12x + 10= 54- 10x
help?

\(Given datasets: (1,7), (2,5), (3,2)We have to find the least squares regression line.\)

is the step-by-step solution: Step 1: Represent the given dataset on a graph to check if there is a relationship between x and y variables, as shown below: {drawing not supported}

From the above graph, we can conclude that there is a negative linear relationship between the variables x and y.

\(Step 2: Calculate the slope of the line by using the following formula: Slope formula = (n∑XY-∑X∑Y) / (n∑X²-(∑X)²)\)

Here, n = number of observations = First variable = Second variable using the above formula, we get:\(Slope = [(3*9)-(6*5)] / [(3*14)-(6²)]Slope = -3/2\)

Step 3: Calculate the y-intercept of the line by using the following formula:y = a + bxWhere, y is the mean of y values is the mean of x values is the y-intercept is the slope of the line using the given formula, \(we get: 7= a + (-3/2) × 2a=10y = 10 - (3/2)x\)

Here, the y-intercept is 10. Therefore, the least squares regression line is\(:y = 10 - (3/2)x\)

Hence, the required solution is obtained.

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The equation of the least squares regression line is:

y = -2.5x + 9.67 (rounded to two decimal places)

To find the least squares regression line, we need to determine the equation of a line that best fits the given data points. The equation of a line is generally represented as y = mx + b, where m is the slope and b is the y-intercept.

Let's calculate the least squares regression line using the given data points (1, 7), (2, 5), and (3, 2):

Step 1: Calculate the mean values of x and y.

x-bar = (1 + 2 + 3) / 3 = 2

y-bar = (7 + 5 + 2) / 3 = 4.67 (rounded to two decimal places)

Step 2: Calculate the differences between each data point and the mean values.

For (1, 7):

x1 - x-bar = 1 - 2 = -1

y1 - y-bar = 7 - 4.67 = 2.33

For (2, 5):

x2 - x-bar = 2 - 2 = 0

y2 - y-bar = 5 - 4.67 = 0.33

For (3, 2):

x3 - x-bar = 3 - 2 = 1

y3 - y-bar = 2 - 4.67 = -2.67

Step 3: Calculate the sum of the products of the differences.

Σ[(x - x-bar) * (y - y-bar)] = (-1 * 2.33) + (0 * 0.33) + (1 * -2.67) = -2.33 - 2.67 = -5

Step 4: Calculate the sum of the squared differences of x.

Σ[(x - x-bar)^2] = (-1)^2 + 0^2 + 1^2 = 1 + 0 + 1 = 2

Step 5: Calculate the slope (m) of the least squares regression line.

m = Σ[(x - x-bar) * (y - y-bar)] / Σ[(x - x-bar)^2] = -5 / 2 = -2.5

Step 6: Calculate the y-intercept (b) of the least squares regression line.

b = y-bar - m * x-bar = 4.67 - (-2.5 * 2) = 4.67 + 5 = 9.67 (rounded to two decimal places)

Therefore, the equation of the least squares regression line is:

y = -2.5x + 9.67 (rounded to two decimal places)

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

12

Step-by-step explanation:

Mark brainliest pls

Answer:

C. 2/3 x 2/3

Step-by-step explanation:

When given a set of values in an inverse variation, it is possible to calculate the value of y for any given x-value. In the example question, when x = 6, y = 4.

Value is the worth of something, whether tangible or intangible, that is determined by its utility or importance, and is relative to the individual or society. Value can be intrinsic or extrinsic, and can be subjective or objective. Intrinsic value is something that is inherent to the object and cannot be taken away. Extrinsic value is based on the opinion of the individual or society and can change over time. Value can also be seen as a measure of the worth of something, and the importance of something to an individual or society.

Inversely proportional relationships can be represented by the equation y = k/x, where k is a constant. In this case, we can substitute the known values of x and y into the equation to solve for k.

y = 12, when x = 2

12 = k/2

k = 24

Now that we have the value of k, we can plug it into the equation and solve for y when x = 6.

y = 24/6

y = 4

Therefore, when x = 6, y = 4.

In conclusion, when given a set of values in an inverse variation, it is possible to calculate the value of y for any given x-value. In the example question, when x = 6, y = 4.

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Complete questions as follows-
If y varies inversely as x, and y = 12 as x = 2, how do you find y for the x-value of 6?

Answer:

She can make nine bracelets! Hope this helps :)

Answer:

9

Step-by-step explanation:

3    |    16

6    |    32

9    |    48

Answer:

false

Step-by-step explanation:

when you move COUNTERclockwise, you go in the opposite direction that a clock goes, so you would go to the left instead of the right

The acceleration a in reference frame Σ is equal to the acceleration a' in reference frame Σ' via the Galilean transformation.

