explain the process of finding the mean of a data set in your own words.

The lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].

Given:

Find the moment of inertia [tex]I_y[/tex] and [tex]I_0[/tex].

The lamina's moment of inertia about the x-axis is:

In the above equation, substitute the given value:

Make use of polar coordinates:

[tex]\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2[tex]\pi[/tex].

As a result, the integral is shown below; simply enter all of the values and then integrate.

[tex]\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}[/tex]

Now, calculate  [tex]I_y[/tex] and [tex]I_0[/tex].

Make use of polar coordinates.

[tex]\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2[tex]\pi[/tex].

As a result, the integral is shown below; simply enter all of the values and then integrate.

[tex]\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}[/tex]

The lamina's moment of inertia about the origin is given by:

[tex]\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}[/tex]

So, the moment of inertia is [tex]I_x=320 \pi[/tex].

The worth of, [tex]I_y=320 \pi[/tex].

Therefore, the lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].

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The correct question is given below:

Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.

Answer: x=138 degrees

Step-by-step explanation:

x+42=180 ==> Angle x and the supplementary angle of 42 are congruent angles, meaning that x and 42 add up to 180 degrees.

x-42+42=180-42

x=180-42

x=138 degrees

The value of the side length of the square-shaped pool is 13 meters

The formula for calculating the area of a square is expressed as;

Area = a^2

Where 'a' is the side length of the square.

It is important to note the properties of a square, they include;

Now, substitute the value of the area into the formula, we have;

169 = a^2

To determine the value of a, find the square root of both sides

√169 = √a^2

13 meters = a

Thus, the value of the side length of the square-shaped pool is 13 meters

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Answer:

10%

Step-by-step explanation:

If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).

Given:

Decrease in coastline=-3

Total number of years=8 years

Hence,

a. Integer that represent the total loss of coastline is:

Integer=8(-3)

Integer=-24 (Total loss)

b. The integer that can be use to represent the decrease is:

Decrease in coastline= -3

c. The expression that represent the total loss of coastline over 8 years is:

Expression= 8(-3)

Therefore If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).

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The zeros of the polynomial function

1.0,3,-1

2.3,-2,+1

3.2,-3,0

The zeros of a polynomial are the x values that satisfy the equation f(x) = 0. In this case, f(x) is a function of x, and the polynomial zeros are the x values for which the f(x) value is zero. The number of zeros in a polynomial is determined by the degree of the equation f(x) = 0. The polynomial zeros are all domain values of the function whose range is equal to zero.

The polynomial zeros are the points on the graph where y = f(x) touches the x-axis. More on this in the page below on expressing polynomial zeros on a graph.

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The rise-over-run formula for the slope of a straight line is the basis of the high-low method.

What is slope of a straight line?

The slope of a straight line by joining two points is the rise over run formula. The subtraction between the two points of the y-coordinates is called the rise. And the subtraction between the two points of the x-coordinates is called the run. The slope can be calculated by dividing the rise by run.

The slope of a line either goes in the upward direction or in the downward direction or left direction or right direction. It determines the direction of the line. When the straight line goes in the upward direction, it means the rising line and slope is positive. When it goes in the downward direction, it means a falling line and slope is negative.

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The equation that is perpendicular to the line is x = -1

The line equation is given as

y = 3

The point is also given as:

(x, y) = (-1, 3)

A linear equation is represented as

y = mx + c

Where m represents the slope

This means that y = 3 can be represented as

y = 0x + 3

So, the slope is 0

Since the slope is 0, the equation of the perpendicular line must be

x = xt

Where

(xt, y) = (-1, 3)

By comparison, we have

x = -1

Hence, the equation that is perpendicular to the line is x = -1

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Answer:

translated 9 units to the right and 2 units down

Answer:The first one is translated 9 units to the right and 2 units down.The second is reflected across the x-axis and the last i reflected across the y-axis.

Step-by-step explanation:Please give brainliest if correct.

1) Converting all to scientific notation gives;

J a p a n = 1.3718 * 10⁸

B r a z i l = 2.75 * 10⁸

G e r m a n y = 8.5619 * 10⁷

United Kingdom = 6.3706 * 10⁷

N i g e r i a = 1.43615 * 10⁸

B a n g l a d e s h = 1.8251 * 10⁰

I n d i a = 1.589143847902 * 10¹²

2) Arranging the populations from least to greatest is;

1.8251 * 10⁰ < 6.3706 * 10⁷ < 8.5619 * 10⁷ < 1.3718 * 10⁸ < 1.43615 * 10⁸ < 2.75 * 10⁸ < 1.589143847902 * 10¹²

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one.

