The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12. Write an equation in slope-intercept form that could be the second equation in the system.

The value of  [tex]tan^{-1}(0.2)[/tex] = -0.19739 + ... i.e. [tex]tan^{-1} (0.2)= (0.2) - \frac{(0.2)^{3} }{3} +\frac{(0.2)^{5} }{5} -\frac{(0.2)^{7} }{7}+...[/tex]

The power series of  [tex]tan^{-1}(x)[/tex] obtained in example 6 is called the Gregory's series. The Gregory series is an infinite series of fractions or rational numbers

After the Scottish mathematician James Gregory (1638-1675) who had anticipated some of Newton's discoveries we have shown that  the Gregory's series is valid when -1 < x < 1.

But it turns out (although it isn't easy to prove) that it is also valid when:

x = 1 or ≠ 1.

According to Example 6, The radius of convergence of the series for

[tex]1/(1 +x^{2} )[/tex]  is 1, the radius of convergence of this series for [tex]tan^{-1}(x)[/tex] is also 1.

                          [tex]tan^{-1} x = x - \frac{x^{3} }{3} +\frac{x^{5} }{y} -\frac{x^{7} }{y} +....[/tex]  

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Answer:28

Step-by-step explanation:

Trick: just check if it's divisible by both numbers

To have the determinant negative, at least one Eigenvalue has to be negative but the reverse of this statement may or may not be true.

If we add all the diagonal elements of the square matrix, we get the trace of the given matrix.

Eigenvalues is a scalar that associates with a set linear equation described as -

(A - λ I) X = 0

If we take the product of all the eigenvalues of a matrix, we'll get the determinant of the matrix. If we consider a case in which the trace of the matrix is +ve, and its determinant is -ve, then at least one or an odd no. of Eigenvalues must be negative, since their product has to be positive when we solve for the determinant of the matrix

Therefore, to have the determinant negative, at least one Eigenvalue has to be negative but reverse may or may not be true.

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The answer to the problem is: row

The correct answer is option D, extraversion, neuroticism, and psychoticism

Eysenck's theory of personality is based on three logical attributes namely:  

a) introversion vs. extroversion – Extroversion leads to sociable life , while introversion causes need of being alone and limited interactions

b) neuroticism vs. stability – Neuroticism leads to anxiousness and overactive sympathetic nervous system while  stability leads to emotional stability

c) psychoticism vs. socialization. - psychoticism  leads to independent thinking, and hostility. While socialization leads to co-operative and conventional behaviour.  

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The slope of the secant line between x = 3 and x = 8 for the function [tex]f(x) = \sqrt{16x - 47}[/tex] is given as follows:

8/5.

The secant line intersects the function f(x) at the coordinates x = 3 and x = 8.

The numeric value for the function at each of these points is given as follows:

Given two points, the slope of a line is calculated as the change in y divided by the change in x, hence:

m = (9 - 1)/(8 - 3)

m = 8/5.

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Answer:129.7

Step-by-step explanation:

Literally just used a calculator but if you need explanation lmk

The range, based on the solution, is between -2,147,483,648 and 2,147,483,647.

When the sample maximum as well as minimum are subtracted, the range of a collection of data seems to be the difference between the greatest and lowest values. It uses the same units as the data to express itself.

The distance between the greatest and smallest data sets in some kind of a set of numerical data is known as the range. The average of the greatest and smallest data points is the middle.

1 byte has 8 bits,

so 4 bytes have 32 bits.

Each bit can have 2 distinct states, so we have 2³² distinct combinations of bits (in 4 bytes) which correspond to 2³² distinct whole numbers.

Normally,

the range is 0 to 4,294,967,295 but if you want to allow negatives,

the range is -2,147,483,648 to 2,147,483,647

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The solution to the system of equations is x = ( -6/5 ) and y = -6.1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Let the second equation be represented as B

Now , the value of A is

5x + 27 = 21   be equation (1)

Now , the value of B is

-2x + 6y = -34   be equation (2)

On simplifying the equations , we get

Subtracting 27 on both sides of the equation , we get

5x = -6

Divide by 5 on both sides of the equation , we get

x = -6/5

Substitute the value of x in equation (2) , we get

-2 ( -6/5 ) + 6y = -34

12/5 + 6y = -34

Subtracting 12/5 on both sides of the equation , we get

6y = -34 - 2.4

6y = -36.4

Divide by 6 on both sides of the equation , we get

y = -6.067

y = -6.1

Hence , the value of y is -6.1

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Answer:

2. <

Step-by-step explanation:

To compare these two fractions we can first find them a common denominator. A common denominator between 4 and 16 is 16.

To get from 16 from 4 we multiply by 4 so we do the same to the numerator, changing 1/4 to 4/16.

5/16 already has a denominator of 16 so we can leave that one as is.

4/16___5/16

In this form it is obvious that 5/16 is the larger fraction because 5 is larger than 4, meaning that 5/16 is larger than 1/4.

The graph of the given equation is given at end.

