what is the best fit line

We can convert the unit kg/m ³ to  g/cm³ by using the formula Kg/m³ = 10⁻³ g/cm³.

We are provided with the unit kg/m ³ that means Kilograms per meter cube.

We have to covert it into g/cm³.

Now, we know, from the standard conversion rates that one kilograms is equal to 1000 grams and one meter cube is roughly equal to 10⁶ centimeter cubes.

So, if we want to do the unit conversion, we should write,

= g/cm³

= 1000/1000000 g/cm³

Kg/m³ = 10⁻³ g/cm³.

Now, the above mentioned relation is our formula for the conversion of the two unit.

So, now we can write that, one kilograms per meter cube is equal to 10⁻³ grams per centimeter cubes.

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The solution of the given problem of probability comes out to be P(not same color) = 236/361.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

There are three cases to consider:

Case 1: both marbles are red

Case 2: both marbles are yellow

Case 3: both marbles are blue

The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):

P(red and red) = (5/19) ×  (5/19) = 25/361

Similarly, the probability of drawing two yellow marbles is:

P(yellow and yellow) = (6/19) × (6/19) = 36/361

And the probability of drawing two blue marbles is:

P(blue and blue) = (8/19) ×  (8/19) = 64/361

So, the probability of drawing two marbles that are the same color is:

P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)

P(same color) = (25/361) + (36/361) + (64/361)

P(same color) = 125/361

d.

There are three cases to consider:

Case 1: one marble is red and one marble is yellow

Case 2: one marble is red and one marble is blue

Case 3: one marble is yellow and one marble is blue

The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):

P(red and yellow) = 2 × (5/19) × (6/19) = 60/361

Similarly, the probability of drawing one red marble and one blue marble is:

P(red and blue) = 2  × (5/19) × (8/19) = 80/361

And the probability of drawing one yellow marble and one blue marble is:

P(yellow and blue) = 2 × (6/19) × (8/19) = 96/361

So, the probability of drawing two marbles that are not the same color is:

P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)

P(not same color) = (60/361) + (80/361) + (96/361)

P(not same color) = 236/361

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Another name for a regression line is Least squares line

Answer:Best-Fit-Line

Step-by-step explanation:

--Or line of best fit

HOP THIS HELPS!!!

The solution set of the system of equations in this problem is defined as follows:

[-3x3 x3 x3]

The system of equations for this problem is defined as follows:

From the third equation, we write x2 as a function of x3, as follows:

4x2 = 4x3

x2 = x3.

Replacing into the first equation, we can write x1 as a function of x3, hence:

3x1+3x2+6x3=0.

3x1 + 3x3 + 6x3=0.

3x1 = -9x3

x1 = -3x3.

Hence the vector solution of the system is given as follows:

[-3x3 x3 x3]

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The two angles in the ratio of 5:18 are 50° and 130° respectively. To determine this, we can use the fact that the sum of the angles in any quadrilateral is 360°.

Therefore,

where x and y are the two angles in the ratio of 5:18.

We can then solve for x and y by setting up the proportion

and then solving for x and y.

This gives us

Therefore, the two angles in the ratio of 5:18 are 50° and 130°.

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To round 0.002391 to 2 significant figures, we need to look at the digits after the first two significant digits (which are 2 and 3 in this case).

The digit in the third decimal place is 2, which is less than 5. Therefore, we leave the second significant digit (3) as it is, and we drop all the digits after that.

So, rounding 0.002391 to 2 significant figures, we get:

0.0024

you need to subtract 2

Answer:

Step-by-step explanation:

4(x + 4) + 2x = 52

4x + 16 + 2x = 52

6x = 52 - 16

6x = 36

x = 36 : 6

x = 6

Answer:

[tex] \sf \: x = 6[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 4(x + 4) + 2x = 52

Then the value of x will be,

→ 4(x + 4) + 2x = 52

→ 4x + 16 + 2x = 52

→ 6x + 16 = 52

→ 6x = 52 - 16

→ 6x = 36

→ x = 36 ÷ 6

→ [ x = 6 ]

Hence, the value of x is 6.