To derive the transformation for acceleration, we differentiate the above equations with respect to time:

dx'/dt = dx/dt - u

dt'/dt = 1

The left-hand side of the first equation represents the velocity in frame Σ', while the right-hand side represents the velocity in frame Σ. Since the velocity is the derivative of the position, we can rewrite the equation as:

v' = v - u

where v and v' are the velocities in frames Σ and Σ' respectively.

Now, let's consider the acceleration. The acceleration is the derivative of the velocity with respect to time. Taking the derivative of the equation v' = v - u with respect to time, we have:

a' = a

where a and a' are the accelerations in frames Σ and Σ' respectively. This means that the acceleration remains unchanged when we transform from one reference frame to another using the Galilean transformation.

In conclusion, the acceleration a as described by the coordinates in frame Σ is equal to the acceleration a' as described by the new set of coordinates in frame Σ' via the Galilean transformation.

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Answer:

slope is -2/3

Step-by-step explanation:

y = mx+b

m = slope

b = y-intercept

given: y = -2/3x

in this case we don't have a b so make it an automatic 0

now we have y = -2/3x +0

slope is m, so our slope is -2/3

Answer:

Step-by-step explanation:we using all values of x in f(x) which is greater than -2 and all the answes we get up to infinity is our range,lets start put x=-1

f(x)=2\3(-1)+1=1/3

put x=0 f(x)=1 so range is [1/3,infinity)

Answer:

The Drama Club scan sell all 100 student tickets at max if they reach their goal of $800.

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

E2020

The expression represents the total number of points the player scored in the game:  2x+ 3x + 9

The correct option is A.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-dependent principles.

When something is expressed, the methods of expression change it in the process of communication. extracted from the Cambridge English Corpus. There were two conceivable orthographic expressions for this awareness.

Let x=number of 2-point attempts.

Free throws made equal 9 points.

A point is scored when x 2-point attempts are made.

After the break,

Number of 3-pointers divided by first-half 2-point attempts equals x

Point scored in x 3-point attempts equals 3 times.

Consequently, the player's overall point total during the contest is provided by : 2x+ 3x + 9

Consequently, the formula that denotes the total amount of points each player scored during the game is as follows: 2x+ 3x + 9

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I understand that the question you are looking for is:

In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?

A. 2x + 3x + 9

B. 2x + 3 + 9

C. 2x + 3x + 9x

D. 2 + 3x + 9

The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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The area of the parallelogram is 78ft².

The area of a parallelogram can be calculated with the following formula:

A= b*h

Where "b" is the length of any base of the parallelogram and "h" is the height.

In this case, you can identify the values of b and h from the question given, which:

b = 6ft

h= 13ft

Then, knowing those values, you can substitute them into the formula shown above, as below:

A= b*h= 6*13

Finally, you must evaluate in order to find the area of the given parallelogram.

A= 78ft²

Thus, the area of the parallelogram is 78ft².

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Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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Answer:

0.01949025487

Step-by-step explanation:

Hey there!

Formula:

SUM of all numbers / TOTAL numbers you have in your data plot

EQUATION:

(10 + 10 + 13 + 14 + 16 + 19 + 23) / 7

10 + 10 + 13 + 14 + 16 + 19 + 23
= 20 + 13 + 14 + 16 + 19 + 23

= 33 + 14 + 16 + 19 + 23

= 47 + 16 + 19 + 23

= 63 + 19 + 23

= 82 + 23

= 105

105 / 7

= 15

So, therefore the answer is: Naeem's Work. Start fraction 10, 10, 13, 14, 16, 19, 23 Over 7 end fraction = StartFraction 105 Over 7 end fraction = 15 (Option A.)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

Subtract 19 from both sides to find the value of t:

\(t=26\)

Answer:

P (Score is not a factor of 6) = 1−31=32

This is my answer

450 / 1000 will give the fraction

450 / 1000 in its simplest form is taken by dividing both with a common factor that is 50

then the ans is

9/20

Answer:

A

Step-by-step explanation:

I’m pretty sure this is the right answer

Answer:

1

Step-by-step explanation:

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

If a scatterplot shows a non-linear relationship between the response and explanatory variable, several options can be considered depending on the purpose of the analysis and the nature of the data.

Here are some possible actions:

Transform the data: One common approach is to transform the data to make the relationship linear. For example, if the relationship appears to be exponential, taking the logarithm of the response variable might make it linear. Similarly, taking the square root, cube root, or inverse of one or both variables might also help.

Use a non-linear model: Another option is to fit a non-linear model that can capture the curvature in the relationship. There are many types of non-linear models, such as quadratic, cubic, exponential, logistic, or spline models. The choice of model depends on the shape of the curve and the underlying theory or hypothesis.

Resample or subset the data: If the non-linear relationship is driven by outliers, influential points, or a subset of the data, it might be helpful to resample or subset the data to remove them. For example, trimming the extreme values, bootstrapping the data, or stratifying the data by a third variable might help.

