability using binomial distribution

= ⁿCₓ pˣ ( 1- p)ⁿ⁻ˣ

a. Out of 5 none is concerned

here x = 0

⁵C₀( 0.37)⁰(0.63)⁵⁻⁰

= 0.09924

b. Out of 5 all are concerned

here x = 5

⁵C₅( 0.37)⁵(0.63)⁵⁻⁵

= 0.02825

c.  Out of 5 three are concerned

here x = 3

⁵C₃( 0.37)³(0.63)⁵⁻³

= 0.4669

Therefore , using binomial distribution the probability of the given percent of adult data is equal to as follow:

a. probability for out of 5 none is concerned is 0.09924.

b. probability for out of 5 all are concerned is 0.02825

c. probability for out of 5 three are concerned is 0.4669.

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Answer:

a) {A,E,I}

b) {red, orange, yellow, green, blue, violet, indigo}

c) {9,18,27,36,45}

d) {12,14,16,18,20,22}

Lol I'm not sure if I did all of these correct :]

(Also what is this for? Like the coding class or something? (Just curious))

Answer: 21 students

Step-by-step explanation:

A number being 30% smaller means that it has reduced to 70% of its original size.

This means we can multiply the original value by its new percentage, 30x0.7=21 students.

Answer:

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

We need to find the remainder when -5x³ + 2x + 3  is divided by x + 2.

According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:

The matching choice is B.

Answer:

B.  39

Step-by-step explanation:

Divide the polynomials using long division:

[tex]\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}[/tex]

The solution is the quotient plus the remainder divided by the divisor.

Solution

[tex]-5x^2+10x-18+\dfrac{39}{x+2}[/tex]

Answer: 20/48

(simplified) 5/12

Step-by-step explanation:

We will use 6/8 - 2/6 for our example

6/8 - 2/6

Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48

Make 48 the denominators on both sides: /48,  /48

Now multiply the denominator on the left side with the numerator on the  left side: 6x6 = 36

Make the first fraction's numerator 36: 36/48

Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16

Now make 16 the numerator of the second fraction: 16/48

Now that the denominators are the same, we can subtract!

36/48-16/48 = 20/48

Now to simplify:

divide 20/48 by 4 = 5/12

So the answer is 20/48 and when it is simplified it comes out to 5/12

This is how you subtract fractions with different denominators.

You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!

By using the unitary method the boy's actual height is 3 meters.

The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.

Given:

12 meters is the height of a boy statue.

The scale used was 4 meters = 1 foot.

1 metre = 1/4 feet

Assume the boy's actual height = H foot

By using the unitary method of unit conversion.

According to the question,

The actual height of the boy = height of the statue×  scale used for 1 meter.

H = 12 × ¼

H = 12/4

H = 3 meters

By using the unitary method the boy's actual height is 3 meters.

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By using the unitary method the boy's actual height is 3 meters.

The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.

Given:

12 meters is the height of a boy statue.

The scale used was 4 meters = 1 foot.

1 metre = 1/4 feet

Assume the boy's actual height = H foot

By using the unitary method of unit conversion.

According to the question,

The actual height of the boy = height of the statue×  scale used for 1 meter.

H = 12 × ¼

H = 12/4

H = 3 meters

By using the unitary method the boy's actual height is 3 meters.

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Answer: Mattie has 16 stamps and Arnav has 4 :)

Step-by-step explanation:

the system of equations used to solve it is

m=4a

m-8=2a

Martie have 48 stamps and Arnav have 12 stamps.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let Matie has x stamps and Arnav has y stamps.

Given that,

Matie has 4 times as stamps as Arnav

Implies that,

x = 4y            (1)

Also, If Matie gives 8 stamps to Arnav will have twice stamps to Arnav.

Implies that,

x - 8 = 2(y+8)

x - 8 = 2y + 16

x = 2y + 24      (2)

From equation (1) and (2),

y = 12

and x = 48

Matie and Arnav each have 48 and 12 stamps respectively.

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The table for the function y = 5^x should be completed as follows;

x           y

-1          0.2

0           1

1            5

2           25

A graph of the given function y = 5^x with the points (0, 1) and (1, 5) is shown in the image attached below.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Next, we would determine the ordered pairs that would complete the table for the function y = 5^x as follows;

When x = -1, the value of y is given by;

y = 5^-1

y = 0.2 or 1/5.

When x = 0, the value of y is given by;

y = 5^0

y = 1

When x = 1, the value of y is given by;

y = 5^1

y = 5

When x = 2, the value of y is given by;

y = 5^2

y = 25

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Answer: There are several statements that could be false if f(x) is continuous on [a, b] and differentiable on (a, b):

1 The function f(x) has a maximum or minimum value at some point in the interval [a, b].

2 The function f(x) is monotonic (either increasing or decreasing) on the interval [a, b].

3 The function f(x) has an inflection point (a point where the concavity of the function changes) in the interval [a, b].

