Ningun número complejo es igual a su conjunto. Verdadero o falso

Answer:

D.

Step-by-step explanation:

this seems to be the line of best fit as it is centered in the data.

hope this helps!!

Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

The solution to the system of differential equations is x(t) = -\(3e^{(31t)\) and z(t) = -\(3e^{(31t\)).

To solve the given system of differential equations, we'll begin by finding the eigenvalues and eigenvectors of the coefficient matrix.

The coefficient matrix is A = [[-22, 54], [-9, 23]]. To find the eigenvalues λ, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

det(A - λI) = [[-22 - λ, 54], [-9, 23 - λ]]

=> (-22 - λ)(23 - λ) - (54)(-9) = 0

=> λ^2 - λ(23 + 22) + (22)(23) - (54)(-9) = 0

=> λ^2 - 45λ + 162 = 0

Solving this quadratic equation, we find the eigenvalues:

λ = (-(-45) ± √((-45)^2 - 4(1)(162))) / (2(1))

λ = (45 ± √(2025 - 648)) / 2

λ = (45 ± √1377) / 2

The eigenvalues are λ₁ = (45 + √1377) / 2 and λ₂ = (45 - √1377) / 2.

Next, we'll find the corresponding eigenvectors. For each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector.

For λ₁ = (45 + √1377) / 2:

(A - λ₁I)v₁ = 0

=> [[-22 - (45 + √1377) / 2, 54], [-9, 23 - (45 + √1377) / 2]]v₁ = 0

Solving this system of equations, we find the eigenvector v₁.

Similarly, for λ₂ = (45 - √1377) / 2, we solve (A - λ₂I)v₂ = 0 to find the eigenvector v₂.

The general solution of the system is x(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂, where c₁ and c₂ are constants.

Using the initial condition x(0) = -3, we can substitute t = 0 into the general solution and solve for the constants c₁ and c₂.

Finally, substituting the values of c₁ and c₂ into the general solution, we obtain the particular solution for x(t).

Since z(t) = x(t), the solution for z(t) is the same as x(t).

Therefore, the solution to the system of differential equations is x(t) = \(-3e^{(31t)\) and z(t) = -\(3e^{(31t)\).

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Answer:

-15

Step-by-step explanation:

a = 3 and b = -6.

- 3a + b

Substitute for a and b

adding negatives is subtracting

-3(3) - 6

Multiply

-9 - 6

add

-15

Answer:

There are 45 pepperoni on 3 large pizzas

Step-by-step explanation:

Here, we want to use proportional relationship to solve this;

75 pepperoni to 5 large pizzas

x pepperoni to 3 large pizzas

75 * 3 = x * 5

x = (75 * 3)/5

x = 15 * 3 = 45

Answer:

3.12

Step-by-step explanation:

Answer:

The Answer is 2

EXPLANATION:

y(x)=2x+3

y(x+Δx)=2(x+Δx)+3

=2x+2Δx+3

Δy=y(x+Δx)−y(x)

=(2x+2Δx+3)−(2x+3)

=2Δx

⇒Δy=2Δx,  Δy/Δx =2

The rate of change in the equation of a line in slope-intercept form

y = 2x + 3 is 2.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, An equation of a line y = 2x + 3.

This is in slope-intercept y = mx + b, where 'm' is the slope.

Therefore, The rate of change in y = 2x + 3 is 2.

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Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Coordinate axes - Ox and Oy. Let this perpendicular intersects AB at the point H. We will also draw a parallel line for Ox that is going through the point A. Let this line intersects CH at the point D. We also will take a point N(3;9). It will lie on the line AD (because the vector AN has coordinates {1; 0}, that means that it is collinear to the position vector that lines on Ox).

We will now find the angle α between AN and AB. For this we will find scalar product of the vectors AN and AB: vector AN has coordinates {1; 0}, and the vector AB has coordinates {6; -5}.

The scalar product of two vectors with coordinates {x1; y1} and {y1; y2} equals to x1 * x2 + y1 * y2. In this case, it equals to 6 * 1 + -5 * 0 = 6.

