EXERCISE 5: Compute: a/ Ln(-3 – 4i) = ... b/ sinh() ( = 2 c/ (1 - 1)3/4+i = = (explain with a sentence after your calculation)

Answer:

X= -10

Step-by-step explanation:

Answer:

Angle Relationship: Alternate exterior angles

x = -10

Angle measurement: 51 °

Step-by-step explanation:

These angles are located "outside" the two parallel lines but on opposite sides of the transversal, therefore they are alternate exterior angles.

Alternate exterior angles are congruent, therefore the angle must be 51 °

51 = 61 + x

subtract 61 from both sides

x = 10

The cost of materials for the cheapest container is $184.67.

Suppose the width is x and it is given that the length of its base is twice the width, so the length of the base is 2x.

The base area is 2x².

Since the volume is $12m³

The height has to be 12/ 2x² = 6/ x²

The cost of making such a container is.

cost of base = 2x² × 10

= 20x²

The cost of sides =( 2 × 2x 6/x² + 2 × x × 6 / x²) 6

= (24/x + 12/x )6

= 36/x × 6

216/x

The overall cost is hence the sum of the base and the sides = f(x)

= 20x² + 216/x

To get the minimum,

df(x) / dx = 20x² + 216/x = 0

= 40x - 216/x² = 0

x³ = 216/40

= 54/10

= 27/5

x = 3/∛5

= 3/ 1.70

= 1.76

f(x) = 20(1.76)² + 216/ 1.76

= 61.952 + 122.72

= 184.67

Therefore we get the cost of the materials to be $184.67.

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Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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Answer:

use the distance formula to find the diameter of the circle.  From there, you can divide the diameter in half to find the radius of the circle

Step-by-step explanation:

so... the distance formula is...

d = \(\sqrt{(x_{2} - x_1)^{2}+(y_2 - y_1)^{2} }\)

so...you just substitute the values into the equation

d = \(\sqrt{(-4-4)^2 + (-3-3)^2}\)

d = \(\sqrt{64+36}\)

d = 10

so...that means the diameter is 10

to find the radius you do 10/2 because radius is half of the diameter

so the radius is 5

hope that helps...that took so long to write out

Step-by-step explanation:

so, I read here

2/3 x + 3x/x = 4x/2 × (3x + 6)

that is

2/3 x + 3 = 4x/2 × (3x + 6)

2x/3 + 3 = 2x × (3x + 6)

2x + 9 = 6x × (3x + 6)

2x + 9 = 18x² + 36x

18x² + 34x - 9 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 18

b = 34

c = -9

x = (-34 ± sqrt(34² - 4×18×-9))/(2×18) =

= (-34 ± sqrt(1156 + 648))/36 =

= (-34 ± sqrt(1804))/36 =

= (-34 ± sqrt(4×11×41))/36 =

= (-34 ± 2×sqrt(451))/36

x1 = (-34 + 2×sqrt(451))/36 =

= 0.235375588...

x2 = (-34 - 2×sqrt(451))/36 =

= -2.124264477...

Answer:

\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)

Step-by-step explanation:

\(\textsf{Given equation}:\)

\(\dfrac{2}{3}x+\dfrac{3x}{x}=\dfrac{4x}{2}(3x+6)\)

\(\textsf{Cancel the common factor } x \textsf{ in }\dfrac{3x}{x}:\)

\(\implies \dfrac{2}{3}x+3=\dfrac{4x}{2}(3x+6)\)

\(\textsf{Simplify }\dfrac{4x}{2}\textsf{ by dividing the numbers}:\)

\(\implies \dfrac{2}{3}x+3=2x(3x+6)\)

\(\textsf{Apply the distributive law}\quad \:a\left(b+c\right)=ab+ac:\)

\(\implies \dfrac{2}{3}x+3=6x^2+12x\)

\(\textsf{Multiply both sides by 3 to cancel the denominator of }\dfrac{2}{3}:\)

