Write a symbolic equation for the location of the center of mass of the three beads relative to the center bead, in terms of the variables given in the problem statement.

Control variables are the type of variable that does not change during an experiment, and serves as a comparison point for all data points.

Control variables are also called constant variables or control variables.

A control variable in an experiment is a variable that is held constant or controlled by the researcher.

A control variable is a variable or item that the researcher wants to keep constant throughout the study so as not to affect the results.

A typical study design measures the influence of an independent variable on the dependent variable. In order for this to be done properly, it is important to control another external or standardized variable. Experimentation is not as simple as changing factors and recording results. In practice, any study has many different factors that can affect its results. A control variable is a way to keep some of these factors constant so that comparisons are unbiased and transparent.

In many experiments, even slight variations in some factors can lead to inaccurate or skewed results. Voxco's Experimental Research Toolkit aims to give researchers greater control over variables to help them achieve the results they want.

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The function are Linear that would best model Monica's and Shanna's total savings.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip.

Here, Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.

Hence, The function for Monica is,

⇒ y = 20 + 14x

Where, x is number of weeks and y is total cost.

And, For Shanna's;

The equation is find as;

Two points from table are (0, 0) and (1, 18)

Hence, The equation is,

⇒ y - 0 = (18 - 0) / (1 - 0) (x - 0)

⇒ y = 18x

Thus, Both function for best model Monica's and Shanna's total savings is Linear function.

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Answer:

C

Step-by-step explanation:

If they both ran a mile its the same thing I think

Answer:

Below

Step-by-step explanation:

Due to the triangle side length rule, these two sides added together must be greater than the third side

so the third side could be     11   10   9      

         8 -7-6-5-4-3-2-1   will not work because 2 + these sidelengths do not sum to greater than  the third side 10

Answer:

90%

Step-by-step explanation:

Do 18 divided by 20 you get 0.9 which equals 90% since the 9 is in the tens place.

The slope-intercept form of the line is y = - 2x - 5.

What is the slope of a line?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the Δy and Δx coordinates, respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx.

Given that the slope of the line is -2.

The line passes through the point (2,-9).

The equation of line that passes through (x₁, y₁)  with slope m is

y - y₁ = m (x - x₁).

y - (-9) = -2(x -2)

y +9 = -2x + 4

y = -2x - 5

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the students that like music also like dance is 30%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

40% of the students like music

12% of the students like music and dance.

p(A)=0.4

p(A∩B)=.12

p(A|B)= p(A∩B)/p(A)

=0.4/0.12= 0.3

Hence the students that like music also like dance is 30%.

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If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

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The size of a matrix is ​​its dimension,

AB and BA are of size 4 x 4 and 2 x 2 respectively

Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4

Matrix:

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .

Product of Matrix:

Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.

A column of B whenever a product of different sizes is such that it is defined.  The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,

Product AB:

The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.

Matrix A has 4 rows and Matrix B has 4 columns.

Therefore, the dimension of the matrix AB is 4 x 4.

Product BA:

The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.

Matrix B has 2 rows and Matrix A has 2 columns.

Therefore the dimension of the matrix BA is 2 x 2.

Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.

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The values of x in the cyclic quadrilateral are 6.67 and 25 and the angle

m∠ ACB is 115°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle.

1)

Let's solve to find the value of x

Using proportions;

12/8 = 10 / x

x = 20 / 3

x = 6.67

2) To find x;

(4x + 15)° + (6x + 3)° + 92° = 360°

Sum of angles in a circle is 360°

4x + 15 + 6x + 3 + 92 = 360

10x + 110 = 360

10x = 250

x = 25

To find the value of m ∠ACB in the quadrilateral, we have to evaluate the value of x in the expression  = 4x + 15

m∠ ACB = 4(25) + 15

m ∠ ACB = 115°

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We have -2 from the values in the provided solution set, which is the necessary value.

what is solution set?

A solution set is a group of values in mathematics that satisfy a specified set of equations or inequalities. A constrained optimization problem's viable zone is its solution set of constraints.

Given: - 5x - 15 > 10 + 20x

Let's eliminate the variable x in order to solve the inequality.

5 times both sides,

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtracting 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Dividing both sides by - 25

-1 > x

x < - 1

We have -2 from the values in the provided solution set, which is the necessary value.

