Which of the following functions are solutions of the differential equation y″−4y′−21y=0? A. y(x)=e7xy(x)=e7x
B. y(x)=0y(x)=0
C. y(x)=exy(x)=ex
D. y(x)=e−3xy(x)=e−3x
E. y(x)=e−xy(x)=e−x
F. y(x)=−3xy(x)=−3x
G. y(x)=7xy(x)=7x

Answer:

i think it is the second one?

Step-by-step explanation:

i hope it helped!

a) The alternative that provides Clay Whybark the greatest expected monetary value (EMV) is an alternative to Large Stock.

b) The expected value of perfect information (EVPI) is $13,800.

a) The alternative large stock's expected monetary value (EMV) = 22000 × 0.3 + 12000 × 0.5 - 2000 × 0.2

The alternative large stock's expected monetary value (EMV) = $12,200.

Expected Financial Value of Alternative Average Stock = 14,000 × 0.3 × 1000 × 0.5 × 6000 × 0.2

Expected Financial Value of Alternative Average Stock = $ 10,400

Expected Financial Value of an Alternative Small Stock = 9,000 × 0.3 + 8,000 × 0.5 + 4,000 × 0.2

Expected Financial Value of an Alternative Small Stock = $7,500

b) The expected value with perfect information (EVPI) = 22000 × 0.3 + 12000 × 0.5 + 6000 × 0.2

The expected value with perfect information (EVPI) = $13,800

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Answer: 3 min 45 sec

Step-by-step explanation:

[tex]\begin{array}{ccll} copies&minutes\\ \cline{1-2} 32 & 1\\ 120& x \end{array} \implies \cfrac{32}{120}~~=~~\cfrac{1}{x} \\\\\\ \cfrac{ 4 }{ 15 } ~~=~~ \cfrac{ 1 }{ x }\implies 4x=15\implies x=\cfrac{15}{4}\implies \stackrel{\textit{3 minutes and 45 seconds}}{x=3\frac{3}{4}}[/tex]

The top interval in a frequency table for a set of scores ranging from a high of X = 75 to a low of X = 23 would be 73-75.

This is because the bottom interval is 18-23, and the intervals in a frequency table are generally of equal size. This means that the highest interval must be of a similar size, and would thus be 73-75. The purpose of a frequency table is to show how often values from a numerical data set occur.

The data is usually divided into intervals of equal size, such as the 18-23 interval mentioned in this scenario. The intervals are usually calculated by subtracting the lowest value from the highest value, and then dividing the result by the number of intervals desired. In this case, the highest interval must be of equal size to the 18-23 interval, resulting in a range of 73-75.

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The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular, and the equation for the set of all points at which f and l are perpendicular is 6x₁ + 3y₁ + 4z₁ = 0.

To find a point at which the vector field F and the line l are perpendicular, we need to find the point at which the dot product of the vector F and the direction vector of the line l is zero.

The direction vector of the line l is given by:

d = (1, 1, 4)

The vector F at the point (x₁, y₁, z₁) is given by:

F(x₁, y₁, z₁) = x₁ i + (x₁ + y₁) j + (x₁ - y₁ + z₁) k

The dot product of F and d is:

F(x₁, y₁, z₁) ⋅ d = x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁)

Setting this equal to zero, we have:

x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁) = 0

Expanding, we get:

6x₁ + 3y₁ + 4z₁ = 0

We can substitute x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t into this equation to find t:

6(3 - 5t) + 3(t - 4) + 4(4 + 4t) = 0

Expanding, we get:

72 - 30t + 3t - 12 + 16 + 16t = 0

Simplifying, we get:

100 = 20t

So, t = 5.

Substituting t = 5 back into x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t, we get:

x₁ = 3 - 5 * 5 = -12

y₁ = 5 - 4 = 1

z₁ = 4 + 4 * 5 = 24

The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular.

The set of all points at which F and l are perpendicular is given by the equation:

6x₁ + 3y₁ + 4z₁ = 0

This represents a plane in 3-dimensional space, perpendicular to the vector F at all points.

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--The given question is incomplete; the complete question is

"Let F = (x)i + (x+y)j + (x-y+z)k. Let the line l be x = 3 - 5t, y = t - 4, z = 4 + 4t.                                 Find a point Q= (x₁, y₁, z₁) at which F and l are perpendicular. Give an equation for the set of all points at which F and I are perpendicular."--

Answer:

−x^2+x−2

Step-by-step explanation:

The length of each of piece of board is 40 cm or 0.4 m.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Gillian has a board that is 2 meters long.

She cuts the board into 5 equal pieces.

Now, the length of each piece is

= 200 cm /5

= 40 cm

Hence, the length is 40cm or 0.4 m.