\(\implies \dfrac{2}{3}x\cdot 3+3\cdot 3=6x^2\cdot 3+12x \cdot 3\)

\(\implies 2x+9=18x^2+36x\)

\(\textsf{Switch sides}:\)

\(\implies 18x^2+36x=2x+9\)

\(\textsf{Subtract }2x \textsf{ from both sides}:\)

\(\implies 18x^2+36x-2x=2x+9-2x\)

\(\implies 18x^2+34x=9\)

\(\textsf{Subtract 9 from both sides}:\)

\(\implies 18x^2+34x-9=9-9\)

\(\implies 18x^2+34x-9=0\)

Solve using the Quadratic Formula:

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

Define the variables:

\(\implies a=18, \quad b=34, \quad c=-9\)

Substitute the defined variables into the quadratic formula and solve for x:

\(\implies x=\dfrac{-34 \pm \sqrt{34^2-4(18)(-9)} }{2(18)}\)

\(\implies x=\dfrac{-34 \pm \sqrt{1156+648} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{1804} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{4 \cdot 451} }{36}\)

\(\implies x=\dfrac{-34 \pm \sqrt{4}\sqrt{451} }{36}\)

\(\implies x=\dfrac{-34 \pm 2\sqrt{451} }{36}\)

\(\implies x=\dfrac{-17 \pm \sqrt{451} }{18}\)

Therefore, the solutions to the given equation are:

\(x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}\)

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Answer:

b>6

Step-by-step explanation:

Answer:

Hi there!

Your answer is:

j= -6

Step-by-step explanation:

-2+13j = 10j -20

-10j

3j -2 = -20

+2

3j = -18

/3

j= -6

Hope this helps

Answer:

60

Step-by-step explanation:

hello there!

If you didn't know an exterior angle of a triangle is equal to the sum of its opposite interior angles

to be more specific ∠5=∠4+∠3

we are given ∠5 and ∠4 and we need to find ∠3

So we plug in what we have and solve for ∠3

130 = 70 + ∠3

subtract 70 from each side

130 - 70 = 60

we're left with ∠3 = 60

The solution to the initial value problem is y(t) = [g(t) - g(to)] / a(t).

The given initial value problem can be solved using the method of integrating factors. To find the solution, we start by rearranging the equation as a quadratic polynomial in terms of y'(t): y'(t) - 2ay(t) + a²(t) = g(t). Next, we identify the integrating factor as e^(-2∫a(t)dt), which allows us to rewrite the equation in its integrated form: [e^(-2∫a(t)dt) * y(t)]' = e^(-2∫a(t)dt) * g(t). Integrating both sides of the equation with respect to t yields: e^(-2∫a(t)dt) * y(t) = ∫[e^(-2∫a(t)dt) * g(t)]dt. Applying the initial conditions y(to) = 0 and y'(to) = 0, we can solve for the constant of integration and obtain the solution: y(t) = [g(t) - g(to)] / a(t).

To solve the initial value problem y(t) — 2ay'(t) + a²(t) = g(t), y(to) = 0, y'(to) = 0, we used the method of integrating factors. This method involves identifying an integrating factor that simplifies the equation and allows for integration. By rearranging the equation and integrating both sides, we obtained the solution y(t) = [g(t) - g(to)] / a(t). This expression represents the solution of the initial value problem in terms of the given functions g(t) and a(t), along with the initial conditions. It provides a relationship between the dependent variable y(t) and the independent variable t, incorporating the effects of the functions g(t) and a(t).

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the given functions represent transfer functions of two systems in a control system, and they can be analyzed using various tools in the Laplace domain to determine their behavior and characteristics.

The given functions represent the transfer functions of two systems in a control system. The first transfer function, g(s), has two poles at s=1 and one pole at s=10. The poles at s=1 are repeated twice, indicating that this is a second-order system. The second transfer function, h(s), is a constant function with a value of 1.