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Answer:

B

Step-by-step explanation:

Answer:

32, 16, 8, 4, 2, 1

Step-by-step explanation:

32, 16, 8, 4, 2, 1

Rule: Divide by 2 the previous number

Two or more figures are said to be similar if and only if there are common properties of the sides and/or angles of the figures. The height of the tree is 8.85 meters.

Similar shapes have some common properties with respect to either their length of sides or measures of the internal angles. The relationship between similar sides can be expressed as a form of ration. But similarity of two or more shapes does not mean that the shapes are congruent.

In the given question, the construction gives similar triangles. Let the height of the tree be represented by h. Thus by similar properties of the sides of the triangles, we have;

[tex]\frac{1.65}{h}[/tex] = [tex]\frac{5.25}{28.15}[/tex]

h = [tex]\frac{1.65*28.15}{5.25}[/tex]  

= 8.8471

h = 8.85 meters

Thus, the height of the tree is 8.85 meters.

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The shortest length possible in the given question is 4.0×[tex]10^{-10}[/tex] cm .

Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.

Most people interpret length to mean an object's longest dimension. Nevertheless, depending on the object's position, this is not always the case.

There are several terms for the length of a fixed object, including height, which is also known as vertical length or vertical extent, and width, breadth, or depth. When a base exists from which vertical measurements can be taken, height is used.

Nanometer(nm)- In the International System of Units (SI), a nanometer (American spelling) is a unit of length that is equal to 1000 picometres and one billionth (short scale) of a meter (0.000000001 m).

now , for find the shortest length we can covert all the given units into centimeter,

1 pm = [tex](10)^{-10}[/tex] cm

1 nm = [tex](10)^{-7}[/tex] cm

1 m =  100 cm

we have , 400 pm = 4× [tex](10)^{-8}[/tex] cm

                4.0 nm  =  4 × [tex](10)^{-7}[/tex] cm

      4.0 x [tex](10)^{-4}[/tex]m = 4 × [tex](10)^{-2}[/tex] cm

and   4.0 x [tex](10)^{-10}[/tex] cm

hence , clearly it is shown that shortest length is 4.0 x [tex](10)^{-10}[/tex] cm .

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For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}. Then the range will be 15 – 2 = 13.

In the given question, we have to find an example of range.

As we know that;

The group of all possible dependent values that a function or relation can produce from its domain values is known as its range. It consists of every potential output.

The difference between both the highest and lowest numbers in a collection or set is known as the range.

For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}

The largest number of the given set is 15.

The smallest number of the given set is 2.

Then the range will be 15 – 2 = 13.

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The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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The probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we

Let K(n) be the probability that Keiko gets n heads, and let E(n) be the probability that Ephriam gets n heads.

K(0) = 1/2

K(1) =1/2

K(2) = 0 (Keiko only has one penny!)

E(0) = 1/2 ×1/2 = 1/4

E(1) =  1/2 ×1/2 +  1/2 ×1/2 = 1/2  (because Ephraim can get HT or TH)

E(2) =  1/2 ×1/2 = 1/4

The probability that Keiko gets 0 heads and Ephriam gets 0 heads is K(0)×E(0). Similarly for 1 head and 2 heads.

We get

P = K(0)× E(0) + K(1)×E(1) + K(2)× E(2)

P = 1/2 ×1/4 + 1/2 ×1/2 +0

P = 3/8

Hence, the probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

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1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Synonym for the word split is given by many words like tear, to break apart,  bisect or divide it into parts and so.

Explanation:

Synonym of the given word split is given by:

Many words represents the synonym of the word split.

Therefore, the synonym of the given word split is given by cleave, tear, divide it into two equal parts.

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D. x=12 and y=-8

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given:

[tex]x+y=4\\2x+3y=0[/tex]

from first equation,

[tex]x=4-y[/tex]

substituting this value x in another equation,

[tex]2(4-y)+3y=0\\8-2y+3y=0\\y=-8[/tex]

putting this value of y in  [tex]x=4-y[/tex]

[tex]x=4-(-8)\\x=12[/tex]

hence D is the correct option.

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If $13.31 in three fourth of the cost then the cost of the present is $17.747   .