We are given countries and their populations as;

J a p a n = 1.3718 * 10⁸

B r a z i l = 2.75 * 10⁸

G e r m a n y = 8.5619 * 10⁷

United Kingdom = 6.3706 * 10⁷

N i g e r i a = 1.43615 * 10⁸

B a n g l a d e s h = 1.8251 * 10⁰

I n d i a = 1.589143847902 * 10¹²

1) Converting all to scientific notation gives;

Japan = 1.3718 * 10⁸

B r a z i l = 2.75 * 10⁸

Germany = 8.5619 * 10⁷

United Kingdom = 6.3706 * 10⁷

N i g e r i a = 1.43615 * 10⁸

Ban glad e s h = 1.8251 * 10⁰

India = 1.589143847902 * 10¹²

2) Arranging the populations from least to greatest is;

1.8251 * 10⁰ < 6.3706 * 10⁷ < 8.5619 * 10⁷ < 1.3718 * 10⁸ < 1.43615 * 10⁸ < 2.75 * 10⁸ < 1.589143847902 * 10¹²

3) The way it was solved was to change all numbers first to scientific notation

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Shureka's present scores of 62, 82, 62, and 68, and a passing score of 71 or higher gives;

Shureka's scores are 62, 82, 62, 68

Grade with which Shureka will pass the course = 71

Number of test her final exam is equivalent to = 2

Let x represent her score in her final exam, we have;

[tex] \frac{62 + 82 + 62 + 68 + x}{4 + 2} \geqslant 71[/tex]

Which gives;

62+82+62+68+x ≥ 71 × (4+2) = 426

274 + x ≥ 426

x ≥ 426 - 274 = 152

x ≥ 152

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The percent increase in population of the city is 17%.

A percentage in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). A percentage lacks dimensions and has no associated unit of measurement.

For instance, 45% (written as "forty-five percent") equates to the fraction [tex]\frac{45}{100}[/tex]  .

The percentage increase is calculated by the ratio of the increase to the original value. So to calculate the percent increase in the population of a city we have to find the ratio of the increase in population to the original population.

The population of the city is given as 117,000 .

The population increased to 136890.

Increase in population=136890-117000=19890

percentage increase in population

[tex]=\frac{19890}{117000} \times 100\%[/tex]

= 0.17×100%

=17%

The percent increase in the population of the city is 17%.

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The following scenario is a good example of a matched-pairs experiment.

So, the given situation of a pesticide manufacturer is a perfect example of a matched-pairs experiment.

Therefore, the following scenario is best described as an example of a matched-pairs experiment.

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The correct question is given below:
A pesticide manufacturer is developing a new type of organic pesticide for a particular plant. To study the effectiveness of the new pesticide, a large sample of young plants is collected. The sample is then separated into many groups of two plants based upon age, size and soil type so that plants with similar characteristics are grouped together. One of the two plants in each group is randomly chosen and administered the pesticide, while both plants are placed in a controlled environment and are exposed to the possibility of attack from the target pests. The plants are inspected regularly over a 3 month period and the results are recorded for comparison.

This scenario is best described as an example of...

1 question answers:

Angle B=70

Angle C=70

Step-by-step explanation:

2 question:

Angle B= 90

Angle C=50

The total distance of the race = 8.91  miles

Solution :

Miles :

There are 5,280 feet in one mile. Simply divide 5,280 feet by your average stride length to learn how many steps it will take to walk a mile. If your average stride length is 2 feet, for example, it will take 2,640 steps to walk a mile.

One part of the race is 3.21 miles

another part of the race is 5.7 miles

Total :

add of both trails

= 3.21+5.7

= 8.91

The total distance of the race = 8.91  miles

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According to the given information multiply the integer by four, add 12 to the product, divide the sum by two, and subtract 6 from the quotient.

The correct option is A.

In both mathematics and computer programming, the order of operations refers to a set of guidelines on which operations to do first in order to evaluate a certain mathematical expression. The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation. We can recall the PEMDAS steps in the following order:

parentheses, exponents, multiplication and division (from Left to right), addition, and subtraction (from left to right).

The term BODMAS is used in the UK (Brackets, Orders, Divide, Multiply, Add, Subtract).