To analyze the behavior of these systems, we can use tools such as the Laplace transform, which allows us to convert differential equations into algebraic equations that are easier to solve. The Laplace transform of g(s) can be written as G(s) = 1/(s+1)^2(s+10), and the Laplace transform of h(s) is H(s) = 1.

Once we have the transfer functions in the Laplace domain, we can use them to compute various system parameters such as the frequency response, step response, and stability. For example, the frequency response of a system is given by the magnitude and phase of the transfer function evaluated at different frequencies. The step response of a system is the output of the system when a unit step input is applied, and it can be computed using the inverse Laplace transform.

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A system is shown below where g(s) = 1/(s 1)^2(s 10) and h(s) = 1. Find the closed loop transfer function.

Answer: 194

Step-by-step explanation:

1. Square both sides to get (b+2)=14^2=196

2. Subtract 2 from both sides to get b=194

To find the y-intercept and x-intercept of the line given by the equation 2x - 3y = -6, we need to determine the points where the line intersects the y-axis (y-intercept) and the x-axis (x-intercept).

To find the y-intercept, we set x = 0 in the equation and solve for y. Plugging in x = 0, we have 2(0) - 3y = -6, which simplifies to -3y = -6. Dividing both sides by -3, we get y = 2. Therefore, the y-intercept is the point (0, 2).

To find the x-intercept, we set y = 0 in the equation and solve for x. Plugging in y = 0, we have 2x - 3(0) = -6, which simplifies to 2x = -6. Dividing both sides by 2, we get x = -3. Therefore, the x-intercept is the point (-3, 0).  The y-intercept of the line is (0, 2), and the x-intercept is (-3, 0).

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Stan's average speed for the total trip is 55 miles per hour.

Given,

Stan drove 300 miles in 5 hours 20 minutes

Again, Stan drove 360 miles in 6 hours 40 minutes

To find,

Stan's average speed in miles per hour for the total trip

Solution

We can start the problem by calculating the total distance and the total time for the trip. Then we can use the formula for average speed which is;

Average speed = Total distance / Total time

First, let's calculate the total distance covered by Stan in the entire trip;

Total distance covered = 300 + 360= 660 miles

Now, let's calculate the total time taken by Stan in the entire trip;

Total time taken = 5 hours 20 minutes + 6 hours 40 minutes= 12 hours

Now, let's use the formula for average speed and calculate the average speed for the entire trip;

Average speed = Total distance / Total time= 660 / 12= 55 miles per hour

Therefore, Stan's average speed for the total trip is 55 miles per hour.

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Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

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The only value of k that makes Ax=0 have non-trivial solutions is k=0. Option (C) is the correct answer.

To determine the values of k such that Ax=0 has non-trivial solutions, we need to find the values of k that make the determinant of the matrix A equal to zero.

This is because the determinant of A is equal to the product of its eigenvalues, and a non-trivial solution exists when at least one of these eigenvalues is zero.
Using the formula for the determinant of a 3x3 matrix, we have:
det(A) = 1 x (-20k) - 0 x (-8k) + 4 x (-2)(-2k) = -20k + 16k = -4k
Setting det(A) equal to zero, we get:
-4k = 0
Solving for k, we get:
k = 0
To find the values of k, if any, such that Ax=0 has non-trivial solutions, we need to find the values of k that make the matrix A singular, i.e., that make the determinant of A equal to 0.

If the determinant of A is not 0, then the only solution to Ax=0 is the trivial solution (x=0).

Using the formula for a 3x3 determinant, we have:

det(A) = 1 x  (1 x (-10k) - 4 x (-2k)) - 0 x (0 x (-10k) - 4 x (-2))) + 4 x  (0 x (-2k) - 1 x (-2)))

det(A) = 10k - 8k

det(A) = 2k

So, the determinant of A is equal to 2k.