Answer:

Line Segment

Step-by-step explanation:

The desired value is the target or goal for the variable, while the controlled value is the actual or measured value.

The difference between the desired value of a variable and the controlled (actual) value is known as the error or deviation. It addresses the sum by which the actual value varies from the desired value, and is normally utilized as criticism in control frameworks to change the framework yield.

The objective of a control framework is to limit this mistake and bring the actual value as close as conceivable to the desired value. The mistake can be positive (assuming the actual value is more noteworthy than the desired value), negative (in the event that the actual value is not exactly the desired value), or zero (in the event that the actual value equivalents the desired value).

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The child is most likely operating at visualization level of van hiele's. The solution has been obtained by using the Van Hiele model.

What is Van Hiele model?

The van Hiele theory explains how children pick up geometry. It makes the claim that there are five different degrees of geometric thinking: visualisation, analysis, abstraction, formal deduction, and rigour. Every level has a unique lingo and set of symbols. The levels are progressed through "step by step" by the students.

We are given that a child tells that square has 4 sides and 4 angles by seeing the quadrilateral.

From this, we get that the child is operating at the visualization level of van hiele's because by looking at a figure he tells the number of sides and angles.

Hence, the child is most likely operating at visualization level of van hiele's.

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Answer:

The value of x would make the ratio 1:1 is 6.

Step-by-step explanation:

The given ratio is:

Surface Area : Volume = 6x^2 : x^3

To find the value of x that makes this ratio 1:1, we need to set the two parts of the ratio equal to each other and solve for x:

6x^2 = x^3

Divide both sides by x^2 to obtain:

6 = x

Therefore, the value of x that makes the ratio 1:1 is x = 6.

1) Note that it can be concluded that Rishi is not doing well with his budget. The actual overshot the by 5%. See attached Spreadsheet.

2) If the driver who hit Rishi does not have Insurance and neither does Rishi (according to the budget) then Rish will have to save up for a new car because he didn't include the cost of insurance in his budget.

A budget is a financial plan that outlines expected income and expenses for a specific period, typically a month or a year.

It helps individuals and organizations to manage their finances by ensuring that they do not spend more money than they earn, and that they allocate their funds in a way that aligns with their goals and priorities.

A budget is important because it enables people to make informed financial decisions, avoid debt, and save money for future expenses.

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Answer:

[tex]2\pi[/tex] inches

Option B

Step-by-step explanation:

The arc length is proportional to the central angle
If L is the arc length and θ is the central angle in degrees
[tex]L = \dfrac{\theta}{360} \times C[/tex]

where C is the circumference of the circle

Given radius r = 6 inches, C = 2πr = 2π·6 = 12π
θ = 60°

So
[tex]L = \dfrac{60}{360} \times 12\pi\\\\= \dfrac{1}{6} \times 12\pi\\\\= 2\pi\;inches[/tex]

The sum formula for geometric sequence is Sn = a(1 - r^n) / (1 - r)

A unique kind of sequence is a geometric sequence. It is a sequence in which each term aside from the first term and is multiplied by a fixed number to obtain its subsequent term. To obtain the following term in the geometric sequence, one must multiply with a fixed term known as the common ratio, and one need only divide the term by the same common ratio to determine the previous term in the sequence.

There are infinite and finite geometric sequences. The formula for the same is Sn = a(1 - r^n) / (1 - r). Here Sn is the sum of the first n terms of the geometric sequence,  a is the first term of the sequence,  r is the common ratio between consecutive terms in the sequence and n is the number of terms in the sequence

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Therefore , the solution of the given problem of equation comes out to be y can be either 3 +√(6) or 3 -√(6) for FG to be equal to HI.

In arithmetic equations, the similar symbol (=) is used to denote equivalence between two statements. It is demonstrated that utilising mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. The equal sign, for instance, splits the number 12 and even the answer y + 6 = 12 into two separate parts. One can compute how many characters are already present on either end of this symbol. Contradictory symbol meanings are common.