A graph is a graphic depiction or diagram that displays data in an organized manner. The points on a graph are typically used to depict the relationships between two or more things.

Determine the slope and y-intercept first, then put the equation in y-intercept (y=mx+b) form to get the equation of a graphed line. The y-to-x change ratio is known as the slope. The two locations you locate on the line should be connected by a sloping triangle.

Common graph types include line graphs, bar graphs, pie charts, scatter plots, and histograms. Graphs are an excellent tool for visualizing data and presenting statistics. An example of displaying numerical data is with a bar graph or chart.

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The numbers that have been omitted from the given series of a number with comparable discrepancies between them are known as missing numbers.

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It is used to perform binary classification with a high level of accuracy.

Support Vector Machines (SVMs) is a powerful algorithm with the potential to perform best in a binary classification problem with a non-linear complex function. SVMs are based on the concept of maximizing the margin between two classes of data points in the feature space. This is done by solving the optimization problem, which is formulated as a quadratic programming problem.

The formulation of the optimization problem for an SVM model is given by:

minimize W,b

subject to

y_i(w^T x_i + b) ≥ 1,  i = 1,2,…,n

where W is the weight vector, b is the bias, x_i is the ith feature vector, and y_i is the ith class label.

The goal of the optimization problem is to find the weight vector W and bias b such that the distance between the two classes is maximized. This is done by minimizing the objective function, which is the sum  of the weight vector. By solving this optimization problem, we can obtain an optimal hyperplane that separates the two classes. SVMs are powerful algorithms capable of dealing with non-linear complex functions, and can thus be used to perform binary classification with a high level of accuracy.

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Answer: A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). Therefore, The scale factor would be 1/2

The polynomial[tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] can be written in the form [tex]a0 + a1(x+1) + a2(x+1)^2 + ... + a16(x+1)^{16} + a17(x+1)^{17}[/tex] where y = x + 1 and a1's are constants.

a polynomial can be written in the form

[tex]a0 + a1x + a2x^2 + a3x^3 + ... + anx^n[/tex]

where a0, a1, a2, ..., an are constants (also known as coefficients) and x is the variable.

In this case, we are given a polynomial in the form [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] and we want to express it in the form [tex]a0 + a1y + a2y^2 + ... + a17y^{17}[/tex], where y = x + 1 and a1's are constants.

By substituting y = x + 1 into the polynomial, we get:

[tex]1 - (x + 1) + (x + 1)^2 - (x + 1)^3 + ... + (x + 1)^{16} - (x + 1)^{17}[/tex]

Each term in this polynomial is a function of y, which is in turn a function of x.

We can then match the coefficients a0, a1, a2, ..., a17 with the corresponding powers of y in the polynomial, i.e, a0 = 1, a1 = -1, a2 = -1, a3 = 0, ..., a16 = -1, a17 = -1, and we get the polynomial

It's important to note that the value of a1's are constants, meaning that they are not dependent on the variable x.

Did you mean: The polynomial [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] may be written in the form [tex]a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}[/tex], where y = x + 1 and a1's are constants?

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The set of inequality that most closely resembles the graph below is called [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.

At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.

Therefore the correct answer is option B ) [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .

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The surface area of a rectangular prism is calculated by adding up the area of all its faces. To calculate the surface area of a rectangular prism, you can use the formula: 2(lw + lh + wh) where l represents the length, w represents the width and h represents the height.

In this case, the rectangular prism measures 7" x 7" x 4", so the surface area can be calculated as: 2(7" x 7" + 7" x 4" + 4" x 7") = 2(49" + 28" + 28") = 2(105") = 210 square inches.

It is important to note that the surface area is a measure of the total area of all the faces of a three-dimensional object, and it is always a positive value. Also, it is measured in squared units, in this case square inches, since all the measurements provided are in inches.

I hope this helps :)

Answer:

210 square

Step-by-step explanation:

just because

Convenience sampling represents the sub-population of the sample strategies.

Convenience sampling is defined as a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand and is a type of sampling that is most useful for pilot testing.

Convenience sampling can be used by almost anyone and has been around for generations. One of the reasons that it is most often used is due to the numerous advantages it provides

Expedited data collection, Ease of research, Ready availability, Cost-effectiveness.

Bias, Power is the disadvantages of convenience sampling.

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When the area in the first quadrant bordered by x=0, y=1, x=y4, and y=10 is rotated about the line y=10, the solid's volume is 11π/3

We using,

V = π ∫|(f(x) - d) 2 - (g (x) - d) 2|dx Integrating from a to b

For this case, a = 0, b = 1, g(x) = 1, f(x) = x1/4

Simplifying the equation,

V = π∫|(x1/4 - 10) 2 - (1 - 10) 2dx = π∫|x1/2 - 20x1/4 + 100 - 81|dx

= π[(2/3) x 3/2 - 20(4/5) x 5/4 + 19x] evaluated from at 1 and 0

= π|(2/3 -16 +19) = 11π/3

The complete question is?

find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10

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Answer:

9

Step-by-step explanation:

72/9 =8

by the same ratio

56/8 = 7

so 3x-20 = 7

so x = 27/3 = 9

An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.

Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:

a = distance from center to vertex = |1 - (-4)|/2 = 2.5

b = distance from center to focus = |1 - (-2)|/2 = 1.5

The equation of the ellipse is:

(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1

which can also be written as:

(x-2)^2/6.25 + (y-1)^2/2.25 = 1

This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

The linear functions for each situation are given as follows:

The interval of hours for which Company A is cheaper than Company B is given as follows:

x > 5.

The linear functions are modeled in slope-intercept format, as follows:

y = mx + b.

In which:

Hence the functions are defined as follows:

Company A will be cheaper when:

45x + 250 < 55x + 200

10x > 50

x > 5.

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A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

A week can be any period of time with 7 days; it is not required to be from Monday through Sunday. Example: The days of Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and Monday all add up to a week.

T stands for Tuesday in the alphabetical list of days of the week. W stands for Wednesday. R stands for Thursday. F is for Friday. Saturday is denoted by the letter S.

You're correct about yesterday, today, and tomorrow.

The word "short" is a five-letter phrase that becomes "shorter" when we add the two letters "e,r."

A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.

The complete question is?

A week has how many ts?

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a) The rank of B can be determined by looking at the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the rank of B is 3.

b) The determinant of BTB can be found by multiplying the eigenvalues of B together. Since the eigenvalues are 0, 1, and 2, the determinant of BTB is 0.

c) The eigenvalues of BTB can be found by taking the square of the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the eigenvalues of BTB are 0, 1, and 4.

d) More information is needed to find the eigenvalues of (B?+1)-!. We need to know the components of B in order to solve this equation.

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The difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

The third option is correct.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

Percentage of Dogs getting their teeth cleaned = 48% = pD

Percentage of Cats getting their teeth cleaned = 35% = pC

Number of Dogs selected = nD = 25

Number of Cats selected = nc = 32

As the sample sizes are large enough, we can apply Central Limit Theorem

According to Central Limit Theorem for proportions –

pD-hat ~ Normal(pD, {pD*(1-pD)}/nD)

Thus, pD-hat ~ Normal(0.48, 0.009984)

Similarly,

pC-hat ~ Normal(pC, {pC*(1-pC)}/nC)

Thus, pC-hat ~ Normal(0.35, 0.0071094)

Now if X ~ N(E(X), Var(X)) and Y ~ N(E(Y), Var(Y))

then X -Y ~ N(E(X)-E(Y), Var(X)-Var(Y)) (If X and Y are Independent)

Thus,

pD-hat - pC-hat ~ Normal(0.48-0.35, 0.009984 – 0.0071094)

pD-hat - pC-hat ~ Normal(0.13, 0.0028746)

Thus, Standard Deviation of pD-hat - pC-hat = (0.0028746^0.5) = 0.0536 that is 0.054 approximately

Hence, the difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

Third Option is correct.

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Answer:

[tex]\frac{-29}{72}[/tex]

Step-by-step explanation:

use a calculator

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC.

Column 1:

1. Given three points A, B and C, draw lines AB and AC.

2. A bisector of angle BAC is the perpendicular bisector of segment AC.

3. The perpendicular bisector of segment AC intersects line AB at the circumcenter of triangle ABC.

Column 2:

1. Given three points A, B and C, draw lines AB and BC.

2. A bisector of angle ABC is the perpendicular bisector of segment BC.

3. The perpendicular bisector of segment BC intersects line AB at the circumcenter of triangle ABC.

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC. Therefore, it is enough to work on two edges to find the circumcenter.

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By using Triangles ABC and ADC given in image, Ladders will cross at 10/3 m above the ground.

What are triangles?

Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorized into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorized into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now,

As shown in image  that the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.

∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the image.

This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.

This means:

AE/ED=AB/DC=5m/10m=1/2

Therefore AE=1/3AD

This means E is 1/3 of the way up from the floor to D, so is at a height of 10/3m=3 1/3m

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Weight of the 13 male eleventh graders is 157.23  pounds. Median is the number in the middle, ranked from least to greatest.

Median weight = 148+140+159+141+151+156+173+167+160+159+146+174+170

                                              = 2044/13

                                                 = 157.23

The value that separates the upper half of a population, a data sample, or a probability distribution from the lower half is known as the median. It could be referred to as "the middle" value for a data set. The value in the middle of a data set is called the median. This means that 50% of the data points have values that are smaller than or equal to the median, and 50% of the data points have values that are higher than or equal to the median. First, you count the number of data points (n) and arrange them in ascending order for a small data set.

The middle value in a set of data is called the median. First, arrange the data in ascending order from smallest to largest. Divide the total number of observations by two to get the midpoint value. Round that number up if there are an odd number of observations, and the value in that position is the median. Take the average of the values found above and below that position if the number of observations is even.

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