If 2k = 0, then det(A) = 0 and the matrix A is singular.

This occurs when k = 0.
Therefore, the only value of k that makes Ax = 0 have non-trivial solutions is k=0. Option (C) is the correct answer.

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Answer:

55

Step-by-step explanation:

The total is 2(2x+15) +2x=360.

4x+30+2x=360

6x+30=360

6x=330

x=55

Answer: your answer is B. 55

Step-by-step explanation: I just took the test

To calculate z table online we put Raw Score, Population Mean, Standard Deviation, σ   then calculator give us answer.

A z-table, also called a standard normal table or unit normal table, is a table of standardized values ​​used to determine the probability that a given statistic is below, above, or below the standard normal distribution. A z-score of 0 indicates that the given point is the same as the mean. Therefore, on the graph of the standard normal distribution, z = 0 is the midpoint of the curve. A positive Z value indicates that the point is to the right of the mean, and a negative Z value indicates that the point is to the left of the mean. There are several different types of Z-tables. The values ​​in the table below represent a range from z=0 to a specific z-score.

Z Means table (0 to Z)  

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Answer:

<GHC congruent to <EHD

Step-by-step explanation:

<GHC congruent to <EHD

By vertical angles

:]

Answer:

option 4, linear pairs

Step-by-step explanation:

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180° (known as supplementary angles)

In a course, your instructional materials and links to course activities are found in a Learning Management System (LMS).

The learning management system (LMS) is the platform where you can access all the necessary instructional materials and links to course activities for your course.

An LMS is a software application that provides an online space for instructors and students to interact and engage in educational activities. It serves as a centralized hub where course materials, assignments, discussions, and other resources are organized and made available to students.

When you enroll in a course, your instructor will usually provide you with access to the specific LMS being used for the course. The LMS may have a unique names. Once you log in to the LMS using your credentials, you will find various sections or tabs where you can access different course materials.

Typically, the course materials section within the LMS contains resources like lecture notes, presentations, textbooks, articles, or videos that are essential for your learning. These materials are often organized by modules or topics to help you navigate through the course content easily.

Additionally, the LMS will provide links to various course activities. These activities may include assignments, quizzes, discussions, group projects, or online assessments. Through these links, you can access and submit your assignments, participate in discussions with your classmates, take quizzes, and engage in other interactive elements of the course.

Overall, the LMS acts as a virtual classroom, bringing together all the necessary instructional materials and course activities in one place, making it convenient for both instructors and students to facilitate learning and collaboration.

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Complete Question

Fill in the blanks :

In a course, your instructional materials and links to course activities are found in ________________.

Answer:

\(\huge\boxed{x = 8}\)

Step-by-step explanation:

\(\sf -18 = -3x+6\\Subtracting \ 6 \ to \ both \ sides\\-18-6 = -3x\\-24 = -3x\\Dividing \ both \ sides \ by \ -3\\8 = x\\OR\\x = 8\)

Answer:

x = 8

Step-by-step explanation:

Here, -3x = -24

x = 8

hope that helps you

By taking the product between the price and the number of meters, we conclude that Mr. Fred spent $135.42

We know that Mr. Fred bought 25.60 meters of fabric, and each meter of fabric costs $5.29

So to get the amount that Mr. Fred spent on fabric, we just need to take the product between the number of meters that he bought and the price of each meter, this is:

25.60*$5.29 = $135.42

In this way, we conclude that Mr. Fred spent $135.42 on the fabric.

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Answer:

Without the greenhouse effect, the Earth would have an average temperature of -18 °C and be covered in ice.

Step-by-step explanation:

Be,

x = number of rental hours

y = The cost of rent

According to the statement, for each rental hour, $3 is charged, so in algebraic language that is: 3x

And in addition to that, $10 dollars is charged, so we have the following amount left

3x + 10

And this sum will result in the rental cost

y = 3x + 10

Answer 1: The linear equation that models the rental cost is: y = 3x + 10

How much does it cost to rent a rowboat for 3 hours?