Here,

To find y such that FG = HI, we need to first calculate FG and HI and then set them equal to each other.

The distance formula can be used to calculate the distance between two points:

Distance between F and G:

FG = √(((-4) - (-5))² + ((-4) - (-7))²)

FG = √(1² + 3²)

FG = √(10)

Distance between H and I:

HI = √((y - 3)² + (10 - 8)²)

HI = √((y - 3)² + 4)

Now we set FG equal to HI:

√(10) = √((y - 3)² + 4)

10 = (y - 3)² + 4

6 = (y - 3)²

y - 3 = ±√(6)

y = 3 ±√(6)

Therefore, y can be either 3 +√(6) or 3 -√(6) for FG to be equal to HI.

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Coterminal angles can have different angle measures.

Therefore the answer is True.

Coterminal angles are angles that have the same initial and terminal sides, but may differ in their angle measures. To find a coterminal angle, you can add or subtract a multiple of 360 degrees or 2π radians to the original angle.

For example, an angle of 45 degrees is coterminal with an angle of 405 degrees (45 + 360), as well as an angle of -315 degrees (45 - 360). Similarly, an angle of π/4 radians is coterminal with an angle of 9π/4 radians (π/4 + 2π), as well as an angle of -7π/4 radians (π/4 - 2π). Coterminal angles are useful in trigonometry and calculus when working with periodic functions, as they allow for simplification and generalization of calculations.

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--The question is incomplete, answering to the question below--

"Coterminal angles can have different angle measures. T or F."

The solution is, pyramid's volume is 96 cm^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given information we get,

So we know that the bar edge length is 8 cm (6+2) and the height is 6 cm....

And a pyramid's volume is 1/3 of a prism's volume.

If the base is square and both sides are 6 cm, the area is 36 cm^2.

Then you multiply that area by the height: 288 cm^3.

BUT you have divide that by 3,

because a pyramid's volume is 1/3 of a prism's volume:

288/3= 96 cm^3.

Answer: 96 cm^3

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The mean weight of a randomly chosen vehicle is 3500 pounds.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean.

We are given that the weight of a randomly chosen american passenger car is a uniformly distributed random variable ranging from 1,749 pounds to 4,039 pounds.

Let X= weight of the passenger car

a/q, X is u(1,749, 4,039)

we know that mean= a+b/2

so a=1,749, b=4,039

hence, mean=1,749 +4,039/2

mean=3500 pounds

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107+73 = 180

107-73 = 34

========================================================

Explanation

Rule: Supplementary angles always add to 180 degrees.

This is our system of equations.

[tex]\begin{cases}x+y = 180\\x-y = 34\\\end{cases}[/tex]

Add the equations straight down.

After the y terms go away, we have this new equation: 2x = 214 which solves to x = 107 after dividing both sides by 2.

Then use this x value to find y

x+y = 180

107+y = 180

y = 180-107

y = 73

Or you could say

x-y = 34

107-y = 34

-y = 34-107

-y = -73

y = 73

Either way, we get the same y value each time. This helps confirm the answer.

Another way to confirm the answer is shown in the next section below.

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

Check:

x+y = 180

107+73 = 180

180 = 180 .... confirms the 1st equation

x-y = 34

107-73 = 34

34 = 34 ... the other equation is confirmed.

In short,

Answer:

A 6-sided shape is a hexagon.

The simplest form is (-2 ±√12)/2.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: x = (-4 ±√48)/4

We have to simplify the given term.

x = (-4 ±√48)/4

x =  (-4 ±√12×4)/4

x =(-4 ±2√12)/4

Now, we take 2 as common and get

x = (-2 ±√12)/2

Hence, the simplest form is (-2 ±√12)/2.

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Shae's monthly payment will be approximately $114.63.

