Find a homogeneous linear differential equation with constant coefficients whose general solution is given.

y = c1e−x cos x + c2e−x sin x

y''' + 2y'' + 2y' = 0

y'' + 1 = 0

y'' − 2y' + 2y = 0

y'' + 2y' + 2y = 0

y''' − 2y'' + 2y' = 0

The correct answer to the question is: a. Two-way ANOVA.

If you have a 4x5 design for your study, you should run a Two-way ANOVA.

The ANOVA (analysis of variance) is a test for comparing the means of two or more groups in one, two, or three-way experiments. The two-way ANOVA is the most common model in most statistical studies. It is usually used in the analysis of the data with two independent factors, A and B, that influence a dependent variable, y, and each factor has levels or sub-groups.

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c = 50 liters (initial amount of soup)

d = 10 liters (amount of water added)

1: Calculate the initial amount of broth in the soup.

The soup is 50% broth, so 50% of 50 liters is (50/100) * 50 = 25 liters of broth.

2: Calculate the final amount of soup after adding water.

The initial amount of soup is 50 liters, and 10 liters of water are added, so the final amount of soup is 50 + 10 = 60 liters.

3: Calculate the final amount of broth in the soup.

The initial amount of broth is 25 liters, and no broth is added or removed during the process, so the final amount of broth remains the same at 25 liters.

4: Calculate the final percentage of broth in the soup.

To find the percentage of broth in the soup, divide the final amount of broth by the final amount of soup and multiply by 100.

(25/60) * 100 = 41.67%

c = 50 liters

d = 10 liters

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Therefore, the coordinates of the terminal points are: (0, 1),(-√2/2, -√2/2) ,(-1/2, -√3/2)

A coordinate is a set of numerical values that uniquely determines the position of a point in space. In two-dimensional space, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal distance from a reference point, and y represents the vertical distance from the same reference point. In three-dimensional space, a coordinate is represented by a triplet of numbers (x, y, z), where x, y, and z represent the horizontal, vertical, and depth distances from the reference point, respectively.

by the question.

Pi/2 is an angle in radians, and it corresponds to an angle of 90 degrees in degrees. The terminal point for this angle lies on the positive y-axis and has coordinates (0, 1).

315 degrees is an angle in degrees, and it corresponds to an angle of 7π/4 radians in radians. To find the terminal point for this angle, we can use the unit circle. Starting from the positive x-axis (the initial side), we rotate 315 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 5π/4 radians. The terminal point lies in the third quadrant and has coordinates (-√2/2, -√2/2).

240 degrees is an angle in degrees, and it corresponds to an angle of 4π/3 radians in radians. To find the terminal point for this angle, we can again use the unit circle. Starting from the positive x-axis (the initial side), we rotate 240 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 4π/3 radians. The terminal point lies in the third quadrant and has coordinates (-1/2, -√3/2).

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ANSWER

EXPLANATION

We want to identify the option that is completely factored.

For an expression to be completely factored, it means that there are no more common terms between the terms in the expression.

That means it can not be factored any further.

Therefore, the only correct option is:

Based on the given options, the linear inequality that represents the graph below is C. y ≥ -3x + 1

To determine the correct option, we need to analyze the characteristics of the graph. Looking at the graph, we observe that it represents a line with a solid boundary and shading above the line. This indicates that the region above the line is included in the solution set.

Option A, y > (-3/6)x + 1, does not accurately represent the graph because it describes a line with a slope of -1/2 and a y-intercept of 1, which does not match the given graph.

Option B, y ≥ x + 1, also does not accurately represent the graph because it describes a line with a slope of 1 and a y-intercept of 1, which is different from the given graph.

Option D, y > x + 1, is not a suitable representation because it describes a line with a slope of 1 and a y-intercept of 1, which does not match the given graph.

Only Option C. y ≥ -3x + 1.

This is because the graph appears to be a solid line (indicating inclusion) and above the line, which corresponds to the "greater than or equal to" relationship. The equation y = -3x + 1 represents the line on the graph.

Consequently, The linear inequality y -3x + 1 depicts the graph.

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The best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.

Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:

(666-444)/666 = 222/666 = 1/3

This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:

180180180/3 = 60060060

rolls to be greater than 444. Therefore, the best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.

Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:

(666-444)/666 = 222/666 = 1/3

This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:

180180180/3 = 60060060

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Answer:

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

Use the formula for simple interest:

where:

Substituting the given values into the formula, we get:

Therefore, the rate of interest per year is 8%.

The definite integral in part (a) cannot be evaluated using only Gamma or Beta functions.

To evaluate the integral ∫√√z e^(-√z) dz using only Gamma or Beta functions, we need to express the integrand in terms of such functions. However, the integrand in this case does not have a direct representation in terms of Gamma or Beta functions. Therefore, we cannot evaluate the integral using only those functions.

Part (b):

To evaluate the integral ∫(e^x)^2 (e^(2x) + 1)^(-3) dx using only Gamma or Beta functions, we can make a substitution: let u = e^x. Then, du = e^x dx, and the integral becomes ∫u^2 (u^2 + 1)^(-3) du. This can be rewritten as ∫u^2 (1 + u^(-2))^(-3) du.

Now, we can rewrite the integrand using the Beta function as (1/u^2)^(-3/2) * (1 + u^(-2))^(-3) = Beta(-3/2, -3) = Γ(-3/2)Γ(-3)/Γ(-6/2).

Using the properties of the Gamma function, we have Γ(-3/2) = -4√π/3, Γ(-3) = 2, and Γ(-6/2) = -4√π/15. Substituting these values back into the expression, we get (-4√π/3)(2)/(-4√π/15) = 10/3.

Therefore, the value of the integral ∫(e^x)^2 (e^(2x) + 1)^(-3) dx is 10/3.

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Yes that's true, A plane is two dimensional.

Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.

Long division is a method of dividing two numbers using written arithmetic. It is a process of breaking down a division problem into a sequence of smaller and easier steps to obtain the quotient and remainder. Long division is typically used for dividing large numbers or when the division is not exact.

To perform long division, we follow the following steps:

The final result is the quotient and the last remainder obtained.

                                   __________________________

        x³ + 6x² - 3x - 5 | -3x⁵ - 22x⁴ - 13x³ + 39x² + 14x - 6

                                    -3x⁵ - 18x⁴ + 9x³ + 15x²

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

                                               -4x⁴ - 4x³ + 54x²

                                              -4x⁴ - 24x³ + 12x² + 20x

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

                                                           18x³ + 42x²

                                                           18x³ + 108x² - 54x - 90

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

                                                                         150x + 84

Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.

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The probability of choosing a white marble from the box can be determined by dividing the number of white marbles by the total number of marbles.

In this case, the box contains 7 green marbles and 6 white marbles, so the total number of marbles is 13.

To find the probability, we divide the number of white marbles (6) by the total number of marbles (13):

Probability of choosing a white marble = 6 / 13

To express this as a decimal number, we divide 6 by 13:

Probability of choosing a white marble ≈ 0.4615 (rounded to 4 decimal places)

The probability of choosing a white marble from the box is approximately 0.4615.

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Answer:

Step-by-step explanation:

\(\angle 2,\angle AEG, \angle GEB\)

Answer:m= 83 degrees

Step-by-step explanation: the sum of all three corners will always add up to 180 so adding 31 and 66 together is 97 an then 180-97 is 83.brainliest?

Answer:

89

Step-by-step explanation:

195+-25=170

170+-81=89

Hope this helps:)

Pls give brainliest.

The perpendicular bisector of the segment is attached in below.

What is meaning of perpendicular bisector?

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

The steps to draw perpendicular bisector mentioned below:

Step 1: Sketch a line segment XY.

Step 2: Using a compass, draw arcs above and below the line segment, with X serving as the center and XY's width being greater than half length of the line segment.

Step 3: Carry out Step 2 but using Y as the center.

Step 4: Write "P" and "Q" next to the junction points.

Join the points "P" and "Q" in step five. The midpoint of the line segment XY is where the perpendicular bisector PQ intersects it. Affix a "O" to it.

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Answer:

\(\frac{-29}{36}\)π

Step-by-step explanation:

Answer:

The measurement of angle PTQ is 40°

Answer:

40

Step-by-step explanation:

2x+16= x+28

(vertical opp. angles)

x=12

PTQ= x+28= 12+28= 40

Hope it will help:)

Answer:

A

Step-by-step explanation:

Answer:   1/2 |x| = -3?