BDMAS is a term used in Canada (Brackets, Exponents, Divide, Multiply, Add, Subtract).

The equation ((4x+12)2)-6 leads to the result 2x, demonstrating that the answer is in multiples of 2.

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When Maria distribute the lunches to the 22 students equally, each person gets 1.6 of the meal.

It should be noted that from the information, Maria must distribute the lunches to the 22 students equally.

Therefore, the total foods will be:

= (3 + 6 + 25 + 2) / 22

= 36 / 22

= 1.6

Therefore each person gets 1.6 of the meal.

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Answer:

i think its x=-12

Step-by-step explanation:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x.

x = −12

Answer:-5

Step-by-step explanation:

Answer:

Dear bro not to use this brainly is app that's why do not search answer on brainly do yourself cause you are the better one

Answer:

x=− 2/5

Alternative Form

x=−2.5

Step-by-step explanation:

If the mileage is more than or equal to 60 miles Company A will charge no more than Company B.

The inequality is:  50 + 0.50m ≤ 35 + 0.75m.

Given:

m = number of miles driven.

initial fee of Company A = $50

initial fee of Company B = $35

additional fee of Company A = 50 cents = $0.50

additional fee of Company B = 75 cents = $0.75

then the inequality will be,

⇒ 50 + 0.50m ≤ 35 + 0.75m

⇒ 50 - 35 ≤ 0.75m - 0.50m

⇒ 15 ≤ 0.25m

⇒ m ≥ 15 /0.25

⇒ m ≥ 60

Therefore, if the mileage is more than or equal to 60 Company A will charge no more than Company B.

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Option c. The next in series is blue picture with 7 lines.

The series is following the trend, Red, Blue, Red…. So, the next in this series should be blue.

Next is the pattern of picture. Straight line, 45 degree to both lines from center, 45 degree from preceding lines. So, next should be 45 degree from both the preceding lines.

Next is the number of lines. This follows the pattern as 1 line, 3 line, 5 line. From this it's clear that here follows the odd number pattern. So the next should be picture with 7 lines.

Finally we cam conclude that the next in this series is option c, the blue picture with 7 lines.

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The graph for the system of linear equation is attached

An equation is said to be linear if the variables are of power not greater than one. This is to say the power of the variables should be one. It is a norm in math not to write the power when the power is one

For the equation given the the powers of both y and x are all 1. Linear equations also have a straight line graph hence have the equation of straight line represented as

y = mx + c

where:

m is the slope

c is the y intercept

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Simplifying quantity x squared plus 3 x plus 2 end quantity over quantity x will give x+2.

It should be noted that the expression given is illustrated as:

(x² + 3x + 2) / (x + 1)

(x² + x + 2x + 2) / (x + 1)

x(x + 2) 1)2(x+1) / (x + 1)

= (x + 2)(x + 1) / (x + 1)

= x + 2.

Therefore, the correct value is x + 2.

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Answer:

90 miles

Step-by-step explanation:

18/12 = ?/60

12*5=60

18*5=90

90/60

Hope that helps :)

Answer:

-2(5y-3)= -10y-6 should instead be -10y+6 because two negatives multiplied together is a positive integer which is why you have +6 and not -6 so it'll be the second bullet point: he should have subtracted (-2x3) resulting in the expression -10y+6

Answer:

f+245=172

Step-by-step explanation:

Applying the definition of a segment bisector, the length of CD is: 59 units.

A line segment that bisects a line segment is known as a segment bisector. It divides the line segment into two smaller segments that are equal in length to each other.

Since line k bisects BD at point C, therefore, based on the definition of a segment bisector, we have the following equation:

2(BC) = BD

BC = 9x - 13

BD = 118

Substitute the values

2(9x - 13) = 118

18x - 26 = 118

18x = 118 + 26

18x = 144

18x/18 = 144/18

x = 8

CD = BC = 9x - 13

CD = 9x - 13 = 9(8) - 13

CD = 59 units

Therefore, applying the definition of a segment bisector, the length of CD is: 59 units.

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The equation that represents the amount of lemonade left in the pitcher will be.(18.5 - 6.4) = 12.1

From the information given, Maikel has a pitcher filled with 18.5 ounces of lemonade and she pours 6.4 ounces into a glass for herself.

Therefore, the equation that represents the amount of lemonade left in the pitcher will be:

= Total amount - amount poured

= 18.5 - 6.4

= 12.1

Therefore the amount left will be 12.1 ounches

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