Explore alternative variables or interactions: If the non-linear relationship is due to an unobserved or omitted variable, it might be useful to explore alternative variables or interactions that could explain the pattern. For example, if the response is sales and the explanatory variable is price, adding a competitor's price or a marketing variable might improve the fit.

Use caution in interpretation: Finally, if the non-linear relationship persists after exploring the above options, it might be necessary to acknowledge the non-linearity and use caution in interpreting the results. Non-linear relationships can be more difficult to interpret and extrapolate, and the statistical inference might be more uncertain or sensitive to assumptions.

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Answer:

46/61 times 100=75.40%

75.40%

Length of sides:

Surface Area:

(perimeter of base)(length) + (base)(height)

(8+10+6)(4)+(8)(6)

(24)(4)+48

96+48

144 ft²

The displacement of the compressor is 628 cubic centimeters. Other factors that affect the performance of a compressor include its operating pressure, flow rate, efficiency, and power consumption.

To find the displacement of the compressor, we need to use the formula:
Displacement = (pi/4) x bore^2 x stroke
Here, the bore is 8 centimeters and the stroke is 10 centimeters. So, substituting these values in the formula, we get:
Displacement = (pi/4) x 8^2 x 10
Displacement = (3.14/4) x 64 x 10
Displacement = 628.32 cubic centimeters

A compressor is a mechanical device that is used to increase the pressure of a gas or air by reducing its volume. It works by compressing the gas or air in a cylinder and then transferring it to a storage tank or other equipment. The displacement of a compressor is a measure of the volume of gas or air that is displaced or compressed during one complete cycle of the compressor. Therefore, the displacement of the compressor is 628 cubic centimeters. This means that during one complete cycle of the compressor, it displaces or compresses 628 cubic centimeters of gas or air. The displacement is an important parameter of a compressor, as it determines its capacity or the amount of gas or air that it can compress in a given time.

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The displacement of the compressor is 160π cubic centimeters.

To find the displacement of the compressor, we first need to understand what displacement means. Displacement is the change in position of an object in a specific direction. In this case, the compressor has a bore of 8 centimeters and a stroke of 10 centimeters. The displacement of the compressor can be calculated as the product of the bore area (πr^2) and the stroke length.

Displacement = π(4^2) * 10 = 16π * 10 = 160π cubic centimeters.

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The function f(x, y ,z) and u(u1, u2, u3) are unit vectors, then;

Duf = ▽f.u = ∂f/∂x u1 + ∂f/∂y u2 + ∂f/∂z u3

The directional derivative is the rate at which any function changes in a fixed direction at a particular point. It is the vector form of any derivative. It characterizes the instantaneous rate of variation of a function.

Since we know that the gradient is defined for the function f(x, y) is as;

▽f = ▽f(x, y) = ∂f/∂xi + ∂f/∂ yj

It can be calculated by assigning the vector operator r to f(x, y) as a scalar function. This vector field is called gradient vector field.

If we have a function f(x, y ,z) and u(u1, u2, u3) are unit vectors, then;

Duf = ▽f.u = ∂f/∂x u1 + ∂f/∂y u2 + ∂f/∂z u3

It is clear that, if we take a dot product of the gradient and the given unit vector, then we get the directional derivative of the function.

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The simplification of the expressions

1. For f(x) = -3x^2 + x - 2

We want to simplify the expression (f(x + h) - f(x)) / h.

Substitute the function into the expression:

(f(x + h) - f(x)) / h = (-3(x + h)^2 + (x + h) - 2 - (-3x^2 + x - 2)) / h

Expand and simplify:

= (-3(x^2 + 2xh + h^2) + x + h - 2 + 3x^2 - x + 2) / h

= (-3x^2 - 6xh - 3h^2 + x + h - 2 + 3x^2 - x + 2) / h

Cancel out like terms:

= (-6xh - 3h^2 + h) / h

Cancel out the common factor of h:

= h(-6x - 3h + 1) / h

Cancel out h

= -6x - 3h + 1

Therefore, the simplified form is -6x - 3h + 1.

2. For f(x) = 5 / (2 - 3x)

We want to simplify the expression (f(x + Δx) - f(x)) / Δx.

Substitute the function into the expression:

(f(x + Δx) - f(x)) / Δx = (5 / (2 - 3(x + Δx)) - 5 / (2 - 3x)) / Δx

Find a common denominator:

= (5(2 - 3x) - 5(2 - 3(x + Δx))) / ((2 - 3x)(2 - 3(x + Δx))) / Δx

Expand and simplify

Combine like terms

= (15Δx) / ((2 - 3x)(2 - 3(x + Δx))) / Δx

Cancel out the common factor of Δx

= 15 / ((2 - 3x)(2 - 3(x + Δx)))

Therefore, the simplified form is 15 / ((2 - 3x)(2 - 3(x + Δx))).

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