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There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.

curing a problem by a method but rather action; explaining the answer. a range of values for a variable that fulfill an equation, specifically The solution of an equations is any value of both a variable that gets the Left Hand Side (LHS) and thus the Nondominant Hand Side (RHS) of the equations equal. To solve an equation is to identify its answer or solutions. One approach to express the concentration of a solvent is as a percentage of the solute in the solvent. The ratio of the mass of something like the solute here to mass of the solution, or the fraction of the mass of something like the solute here to mass of the solution, is one of two supplementary techniques for computing the percentage.

given

When we multiply equation 1 by 4 we get:

-3x + y = 4

-12x + 4y = 16

Due to the fact that there is no solution for x, -12x + 4y = 16

There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.

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For congruent segments, the following are required:

Perpendicular Bisector of a Segment:

Congruent Angles:

Angle Bisector:

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Answer:C

Step-by-step explanation:

The least number of hours from now when the clock will again show the correct time is 720 minutes

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

The clock will show the correct time again when it lost 12 hours

As every hour it loses 1 minute,  the clock have to lose 12 hours in minutes, so we get:

12 hour * (60 minutes / 1 hour) = 720 minutes

Therefore, the least number of hours from now when the clock will again show the correct time is 720 minutes.

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Answer:

x = 24

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ x/12 = 2

Then the value of x will be,

→ x/12 = 2

→ x = 2 × 12

→ [ x = 24 ]

Hence, the value of x is 24.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{12} = 2}[/tex]

[tex]\mathsf{\dfrac{1}{12}x = 2}[/tex]

[tex]\large\text{MULTIPLY 12 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{1}{12}x\times 12 = 2 \times 12}[/tex]

[tex]\large\text{Simplify it}[/tex]

[tex]\mathsf{x = 12\times 2}[/tex]

[tex]\mathsf{x = 24}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 24}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

False, P(A and B) is not always greater than or equal to P(A).

From the question, we have the following parameters that can be used in our computation:

P(A B) ≥ P(A)

This means that

Is P(A and B) always greater than or equal to P(A)?

The value of the probability is calculated a

P(A and B) = P(A) * P(B)

This means that there is a direct variation between P(AB) and P(A)

Since P(B) is less than 1, then P(A B) ≥ P(A) is false

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The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Let the angle be 'x'. Then the equation is given as,

x + 13° = 71°

x = 71° - 13°

x = 58°

The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.

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Answer:

16.7 years (not sure)

Step-by-step explanation:

To solve this problem, we can use the formula for exponential decay:

y = y0 * (1 - r)^t

Where y is the number of cars after t years, y0 is the initial number of cars (54 million), r is the annual decrease rate as a decimal (6.8% = 0.068), and t is the number of years.

We want to find t when y = 46 million:

46 million = 54 million * (1 - 0.068)^t

Dividing both sides by 54 million:

46 million / 54 million = (1 - 0.068)^t

Taking the natural logarithm of both sides:

ln(46 million / 54 million) = ln((1 - 0.068)^t)

Using the logarithmic identity:

ln(46 million / 54 million) = t * ln(1 - 0.068)

Dividing both sides by ln(1 - 0.068):

t = ln(46 million / 54 million) / ln(1 - 0.068)

Using a calculator, t = approximately 16.7 years. Rounding to the nearest year, it will take 17 years for this country to have 46 million cars.

Sexuality is boundary marker that organizers of New York City's annual India Day Parade use to exclude a particular group from participating.

The proclivity to think and act as members of a group: the proclivity to conform to a group’s cultural pattern at the price of individualism and cultural variety. Groupism… is founded not on evident group emergencies, but on the nebulous unease of lonely individuals. Mr. David Riesman.

Tangible culture (such as buildings, monuments, landscapes, literature, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage are all examples of cultural heritage (including culturally significant landscapes, and biodiversity).Sexuality, gender, religion, race, socioeconomic status, and area are examples of cultural identities.

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The sequence diverges.

There is just one possible outcome for a sequence: either it converges or it diverges. This does not imply that we can always detect whether the sequence converges or diverges; in fact, there are occasions when it can be very challenging for us to do so.

The limit of the sequence an = cos(2n) / 5n as n approaches infinity does not exist, so the sequence diverges.

The cosine function oscillates between -1 and 1, so the value of cos(2n) can be arbitrarily large or small as n gets larger. As a result, the ratio of cos(2n) to 5n also becomes arbitrarily large or small, and the limit does not exist.

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Response variable defined with:

B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.

Option B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.

On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.

Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.

The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.

The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.

Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.

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The equation of the circle,

x² + (y – 3)² = 36.

The correct option is A.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

A circle that has a diameter of 12 units and a center that lies on the y-axis.

That means, radius = 6.

And h = 0.

From the given choices:

Now, the equation of the circle,

x² + (y – 3)² = 36.

