Need help with question #9

Thus, the derivative of the given function is found as: [tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex].

The derivative of a function f(x), also known as f'(x) or df/dx, is a measure of how quickly a function changes.  A shift in the value of x is depicted in the image by the symbol x.

Hence, df/dx is a single phrase and should not be mistaken for a fraction. It is also a clue that x is the independent variable because it can be interpreted as the derivative of a function having respect to x.

Given function:

[tex]f(x ) = \sqrt{9 + x^{2} } .dx[/tex]

Differentiating the function with respect to x, using the chain rule.

[tex]f'(x) = (9 + x^{2} )^{1/2 - 1} .(0 + 2x)[/tex]

[tex]f'(x) = (9 + x^{2} )^{-1/2} .(2x)[/tex]

[tex]f'(x) = (2x) /(9 + x^{2} )^{1/2}[/tex]

[tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex]

Thus, the derivative of the given function is found as: [tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex].

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The prοperties that bοth rectangles and parallelοgrams share are 2 pairs οf parallel sides & 2 pairs οf sides with equal length.

Thus, οptiοn C & D is cοrrect.

Prοperties οf bοth rectangles and parallelοgrams:  

Rectangles and parallelοgrams are bοth types οf quadrilaterals, which are pοlygοns with fοur sides.

Certain prοperties are unique tο each type οf quadrilateral, as well as sοme that they share in cοmmοn. Here are the prοperties that rectangles and parallelοgrams share:

1. Bοth rectangles and parallelοgrams have parallel οppοsite sides.

2. Bοth rectangles and parallelοgrams have cοngruent οppοsite sides  

3. Bοth rectangles and parallelοgrams have cοngruent, οppοsite angles  

4. Bοth rectangles and parallelοgrams have cοnsecutive angles that are supplementary  

Therefοre,

The prοperties that bοth rectangles and parallelοgrams share are

C. 2 pairs οf parallel sides

D. 2 pairs οf sides with equal length

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The probability of selecting at random, without replacement, two blue marbles is 5/12.

What is Probability ?

Probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty and provide a basis for making informed decisions in various fields such as science, engineering, economics, and finance.

To solve the problem, we first need to find the total number of marbles in the urn. Since there are 3 red marbles and 6 blue marbles, there are a total of 9 marbles.

The probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of 9 total marbles.

Since we are selecting without replacement, the number of marbles left in the urn changes after each draw. After the first blue marble is selected, there are only 5 blue marbles left out of a total of 8 marbles. Therefore, the probability of selecting a second blue marble is 5/8.

To find the probability of selecting two blue marbles, we multiply the probability of the first draw (6/9) by the probability of the second draw (5/8):

(6/9) x (5/8) = 30/72 = 5/12

Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.

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Surface area and of rectangular prism are  502ft² and 390ft³ respectively.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces, where each face is perpendicular to the adjacent faces. It is also known as a rectangular cuboid.

The rectangular prism has three pairs of congruent faces, which are opposite to each other, and each pair of faces has the same dimensions. The dimensions of a rectangular prism are typically measured by its length, width, and height, and these dimensions can be different from each other.

The formula for the volume of a rectangular prism is:

Volume = length x width x height

The formula for the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

Sides of rectangular prism are 2ft,15ft and 13ft.

Surface area of rectangular prism=2(lb+bh+lh)

=2(2×15+15×13+13× 2)

=502ft²

Volume of rectangular prism

=lbh

=2×15×13

390ft³

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The complete question is;

Image is attached below.

The geometric solid associated with each situation are

a. a stack of 100 copies of the same book

A stack of 100 copies of the same book can be visualized as a rectangular prism because each book has the same dimensions.

b. a stack of 100 tires, all with the 19 same radius no

A stack of 100 tires, all with the same radius, can be visualized as a cylinder because each tire has a circular shape with the same radius, and when they are stacked on top of each other, they form a cylinder.

c. a stack of 100 stop signs

A stack of 100 stop signs can be visualized as a regular polygonal prism because each stop sign has the shape of a regular octagon, and when they are stacked on top of each other, they form a regular polygonal prism with a base of an octagon.

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The measures of the angles and arcs of the circle are;

The sum of the digits in the shaded = 1  + 3 + 7 + 2 + 3 + 4 + 6 = 26

26 - 14 = 12

Using the decoder wheel, we get; FVMMO

An arc is a portion or part of the circumference of the circle.