Step-by-step explanation:

Answer:

1.5x + 2

Step-by-step explanation:

(3x + 4)/2 = 1.5x + 2

Answer:

D. Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.

Step-by-step explanation:

I did it and got it right.

Poor eyesight can occur for other reasons, such as genetics. Hence option D is correct.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Since,  sitting close to the television and poor eyesight dose not have implicit relation because the it not necessary the person who has poor eyesight cause of watching television from close distance. It could be depends upon other heads like genetic problem or some accident or deceases.

Thus, causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.

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The term that best describes the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs is independent.

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

In independent events, the occurrence or non-occurrence of one event has no influence on the probability of the other event happening. The probability of one event does not depend on the outcome of the other event.

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Answer:

75%, 0.75, 3/4. 3 quarters.

Step-by-step explanation:

Answer:

(0,320) and (4,0)

Step-by-step explanation:

The question has missing details. So, I've added the complete question as an attachment.

From the question, we understand that:

Justine started when Michael was 320 yards from the top.

This coordinate can be represented as (0,320)

0 represents the time Justine started and 320 represents the number of yards left.

Every minute, Justine covers 80 yards.

This implies that:

At 1 minute, Justine will have: (320 - 80) yards left

At 2 minutes, Justine will have: (320 - 80 - 80) yards left

At 3 minutes, Justine will have: (320 - 80 - 80 - 80) yards left

At n minutes, Justine will have (320 - 80n) yards left

So, possible coordinates are:

\((x_1,y_1) = (0,320)\)

\((x_2,y_2) = (1,320-80*1) = (1,240)\)

\((x_3,y_3) = (2,320-80*2) = (2,160)\)

\((x_3,y_3) = (3,320-80*3) = (3,80)\)

\((x_4,y_4) = (4,320-80*4) = (4,0)\)

Answer:

Select any two pairs of values from the given table. But, for simplicity, it’s a good idea to select coordinates with integer values. So, two points that represent Justine’s function for the yards left to hike in terms of the hours she’s spent hiking are (1, 270) and (2, 150).

Step-by-step explanation:

Sample Answer

C) The ordered pair that represents the initial value of the function is of (0,3840), meaning that the graph of the function crosses the y-axis at the value of y = 3840.

D) The rate of change of the equation is of -128, meaning that when x increases by one, y is decreased by 128.

The following is the definition of a linear function's slope and intercept:

y = mx + b.

In which:

m is the slope, representing the rate of change, that is, by how much y changes when x is increased by one.

The value of y at x=0 is represented by the intercept, b. Hence the ordered pair is of (0,b).

The function is defined as follows for this problem:

y = -128x + 3840.

The slope and intercept are therefore given as follow:

m = -128, b = 3840.

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Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

Step-by-step explanation:

You have it right on the picture:

The equations are:

and

The intersection of two lines is the solution of the system, which is:

The point is (5, 23) at which both rentals are same

Answer:

25%

Independent evemt

Step-by-step explanation:

The posibility of it shows head on the first flip is 50%

The posibility of it shows tail on the second flip is 50%

=> The posibility of it shows head on the first flip and shows tail on the second flip is:

0.5 × 0.5 = 0.25 = 25%

Two events are independent because the result on the first flip doesn't affect the second one.

Ava method of simplifying the expression was wrong

Ava's mistake is (−(2x−3y))^2 = −1⋅(2x−3y)^2 this was wrong. the square of a negative is positive. (−(2x−3y))^2 = (2x−3y)^2 this is correct

(2x - 3y)^2 / (3x - 2y)^2

Simplifying the numerator

= (2x - 3y)^2

= (2x - 3y) * (2x - 3y)

= 4x^2 - 6xy - 6xy + 9y^2

Simplifying the denominator

= (3y - 2x)^2

= (3y - 2x) * (3y - 2x)

= 9y^2  - 6xy - 6xy + 4x^2

rearranging gives

= 4x^2 - 6xy - 6xy + 9y^2

putting together

= (4x^2 - 6xy - 6xy + 9y^2) / (4x^2 - 6xy - 6xy + 9y^2)

= 1

In Ava's method, at this stage (−(2x−3y))^2

(−(2x−3y))^2 = (2x−3y)^2

(−(2x−3y))^2 ≠ −1⋅(2x−3y)^2 -  this was wrong

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