In the question ,

it is given that ,

the amount of money that mother gave to buy the present is = $13.31 ,

the part of cost that the amount covered is = three fourth ,

that means the fraction is 3/4 = 13.31

So , the cost of the present will be = (13.31*4)/3

Simplifying further ,

we get ,

= 53.24/3

Simplifying further ,

we get ,

= 17.746666

rounding off ,

we get,

≈ 17.747

Therefore , the cost of the present is $17.747  .

The given question is incomplete , the complete question is

Your mother gave you $13.31 with which to buy a present. This covered 3 fourth of the cost. How much did the present cost ?

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∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180

If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Given,

∠1 and ∠2 form a linear pair

m∠2 + m∠3 = 180

Statements                     Reasons

∠1 and ∠2                            Linear pair

∠1 and ∠3                             Linear pair theorem

m∠2 and m∠3                     Given

∠3 and ∠2                           Definition of supplementary angle

∠1 ≅ ∠3                               AAA postulate

∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180

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Equation which is used to find the distance between the given points A and B for the given θ = 28° is equal to AB = x cos28°.

Diagram is attached.

As given in the question,

Diagram is attached.

Given angle θ = 28°

Hypotenuse = x

Two points A and B is on the base

Base - length = AB

In the given triangle,

Equation represents the distance between two points is:

cosθ = base / hypotenuse

⇒ cos 28° = AB / x

⇒ AB = x cos 28°

Therefore, the equation used to represent the distance between two point A and B is equal to AB = x cos28°.

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When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split. Split infinitive might occasionally help to clarify a sentence's meaning.

In the given question we have to explain, when we allow a split infinitive and why.

When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split.

A split infinitive might occasionally help to clarify a sentence's meaning. It is not apparent if the requesting was done softly or whether the leaving should be done quietly in the sentences "I requested her gently to leave" or "I asked her to leave quietly."

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Answer:

Step-by-step explanation:

10% of $520 is $52, so that's what Oliver usually saves each week.

This week he earned 10% more, which is $52. $520 + $52 = $572

10% of $572 is $57.20

His pay minus his living expenses is $572 - 57.20

He has $514.80 to spend

Since 10% of $520 is $52 and that's what he usually saves, it looks like he just went with that instead of adding the $52 to the $520 and then deducting 10%

People who are looking for a job are unemployed that is the term used  by the bureau of labor statistics which classified people who would like to work but have given up .

Step to Step explanation:

Therefore, the people who would like to work but given up who are looking for a job are unemployed classified by bureau of labor statistics.

The complete question is:

The bureau of labor statistics classifies people who would like to work but have given up looking for a job as:______.

a. Unemployed

b. A discouraged worker

c. Not in the labor force

d. Employed

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The effort you put in while ascending the stairs is equal to the sum of the force you exerted (your weight) and the elevation you moved.

Which is: Work (in joules) is equal to your weight in newtons divided by the stairs' height in meters.

Your Body Weight It goes without saying that moving a heavy object up a flight of stairs takes more strength than moving a light object. However, you still need to push your body weight against gravity even if you don't carry anything. Therefore, the more weight you have, the more power you need to climb the stairs.

Student 1 would have a power of 467 W, while Student 2 would have a power of 433 W. The fourth option—student 1 would have a power of 467 W, while student 2 would have a power of 433 W—is the correct one.

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The system of inequalities that represents the possible dimensions of the pen is given as follows:

The graph of the system is given by the image given at the end of the answer.

The first step in building the system of inequalities is identifying the variables, which are given as follows:

The length of the fence should be at least 60 ft, hence:

x ≥ 60.

The distance around should be no more than 260 ft, hence, considering the perimeter of the fence:

2x + 2y ≤ 260

x + y ≤ 130.

The dimensions cannot be negative, hence another restriction needed is:

y > 0.

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The slope of the points (3, -5) and (-2, 4) is -9/5.

Slope in general term means that the elevation or the steepness of any curve. We use slope in order to find the equation of the line between two points. The formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as

m = (y₂ - y₁)/(x₂ - x₁)

where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates for the same y coordinates.

We have  (x₁, y₁) = (3, -5) and (x₂, y₂) = (-2, 4)

So, the slope will be

m = (4 + 5)/(-2 -3)

m = 9/(-5)

m = -9/5 which is the required slope.

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Complete Question:

What is the slope given the points (3, -5) and (-2, 4)?