The arc angles from the diagrams indicates;

1. mPR = 90 + (90 - 67) = 113

2. mQST = mQR + mRST

mQST = 23 + 180 = 203

3. 8·x - 15 + (3·x + 8) = 180 (Linear pair angles)

11·x - 7 = 180

11·x = 187

x = 187/11 = 17

x = 17

4. LM = 3·x + 8

Therefore; LM = 3 × 17 + 8 = 59

LM = 59

5. m∠DAC = 156/2 = 78

6. mBC = 180 - 156 = 24

7. m∠ADB = 43

mAB = 43 × 2 = 86

mABD = 180 + 86 = 266

8. 2 × (7·x -3) = 17·x - 30

14·x - 6 = 17·x - 30

17·x - 14·x = 3·x = 30 - 6 = 24

x = 24/3 = 8

x = 8

9. m∠YZX = 7·x -3

m∠YZX = 7 × 8 - 3 = 53

m∠YZX = 53

10. m∠WXZ = 62/2 = 31

The angle formed by the intersection of WY and XZ is therefore;

mWZY = 180 - (2 × 53) + 63 = 137

mWXY = 180 - (2 × 31) + (17 × 8 - 30) = 224

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Answer:

Let's start by using the formula for finding the percentage: percentage = (part/whole) x 100 In this case, we know the percentage (2%) and the part (88 problems), but we don't know the whole (total number of problems on the test). So we can write: 2% = (88/whole) x 100 Simplifying, we get: 0.02 = 88/whole Multiplying both sides by the whole, we get: whole x 0.02 = 88 Dividing both sides by 0.02, we get: whole = 4400 Therefore, there were 4400 problems on the English test.

Answer:90 problems

Step-by-step explanation:

To solve the problem, we can use the formula:% correct = (number of correct answers / total number of questions) * 100%Since the student received a grade of 2%, we can write:2% = (number of correct answers / total number of questions) * 100%Simplifying this equation, we get:total number of questions = number of correct answers / 0.02We know that the student missed 88 problems, so the number of correct answers is:number of correct answers = total number of questions - 88Substituting this into the equation above, we get:total number of questions = (total number of questions - 88) / 0.02Simplifying this equation, we get:total number of questions = 50 * (total number of questions - 88)Solving for the total number of questions, we get:total number of questions = 90Therefore, there were 90 problems on the English test

Remark

I take it the semicircles cover the full width of the paper.

So the radius is [tex]24\div2 = 12 \ \text{cm}[/tex]

Since there are two of them, the area = a full circle.

Step One

Find the area of the rectangle before the cuts were made.

[tex]\text{Area = L} \times \text{W}[/tex]

[tex]\text{L = 30}[/tex]

[tex]\text{W = 24}[/tex]

[tex]\text{Area} = 30 \times 24 = 720 \ \text{cm}^2[/tex]

Step Two

Find the area of the circle cut outs.

[tex]\text{r} = 12[/tex]

[tex]\text{Area} = \pi \times \text{r}^2[/tex]

[tex]\text{Area} = 3.14 \times 12^2[/tex]

[tex]\text{Area} = 3.14 \times 144[/tex]

[tex]\text{Area} = 452.16 \ \text{cm}^2[/tex]

Step Three

Find the total area left

[tex]\text{Total Area Left = rectangle - circle}[/tex]

[tex]\text{Total Area Left} = 720 - 452.16[/tex]

[tex]\text{Total Area left} = 267.84 \ \text{cm}^2[/tex]   Answer

Answer:

what is it

Step-by-step explanation:

The answer is A. 3>m.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

First, let's simplify the left side of the inequality:

-2 > (m-12)/(-9) - 3

-2 > -(m-12)/9 - 3 (dividing both sides by -1 and flipping the inequality)

-2 + 3 > -(m-12)/9

1 > -(m-12)/9

9 > -(m-12)

-9 < m-12

-9 + 12 < m

3 < m

So the solution is: m > 3.

Therefore, the answer is A. 3>m.

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Answer: 456,976,000

Step-by-step explanation:  Assuming that repetition is allowed

Answer:

The least possible degree is 5.

Step-by-step explanation:

this an extreme case of 2 lines emanating from the same point crossing through a circle. but the same principles apply.

the angle at J is 1/2 of the difference of the outer and the inner arc angles of the intersected arcs.

the inner arc angle of the HK arc is exactly the angle at G = 138°.

that means the outer arc angle of the arc HK is the remainder of the whole circle arc angle (360°) to the inner arc angle HK

360 - 138 = 222°

so,

angle J = 1/2 × (222 - 138) = 84/2 = 42°

A rotation can be  transformation which turns a figure. It changes its position

what is rotation ?