Also, it equals to the product of the lengthes of those vectors on the cos of angle between thise vectors. In this case, the length on AN equals to 1, the length of AB equals to √(6² + 5²) = √61.

So we can get that cosα * √61 = 6; cosα = 6/√61. Let β be the angle ADH. Because ADH is the right triangle, we get that cosα = sinβ, so sinβ = 6/√61; we know that β is acute, because it is the angle of the right triangle AHD, so cosβ > 0. We can find cosβ through the Pythagoren trigonometric identity. It tells us that cosβ = 5/√61, so tanβ = sinβ/cosβ = 6/5. But β is the interior alternate angle for the pair of parallel lines AD and Ox, so this is the angle between CD and Ox.

Reminder: for the line y = kx + b, k equals to the tan of the angle between this line and Ox.

So we have got that k = 6/5, and y = 6/5 * x + b. But we know that C lies on y, so we can substitute its coordinates in this equality:

-2 = 6/5 * -3 + b.

b = 18/5 - 2 = 8/5 = 1.6

k = 6/5 = 1.2

y = 1.2x + 1.6 - this is the answer.

Answer:

26

Step-by-step explanation:

(5 * 7) - 9

35 - 9

26

Hope that helps

In a time series design, a researcher collects data on a dependent variable (DV) at multiple time points before and after the implementation of a treatment. If the researcher notes that every time sampled individuals are observed on the DV, the average score increases, it may be tempting to attribute this variation to the treatment.

However, caution should be exercised when making such conclusions. While the observed trend in the DV may be associated with the treatment, it's essential to consider alternative explanations, such as maturation, history, or regression to the mean. Maturation refers to the natural developmental processes that occur in participants over time, which might contribute to the observed changes. History refers to external events that could impact the DV, unrelated to the treatment. Regression to the mean occurs when extreme scores naturally become closer to the average over time, which might be mistaken as a treatment effect.

To confidently attribute variation in the DV to the treatment, the researcher should consider using a control group and a comparison group design. This allows for the comparison of changes in the DV between those who received the treatment and those who did not, reducing the likelihood of confounding variables.

In summary, although the increasing average scores in a time series design may suggest a relationship between the treatment and the DV, the researcher should be cautious when attributing this variation solely to the treatment. Other factors and potential confounding variables must be considered before making any definitive conclusions.

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A presentation aid which is a pictorial representation of statistical data is called a Graph. Graph is defined as a statistical diagram or chart which is used to represent statistical data in an easy-to-understand format.

Graphs are very effective in helping people understand large quantities of complex data.Graphs can be used to represent different kinds of data such as line graphs, bar graphs, pie charts, scatter graphs, and more. Line graphs are used to show how a variable changes over time, bar graphs are used to compare different quantities, pie charts are used to show the proportion of different parts of a whole, and scatter graphs are used to show how two variables are related to each other.Graphs have a number of benefits over tables when it comes to representing data.

For one thing, they are often easier to read and understand than tables. They are also more visually appealing, which makes them more likely to grab people's attention. Finally, they can be used to show trends and relationships in data that would be difficult to see in a table.

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The variance of the mean length of the steel rods in a bundle of 10 is 0.196 cm².

The distribution of the mean lengths of the steel rods in a bundle of 10 can be approximated by a normal distribution.

The mean length of a single steel rod is given as 154.4 cm, and the standard deviation is 1.4 cm. When we bundle 10 rods together, the total length of the bundle is the sum of the lengths of the individual rods. Since the mean is a linear operator, the mean length of the bundle is simply the sum of the mean lengths of the individual rods, which is 10 times the mean of a single rod, or 10 * 154.4 = 1544 cm.

To calculate the variance of the mean length of the steel rods in the bundle, we need to consider the variance of the individual rods. Since the rods are bundled together, we assume that they are independent and identically distributed (i.i.d.).

The variance of the sum of independent random variables is equal to the sum of the variances of the individual random variables. Since we have 10 identical rods, the variance of the sum is 10 times the variance of a single rod. The variance of a single rod is the square of the standard deviation, which is (1.4 cm)² = 1.96 cm². Therefore, the variance of the sum of the lengths of the 10 rods is 10 * 1.96 = 19.6 cm².