Therefore, x² + (y – 3)² = 36 is the equation.

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Choosing h and k in the given system of linear equations such that they they have no solution, a unique solution, and  many solutions is determined by the augmented matrix.

The augmented matrix is

  [1     h      2

  4     8      k].

Reduce matrix to row echelon form

a)We need to determine the values of h and k such that the system has no solution

8 - k =/ 0 and h -2 = 0

Hence, The System has No solution only when h=2, and k not equal to 18.

b)We need to determine the values of h and k such that the system has unique solution when

h - 2 =/ 0

The System has a Unique Solution only when h not equal to 2 and k is any Real number

c)We need to determine the values of h and k such that the system many solution when

8 - k = 0 and h -2 = 0

The system has many solutions only when h=2 and k= 8

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The complete question is :

choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. h & k

      x1 + hx2 = 2

     4x1 + 8x2 = k

The equation that can be used to find d is 0.25d - 3.50 = $55.

The first step is to determine the total cost when the distance travelled is d.

Total cost when the first rental company drives d miles = $55

Total cost when the second rental company drives d miles = cost per day + [cost per mile x (d - 150)

= $34 + [$0.25 x (d - 150)]

$34 + 0.25d - 37.50

0.25d - 3.50

When the total charges are the same, the two equations would be equal

0.25d - 3.50 = $55

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The required match for the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
Length of C'D' = 5.4
Length of A'D' = 8.4  
The Slope B'C' = 0.25

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
After the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
[scale dilation does not affect the orientation of geometry.]

Length of C'D' = 5.4   [length of C'D' = 1.2 × CD]

Length of A'D' = 8.4  [length of A'D' = 1.2 × AD]

The Slope B'C' = 0.25
[scale dilation does not affect the orientation of geometry.]

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Answer:

20 dumplings.

Step-by-step explanation:

Keith can make 16 / (4/5) = 16 * 5/4 = 20 dumplings.

The perimeter is  6x + 8 feet and the area is (2x^2 + 5x + 3) square feet

The perimeter of a rectangle is equal to the sum of the lengths of all four sides.

The length of the shed is 2x + 3 feet, and the width is x + 1 feet, so the perimeter of the shed is:

2 * (2x + 3) + 2 * (x + 1) = 4x + 6 + 2x + 2 = 6x + 8 feet

The area of a rectangle is equal to the product of its length and width.

So, the area of Shirley's shed is:

(2x + 3) * (x + 1) = (2x^2 + 5x + 3) square feet

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4.5 cups of lemonade is required to fill 6 containers.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is used to make repetitive adding of the same number easier.

As per the data given in the questions,

We have,

To fill one container, Tyreick needs 3/4 of a cup of lemonade.

So, to fill 6 containers, he will need 6 * 3/4 = 4.5 cups of lemonade.

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An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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Answer:

B. 4w + 10 = 46

Step-by-step explanation:

If we let l be the length of the rectangle and w its width

Fact 1: A rectangle's length is 5 centimeters greater than its width
This translates to l = w + 5 (1)

Fact 2: he perimeter of the rectangle is 46 centimeters
Perimeter is given by 2(l + w)
So fact 2 translates to:
2(l + w) = 45
2l + 2w = 46  (2)

Substitute l = w + 5 from (1) for l in (2):

2(w + 5) + 2w = 46
2w + 10 + 2w = 46

4w + 10 = 46

This is Option B

Answer:

C. 2w + 5 = 46

Reason why is because a rectangle has 4 sides, but you only want to multiply length times the width, to get the perimeter, which is why 2w in the equation is correct.

It also says 5 centimeters greater, the is why it would be + 5 instead of 10.

Step-by-step explanation:

Hope it helps! =D

The area of the rhombus would be [tex]$\mathbf{5 0} \sqrt{3}$[/tex].

A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus.

Given:

Each side length in a rhombus is $10, and one of the angles is equal to $120 circumference.

If the angle is 120 degrees, its half, 60 degrees, creates a right-angled triangle.

[tex]& \sin 60=\text { Height } / 10 \\[/tex]

[tex]& \sqrt{3} / 2 * 10=\text { height } \\[/tex]

[tex]& \text { height }=5 \sqrt{3} \text {. } \\[/tex]

Let the equation be

[tex]& \text { Area of rhombus = base }* \text { height } \\[/tex]

simplifying the above equation, we get

[tex]& =10 * 5 \sqrt{3} \\[/tex]

[tex]& =50 \sqrt{3}[/tex]

Therefore the area of the rhombus is [tex]$\mathbf{5 0} \sqrt{3}$[/tex].

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Answer: x+42

Step-by-step explanation:

If red tomatoes was 42 more than yellow, it would be x=yellow tomatoes, x+42 because we do not know how many yellow tomatoes there are.