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, and is used to describe the movement of objects in space.

In the given question,

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, A rotation can be  transformation which  turns a figure. It changes its position

when their is rotations it turns around its axis and their will be change in its position

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The phase shift for the given equation is π/8.

In the study of waveforms and the transmission of signals, the phrase "phase shift" is frequently used. It speaks of the movement caused by two impulses as they spread over time. A signal processing device like an electronic amplifier or a low- or high-pass filter that applies specific operations to the signal and causes the output signal phase to change from its initial input signal phase can be the culprit behind this displacement.

The general form of a sinusoidal function is y = A sin(Bx - C) + D, where A is the amplitude, B is the frequency (and also related to the period T by T = 2π/B), C is the phase shift, and D is the vertical shift.

Comparing this form to the given equation y = -3sin(4x - π/2) - 1, we can see that the amplitude A is 3, the frequency B is 4, and the vertical shift D is -1. To find the phase shift C, we need to rearrange the equation to isolate the argument of the sine function:

y + 1 = -3sin(4x - π/2)

Dividing both sides by -3, we get:

(sin(4x - π/2)) / (-1/3) = -(y + 1) / 3

Recall that sin(θ - π/2) = cos(θ), so we can rewrite the argument of the sine function as:

4x - π/2 = 4(x - π/8)

Now, the equation becomes:

(sin[4(x - π/8)]) / (-1/3) = -(y + 1) / 3

Comparing this to the standard form y = A sin(Bx - C) + D, we can see that B = 4 and A/B = -1/3, so A = -4/3. Thus, we have:

y = (-4/3) sin[4(x - π/8)] - 1

The phase shift is the horizontal shift of the graph, which is given by C = π/8. Therefore, the phase shift for the given equation is π/8.

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The number of pairs that should be sold to earn an after-tax profit of GH¢12,000 is approximately 25769, which is closest to option B, 30000 units.

What is profit?

Gain is the best definition of profit, particularly when it is attained by raising the price of goods so that customer spending exceeds producer expenses and a sizable return on investment is left. Profit is the amount of money that remains after costs and expenditures have been paid.

First, let's calculate the total revenue from selling 25,000 pairs of shoes:

Total revenue = selling price per unit * number of units sold

Total revenue = GH¢40 * 25,000

Total revenue = GH¢1,000,000

Next, let's calculate the total cost of producing and selling 25,000 pairs of shoes:

Total cost = (purchase cost per unit + fixed cost per unit) * number of units sold

Total cost = (GH¢25 + GH¢2 + (GH¢100000 + GH¢40000 + GH¢100000)/25000) * 25000

Total cost = (GH¢25 + GH¢2 + GH¢16) * 25000

Total cost = GH¢43 * 25000

Total cost = GH¢1,075,000

Now, we need to calculate the before-tax profit:

Before-tax profit = Total revenue - Total cost

Before-tax profit = GH¢1,000,000 - GH¢1,075,000

Before-tax profit = -GH¢75,000

Since the before-tax profit is negative, the company is making a loss. To make an after-tax profit of GH¢12,000, we need to add this amount to the before-tax profit and then adjust for the tax rate:

Before-tax profit + After-tax profit = Target profit

-GH¢75,000 + GH¢12,000 = Target profit

Target profit = -GH¢63,000

Adjusted Target profit = Target profit / (1 - tax rate)

Adjusted Target profit = -GH¢63,000 / (1 - 0.4)

Adjusted Target profit = -GH¢105,000

To make an adjusted target profit of GH¢105,000, we can use the following formula to calculate the number of units that need to be sold:

Number of units sold = (Fixed cost + Target profit) / (Selling price per unit - Purchase cost per unit - Selling commission per unit)

Number of units sold = (GH¢100,000 + GH¢40000 + GH¢100,000 - GH¢105,000) / (GH¢40 - GH¢25 - GH¢2)

Number of units sold = GH¢335,000 / GH¢13

Number of units sold ≈ 25769.23

Therefore, the number of pairs that should be sold to earn an after-tax profit of GH¢12,000 is approximately 25769, which is closest to option B, 30000 units.

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a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

What is the association test?