To find the variance of the mean length of the steel rods in the bundle, we divide the variance of the sum by the number of rods in the bundle squared. In this case, it is 19.6 cm² divided by 10², which is 19.6 cm² divided by 100, resulting in 0.196 cm².

Therefore, the variance of the mean length of the steel rods in a bundle of 10 is 0.196 cm².

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Given:

Perimeter of a regular pentagon = 10 cm

The pentagon is dilated by a scale factor = \(\dfrac{3}{2}\).

To find:

The perimeter of the new pentagon.

Solution:

If a figure is dilated by a scale factor k, then

Perimeter of new figure = k × perimeter of original figure

The scale factor is \(\dfrac{3}{2}\) and the perimeter of a regular pentagon is 10 cm. So, the perimeter of a new pentagon is:

\(\text{Perimeter of new pentagon}=\dfrac{3}{2}\times 10\)

\(\text{Perimeter of new pentagon}=3\times 5\)

\(\text{Perimeter of new pentagon}=15\)

Therefore, the perimeter of the new pentagon is 15 cm.

Answer: \(x=1\)

Step-by-step explanation:

\(2^x-4=4^x-6\) is the equation that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that \(x=1\).

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

\(2^x-4\)

Step 2: Substitute x for the numerical value we found.

\(2^1-4\)

Step 3: Find the square of \(2^1\), which is itself, 2.

\(2-4\)

Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.

\(-2\)

The right side of the equal sign:

Step 1: Write the equation down:

\(4^x-6\)

Step 2: Substitute x for the numerical value we found.

\(4^1-6\)

Step 3: Find the square of \(4^1\), which is itself, 4.

\(4-6\)

Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.

\(-2\)

We know that \(x=1\) because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.

\(-2=-2\)

Let the score she needs be x.

\(\frac{79+82+74+59+96+2x}{7}=80 \\ \\ 79+82+74+59+96+2x=560 \\ \\ 2x=170 \\ \\ \boxed{x=85}\)

To calculate the debt-equity ratio, we need to divide the total debt by the owners' equity.

The equation for the debt-equity ratio is:

Debt-equity ratio = Total debt / Owners' equity

Given the balance sheet information for 2013 and 2014:

2013:

Total debt = Long-term debt = $271,700

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $132,481 = $332,481

Debt-equity ratio (2013) = $271,700 / $332,481

2014:

Total debt = Long-term debt = $285,300

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $171,358 = $371,358

Debt-equity ratio (2014) = $285,300 / $371,358

Equity Multiplier:

The equity multiplier is a measure of how much of a company's assets are financed through debt. It is calculated by dividing total assets by owners' equity. The equation for the equity multiplier is:

Equity multiplier = Total assets / Owners' equity

2013:

Total assets = $917,617

Owners' equity = $332,481

Equity multiplier (2013) = $917,617 / $332,481

2014:

Total assets = $983,646

Owners' equity = $371,358

Equity multiplier (2014) = $983,646 / $371,358

Total Debt Ratio:

The total debt ratio is a measure of the proportion of a company's assets that are financed through debt. It is calculated by dividing total debt by total assets. The equation for the total debt ratio is:

Total debt ratio = Total debt / Total assets

2013:

Total debt = Long-term debt = $271,700

Total assets = $917,617

Total debt ratio (2013) = $271,700 / $917,617

2014:

Total debt = Long-term debt = $285,300

Total assets = $983,646

Total debt ratio (2014) = $285,300 / $983,646

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Answer:

16 - x = -2

16 + 2 = x

x = 18

hope it helps!

Answer:

A point (a, b) rotated around a point (x, y) 180 degrees will transform to point (-(a - x) + x, -(b - y) + y). A point (a, b) rotated around the origin 270 degrees will transform to point (b - y + x, -(a - x) + y).

Step-by-step explanation:

4567olur

give up I'm a special station

Answer:

wdym? like the app remind?