First we can use the formula for the present value of an annuity:

P = (r * A) / (1 - (1 + r)^(-n))

where

First, we need to convert the annual percentage rate (APR) to a monthly rate, which is done by dividing it by 12:

r = 13.5% / 12 = 0.01125

Next, we can plug in the values and solve for A:

2400 = (0.01125 * A) / (1 - (1 + 0.01125)^(-24))

Simplifying this equation, we get:

A = (0.01125 * 2400) / (1 - (1 + 0.01125)^(-24)) = 114.63

Therefore, Shae's monthly payment will be approximately $114.63.

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The rate of change of a circle's diameter with respect to its radius is a constant value of 2.

The diameter (d) of a circle is twice the radius (r), so we can write:

d = 2r

To find the rate of change of diameter with respect to radius, we can take the derivative of both sides of this equation with respect to r using the chain rule:

d/dx [d] = d/dx [2r]

d' = 2r'

Here, d' is the derivative of diameter with respect to radius, and r' is the derivative of radius with respect to some independent variable (e.g. time).

Since r' is simply equal to 1 (because the derivative of a variable with respect to itself is always 1), we have:

d' = 2

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The radical form of the exponential expression is given as follows:

[tex]\sqrt[4]{7}[/tex]

Hence the values of a and b are given as follows:

a = 7, b = 4.

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

To obtain the radical form, we have that:

Hence:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

Meaning that the equivalence for this problem is given as follows:

[tex]7^{\frac{1}{4}} = \sqrt[4]{7}[/tex]

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The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

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The procedure to obtain the equation of the graphed line is presented in this answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The standard definition of a linear function is given as follows:

mx - y = -b.

To obtain the intercept b, you must observe the value of y when x = 0, which is the value of y when the graph of the function touches the y-axis.

To obtain the slope, you must take two points, and then calculate the rate of change between the two points.

Suppose that the points are (a,b) and (c,d), then the slope is given as follows:

m = (d - b)/(c - a).

In case the slope is fractional, you should multiply the entire equation by the denominator of the fraction all the coefficients of the standard form of the equation are integers.

The problem is incomplete, hence the general procedure to obtain the equation of the line is presented.

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The conversion of 5kg in pounds is 11.0231 pounds (rounded to four decimal places).

A kilogram is greater than a pound. I know that a kg is greater than a lb because of something called conversion factors.

Put very simply, a conversion factor is a number that can be used to change one set of units to another, by multiplying or dividing it. So when we need to convert 5 kilograms into pounds, we use a conversion factor to get the answer.

The conversion factor for kg to lb is:

1 kg = 2.2046244201838 lb

Now that we know what the conversion factor is, we can easily calculate the conversion of 5 kg to lb by multiplying 2.2046244201838 by the number of kilograms we have, which is 5.

5 x 2.2046244201838 = 11.023122100919 lb

To convert 5kg to pounds, you can use the conversion factor of 2.20462 pounds per kilogram. Multiplying 5kg by this conversion factor gives:5 kg * 2.20462 pounds/kg = 11.0231 pounds.

Therefore, 5kg is equivalent to 11.0231 pounds (rounded to four decimal places).

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In statistics, the chi-square critical value is the threshold value that is used to determine whether the calculated chi-square test statistic is significant or not.

The chi-square critical value is determined based on the significance level (also known as alpha), which is the probability of rejecting the null hypothesis when it is true. The significance level is typically set at 0.05 or 0.01.

The chi-square critical value can be found using a chi-square distribution table or a statistical software program. The critical value is determined based on the degrees of freedom (df), which is the number of categories minus one.

Once the chi-square critical value is determined, it can be compared to the calculated chi-square test statistic to determine whether the test is statistically significant or not. If the calculated chi-square test statistic is larger than the critical value, we can reject the null hypothesis and conclude that there is a significant association between the variables.

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The drop at the end destination of the aqueduct would be 15 meters.

To see why, we can use the formula:

drop = slope * length

where the slope is given as 0.5% (or 0.005 as a decimal) and the length is given as 3000 meters.

So,

drop = 0.005 * 3000 = 15

Therefore, the drop at the end destination of the aqueduct would be 15 meters.