An association test is a statistical test used to determine whether there is a relationship or association between two or more variables. The type of association test used depends on the nature of the variables being examined.

a) The association test, in this case, is a chi-square test of independence, which is used to determine whether there is a significant association between two categorical variables.

b) The conditions for the chi-square inference procedure are:

Independence: The sample is a simple random sample, so independence is satisfied.

Sample size: The expected count for each cell should be at least 5, which is satisfied for all cells in the table.

c) The degrees of freedom for the chi-square test are (r - 1) x (c - 1), where r is the number of rows and c is the number of columns in the table.

In this case, the degrees of freedom are (3-1) x (4-1) = 6. The p-value associated with a chi-square test statistic of 18.930 and 6 degrees of freedom is less than 0.01.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

However, it may not be appropriate to generalize to other populations without further research to ensure the characteristics of the population are similar to those of the sample.

Hence,  a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

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Answer:

bro give some choices

Step-by-step explanation:

They are different because they are inverse expressions.

what is prime factor ?

A positive integer factor that is also a prime number is known as a prime factor in mathematics. Otherwise put, a prime factor is a prime number that may be multiplied by additional prime factors to produce the original integer. For instance, since 24 can be written as the product of the numbers 2, 2, 2, and 3, the prime factors of 24 are 2, 2, 2, and 3. There is only one set of prime factors for every positive integer since a number's prime factors are always unique. Finding a number's prime factors is a technique called prime factorization. It is a fundamental idea in number theory and has lots of real-world uses, including in computer science and cryptography.

given

Due to the way division operates, the quotient of three by one-fifth differs from the quotient of one-fifth by three. You get a greater quotient when you divide a larger number by a smaller number, and a smaller quotient when you divide a smaller number by a larger number.

To demonstrate these two scenarios, consider the following two tales:

The Quotient of Three Divided by One-Fifth is the first story.

There once were three pals named Chris, Ben, and Alex. They made the decision to split the five equally sized slices of pizza. Due to his extreme hunger, Alex chose to grab three of the slices for himself, leaving Ben and Chris with just two pieces each.

We write the expressions first mathematically:

three divided by one-fifth:

(3) / (1/5)

one-fifth divided by three:

(1/5) / (3)

We now use the double c method to find the results:

(3) / (1/5) = (3 * 5) / (1 * 1) = 15/1 = 15

(1/5) / (3) = (1 * 1) / (5 * 3) = 1/15 = 0.066666667

The difference between the two is:

15-0.066666667 = 14.93333333

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Answer:

There were 60 audience members at the seminar.

Step-by-step explanation:

Let's assume that the total number of audience members at the seminar is "x".

From the given information, we know that:

2/5 of the audience were students, so the number of students was (2/5)x

3/10 of the audience were retirees, so the number of retirees was (3/10)x

The rest were professionals, so the number of professionals was x - (2/5)x - (3/10)x = (1/10)x

We also know that there were 18 more students than professionals, so:

(2/5)x - (1/10)x = 18

Multiplying both sides by 10, we get:

4x - x = 180

Simplifying, we get:

3x = 180

x = 60

Therefore, there were 60 audience members at the seminar.

The area of the given polygon ABCDE divided into three triangles ABC, ACD and AED is 79.5 sq. units.

What is a polygon?

A polygon is a closed figure or shape formed using line segments. Smallest polygon is a triangle containing three sides. On the basis of its sides polygons are classified as triangle, quadrilateral, pentagon, hexagon, heptagon, octagon etc. The sum of interior angles of a polygon is found by the formula (n-2)180 , where 'n' refers to the number of sides in a polygon. The sum of exterior angles of any polygon is always equal to 360°. The area of any irregular or regular polygon may be evaluated by dividing the given shape into standard shapes like square, rectangle, triangle etc and then adding up the areas of all shapes.

Here the given pentagon ABCDE is further divided into three triangles,

ABC, ACD and AED

Also given the areas of triangles:

area of ΔABC = 23.85 sq. units

area of ΔACD = 29.40 sq. units

area of ΔAED = 26.25 sq. units

∴The area of given figure= Sum of the areas of ΔABC, ΔACD and ΔAED

                                         =area of ΔABC+area of ΔACD+area of ΔAED

                                         =23.85+ 29.40+26.25

                                         =79.5 sq. units.

The area of the given figure is 79.5 sq. units

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Refer to the attached figure below for complete question.