4 The function f(x) has an asymptote (a line that the function approaches but never touches) in the interval [a, b].

5 Note that these statements are not necessarily false, but they could be false depending on the specific function f(x).

Answer:

x ≈ 10.6

y = 15

Step-by-step explanation:

The opposite angles in an inscribed quadrilateral are supplementary.

Therefore:

(4y+14) + (7y+1) = 180

=> 11y + 15 = 180

=> 11y = 165

=> y = 15

7x+1 + 105 = 180

=> 7x + 106 = 180

=> 7x = 74

=> x ≈ 10.6

The value of (f . g) (3) is 594 and  (f + g) (3) is 42 when function is f(x) =  4x² - 3 and g(x) = 2x + 3.

i) (f . g) (3)

(f . g) (x) = f(x) . g(x)

(f . g) (3) = f(3) . g(3)

= 4(3)² - 3 * 2(3) + 3

= 36 - 3 * 6 + 3

= 33 * 18

(f . g) (3) = 594

The value of (f . g) (3) is 594 when function is f(x) =  4x² - 3 and g(x) = 2x + 3

ii) ( f +​ g )( ​3 )

( f + g )( x ) = f ( x ) + g ( x )

​( f +​ g )( ​3 ) = f (3 ) + g ( 3 )

= 4(3)² - 3 + 2(3) + 3

= 4(9) + 6

= 36 + 6

​( f +​ g )( ​3 ) = 42

The value of (f + g) (3) is 42 when function is f(x) =  4x² - 3 and g(x) = 2x + 3.

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Dude I am so sorry that I do not know this answer

An inequality that can be used to determine how much material, x, Paul should buy is x ≥ 196.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

Given:

Paul is making picture frames.

He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.

To find the total material for 8 frames:

Multiply by 8 to material for one form

24.5 x 8

= 196 inches

To write an inequality that can be used to determine how much material, x, Paul should buy:

x ≥ 196 inches.

To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more.

You must flip the inequality sign if you multiply or divide either side by a negative number.

Therefore, the inequality is x ≥ 196.

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The income of the man is 24000.

Step-by-step explanation:

income of man =24000

Let the income of man be x

According to the question,

20%*x = 4800

0.2x=4800

As a result, x =24000

(4800*10= 48000/2= 24000)

So the income of a man is 24000.

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Man's income is, 24000 rupees.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, 20% of an income of a man is Rs 4,800.

To find the income:

Use percentage formula,

let m be the man's income.

So, m x 20 / 100 = 4800

Rearranging,

m = 4800 x 100 / 20

m = 24000

Therefore, the income is, 24000 Rs.

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The length of the congruent triangles are as follows:

BC = 36

EF = 36

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

ΔABC≅ΔDEF

Let's find the length of the given sides as follows:

BC = x + 20

EF = 2x + 4

Therefore,

BC = EF

x + 20 = 2x + 4

x - 2x = 4 - 20

- x = -16

x = 16

Therefore,

BC = x+20 = 16 + 20 = 36

EF = 2x+4 = 2(16) + 4 = 32 + 4 = 36

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The equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

We have given the line passes through the points(0, 3) & (3, 0),

so, m = (0-3)/(3-0)

= -3/3

m = -1

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through the point (3, 0), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:

y = mx + b

0 = -1 * 3 + b

b = -3

Solving for b gives us:

b = -3

Therefore, the equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

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Solving for y, the linear equation is: y = -4/5x - 2/5.

The table showing the corresponding y-value for each x-value is:

x |  -8  -3   2   7

y |   6   2  -2  -6

The graph is in the attachment.

To graph the linear equation of 4x + 5y = -2, rewrite in slope-intercept form by solving for y.

4x + 5y = -2

5y = -4x - 2

y = -4/5x - 2/5

Complete the table given by plugging each value of x into the linear equation, y = -4/5x - 2/5.

For x = -8:

y = -4/5(-8) - 2/5

y = 6

For x = -3:

y = -4/5(-3) - 2/5

y = 2

For x = 2:

y = -4/5(2) - 2/5

y = -2

For x = 7:

y = -4/5(7) - 2/5

y = -6

The complete table is:

x |  -8  -3   2   7

y |   6   2  -2  -6

See the graph below.

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Answer: y = 3/2x +-9

Step-by-step explanation:

      The equation in slope-intercept form, y = mx + b, is the equation y = 3/2x +-9.

      See attached for more information on slope-intercept form.

Answer: $5,250

Step-by-step explanation:

1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.

It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.

Answer:

D) [tex]x^2+8x+16=(x+4)^2[/tex]

Step-by-step explanation:

[tex]x^2+8x+(8/2)^2=x^2+8x+16=(x+4)^2[/tex]

Answer:

4 and 1/2

Step-by-step explanation:

left side must be ewual to right side. after you substract 12x-4x you get 8x+2 on right side. you than find a number on the left side, whit which you have to multiply 2x to get 8x(same number as on the other side) and you get 4. lastly you have to find a number that gives you 2 when multiplied with 4 and it is 1/2