Answer:

you have to download the remind app

Answer:

x = 18

Step-by-step explanation:

sum of interior angles of a polygon is determined by the formula

(n - 2) · 180° where 'n' is the number of sides the polygon has

there are 5 sides in this problem so the number of degrees is 3 · 180 = 540°

we can get the sum of all 5 angles and set it equal to 540

3x + 23 + 9x - 6 + 7x - 4 + 90 + 95 = 540

19x + 13 + 185 = 540

19x + 198 = 540

19x = 342

x = 342/19 = 18

The Simplified value of the "algebraic-expression" (12x³y² - 18xy)/6xy is 2x²y - 3.

An "Algebraic-Expression" represents a combination of numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division, that represents a mathematical relationship or rule.

To simplify the expression, (12x³y² - 18xy)/6xy,  we factor out a common factor of "6xy" from the numerator;

We get,

⇒ (12x³y² - 18xy)/6xy = 6xy(2x²y - 3)/6xy,

The 6xy in the numerator and denominator cancel out,

We get,

⇒ 2x²y - 3

Therefore, the simplified expression is 2x²y - 3.

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The given question is incomplete, the complete question is

Simplify and evaluate the given algebraic expression

(12x³y² - 18xy)/6xy.

Answer:

1. 2/25

2. 4/15

Step-by-step explanation:

1. P(Y∩X)

Since  P(X) =2/3 , P(Y) =2/5 , and P(X|Y) =1/5, this is a conditional probability.

So  P(Y∩X) = P(Y)P(X|Y) = 2/5 × 1/5 = 2/25

2. P(Y)· P(X)

P(Y)· P(X) = 2/3 × 2/5 = 4/15

Answer:

A. 35 million

B. $1519 increase

$7719 year end

Step-by-step explanation:

growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Answer:

Below.

Step-by-step explanation:

tan < XYZ = opposite/adjacent

= 8/20  = 0.4.

XYZ = 21.8 degrees to 3 s f.

The missing frequency in the given table is 24.

What is frequency?

To find the missing frequency, we need to use the information given in the histogram and the frequency table.

We can see from the histogram that the missing class interval is 26-28.

The total frequency for all class intervals is the sum of the frequencies in the table:

110 + 36 + 180 + f = 326 + f

We also know that the total frequency is the number of phones recorded by the manufacturer, so we can assume that the total frequency is a whole number.

Since the sum of the frequencies in the table is 326, the missing frequency must be:

f = total frequency - sum of the other frequencies

f = 350 - 326

f = 24

Therefore, the missing frequency is 24.

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12 is the least common denominator between 3/4 and 7/12.

The least common denominator (LCD) of two or more fractions is the smallest number that can be divided by the denominators of each of the fractions without leaving a remainder.

The smallest number among all the common multiples of the denominators is the least common denominator when two or more fractions are provided.

Finding the least common multiple (LCM) of the denominators 4 and 12 will allow you to get the least common denominator of 3/4 and 7/12.

12 is the least frequent multiple of 4 and 12. Therefore, 12 is the least common denominator between 3/4 and 7/12.

Finding the denominators' multiples is another way to locate it. 43 = 12 is the least common multiple and the least common denominator, respectively.

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x ≈ 0.625.

To solve the exponential equation 3 + 4^(4x-3) + 6 = 11, we first need to isolate the exponential term.

Subtracting 3 and 6 from both sides, we get:

4^(4x-3) = 2

To solve for x, we can take the natural logarithm of both sides:

ln(4^(4x-3)) = ln(2)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left side:

(4x-3)ln(4) = ln(2)

Dividing both sides by ln(4), we get:

4x-3 = ln(2)/ln(4)

Simplifying the right side using a calculator, we get:

4x-3 ≈ -0.5

Adding 3 to both sides, we get:

4x ≈ 2.5

Dividing by 4, we get:

x ≈ 0.625

Therefore, the exact solution with natural logarithms is:

x = (ln(2)/ln(4) + 3)/4

And the approximate solution correct to three decimal places is:

x ≈ 0.625

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