The answer to the given question about inscribed angles intercepting an arc is option A. 100

As we know that the measure of an inscribed angle is half the measure of the intercepted arc, we can use the formula:

Measure of inscribed angle = 1/2 × Measure of intercepted arc

So, if the intercepted arc has a measure of 200 degrees, then the measure of the inscribed angle is:

Measure of inscribed angle = 1/2 × 200 degrees

= 100 degrees

Therefore, the answer is A. 100 degrees. In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if an arc has a measure of 200, then an inscribed angle that intercepts that arc will have a measure of half of 200, which is 100 degrees.

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The probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails is 1÷6 or approximately 0.1667.

What is Probability ?

Probability is a mathematical concept that measures the likelihood of an event or set of events occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability can be determined using mathematical formulas or by analyzing empirical data.

The probability of choosing a green marble at random from a bag of 5 green and 10 white marbles is:

P(green marble) = number of green marbles ÷ total number of marbles

P(green marble) = 5 ÷ 15

P(green marble) = 1÷3

The probability of flipping a coin and getting tails is:

P(tails) = 1÷2

The probability of choosing a green marble at random from the bag and then flipping a coin and getting tails is the product of the two probabilities:

P(green marble and tails) = P(green marble) x P(tails)

P(green marble and tails) = (1÷3) x (1÷2)

P(green marble and tails) = 1÷6

Therefore, the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails is 1÷6 or approximately 0.1667.

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The height of the cliff diver after 1.25 seconds is 35 feet.

A mathematical notion known as a function connects an input to an output. It resembles a mechanism with an input and an output, where the input and output are somehow connected. For instance, if we have a function f(x) = x + 1, we can enter 2 and get 3 as the result.

To find the height of the cliff diver after 1.25 seconds, we can plug in t = 1.25 into the height function H(t) = -16t^2 + 32t + 20 and evaluate it.

H(1.25) = -16(1.25)² + 32(1.25) + 20

Let's do the calculations:

H(1.25) = -16(1.5625) + 40 + 20

H(1.25) = -25 + 40 + 20

H(1.25) = 35

So, the height of the cliff diver after 1.25 seconds is 35 feet. This assumes that the height is measured above a reference point (e.g., ground level).

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(a) This test is appropriate because it assesses whether there is a relationship between two categorical variables (fingerprint patterns and blood types) in the sample.

(b) Yes the conditions of the chi-square test are met.

(c)  The degrees of freedom and p-value of the test are 6 and 0.0043 respectively.

(d) The population to which the researchers can generalize their results depends on the sampling method used in the study.

(a) The test for an association in this case is a chi-square test of independence.
(b) The conditions for the chi-square test of independence are:
1. A random sample: The sample is stated to be a simple random sample.
2. Independence: The sample size should be less than 10% of the population, which seems to be met as the region has a large student population.
3. Expected cell counts: Each expected count should be at least 5.

All expected counts in the table are above 5.
All conditions for the chi-square test of independence are met.
(c) To find the degrees of freedom for the chi-square test, use the formula (r - 1)(c - 1), where r is the number of rows and c is the number of columns.

In this case, there are 3 rows (fingerprint patterns) and 4 columns (blood types), so the degrees of freedom are (3 - 1)(4 - 1) = 2 x 3 = 6.

The chi-square test statistic is approximately 18.930, and with 6 degrees of freedom, you can look up the p-value in a chi-square distribution table or use statistical software.

The p-value is approximately 0.0043.
(d) Given the sampling design in this study, it is reasonable for the researchers to generalize their results to the male student population from the specific region where the sample was taken.

This is because the sample was a simple random sample, which helps ensure that the sample is representative of the population.

However, it is important to note that generalizing the results to a wider population or to different regions or groups may not be valid.

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Answer:

sp= 8000.00.

loss percent= 20%

loss amount = 20% of sp

= 20÷100 × 8000

= 1600

now,

costprice = sp + loss amount

= 8000 + 1600

= 9600

Step-by-step explanation:

The answer is 262.5%

5/8=5÷8=0.625

2 5/8=2.625

2.625=262.5%

262.5%  and   2.625

5/8=5÷8=0.625 then 2 5/8=2.625 then we get 2.625=262.5%

All we do here Is divide then round It to the nearest 1, 10, or 100.

Division Is separate or be separated into parts, and noun of division Is a wide divergence between two groups, typically producing tension or hostility.

Adjusting the digits (up or down) to make rough calculations easier.