Let's remember that "x" is equal to the number of rental hours, so substituting x = 3 in the equation y = 3x + 10, we have that

y = 3(3)+ 10 = 9 + 10 =19

Answer 2: Renting a boat for 3 hours costs $19

The complete statement is: |a| = 5 if and only if |a^2| = 25.

The statement |a| = 5 means that the absolute value of a is equal to 5. Absolute value is the distance of a number from zero on a number line, so this tells us that a is either 5 or -5.

Now, we need to determine when |a^2| is equal to 25. The absolute value of a^2 is equal to the positive square root of a^2, which means that |a^2| = sqrt(a^2). Since 25 is a perfect square, the only possible values for a that satisfy this condition are a = 5 and a = -5, since sqrt(5^2) = sqrt((-5)^2) = 5.

Therefore, we can conclude that |a| = 5 if and only if |a^2| = 25, and this is true only for a = 5 or a = -5.

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Answer:

5x + 35 = 175

$28

Step-by-step explanation:

She paid 35 for 1 pair of skis. She paid a certain amount(x) for 5 hours (5x + 35). Therefor making the expression 5x + 35 = 175.

Then, solve the equation with inverse operations.

5x + 35 = 175

Step 1: Subtract 35 from both sides.

5x = 140

Step 2: Divide 5 from both sides.

x = 28

Therefore, Kylie paid $28 each hour of the group skiing lessons.

The case fatality rate is 400 * 100 / 1500 = 26.67 (option d).

For the first scenario, the data determine that there is a difference in average expenditure between the two countries (option c). The P-value of 0.063 suggests that there is a moderate level of statistical significance, indicating that the difference in average expenditure is likely not due to random chance.

In the second scenario, the fact that the 95% confidence interval for the average number of times participants saw their provider per year (3.3) ranges from 0.1 to 6.1 is of statistical use because it provides a range estimate within which the true population means is likely to fall. This interval helps account for the uncertainty associated with the sample estimate and provides a measure of the precision of the estimate (option a).

For the third scenario, the average operating margin is appropriate to use because it is a measure of central tendency that represents the typical financial performance of rural hospitals. The standard deviation provides information about the variability of the operating margins (option d).

In the fourth scenario, the consideration factor that will ultimately contribute to the spread of Ebola is the population density of the affected area (option b). While factors like the influence of non-indigenous people and climatic conditions may play a role, population density is a key determinant in the transmission and spread of infectious diseases.

For the fifth scenario, the case fatality rate is calculated by dividing the number of deaths from the disease (400) by the total reported cases (1500) and multiplying by 100. Therefore, the correct calculation is 400 * 100 / 1500 = 26.67 (option d). This indicates that the case fatality rate is approximately 26.67%.

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Given that 90 < θ < 180 and csc θ = 5/4, we can find tan θ by using the reciprocal trigonometric identity. The reciprocal of the cosecant function is the sine function, so we can use the fact that csc θ = 5/4 to find the value of sin θ. Therefore, tan θ is equal to 4/3 when 90 < θ < 180 and csc θ = 5/4.

Since csc θ = 5/4, we know that the reciprocal of sine, which is csc, is equal to 5/4. In other words, sin θ = 4/5. To find tan θ, we can use the relationship between sine, cosine, and tangent: tan θ = sin θ / cos θ.

To determine the value of cos θ, we can use the Pythagorean identity: sin^2 θ + cos^2 θ = 1. Plugging in sin θ = 4/5, we have (4/5)^2 + cos^2 θ = 1. Solving for cos θ, we find cos θ = 3/5.

Now, we can calculate tan θ by dividing sin θ by cos θ: tan θ = (4/5) / (3/5) = 4/3.

Therefore, tan θ is equal to 4/3 when 90 < θ < 180 and csc θ = 5/4.

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