NEED HELP ASAP PLEASE! What is the equation of the function shown in the table?
Input x: -2 -1 0 1 2
Output y: -3 -1 1 3 5

A: y = -2 x + 1
B: y = 2 x + 1
C: y = 2 x - 2
D: y = - 1/2x - 1

The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]

Now, we have to find the particular solution by method of undetermined coefficient.

   [tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]

⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]

⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]

⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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Note that the Upper limit and the lower limit of the Proportion Interval are given as follows:

Upper limit-  27%

Lower limit - 19%

The proportion interval, also known as the confidence interval, can be calculated using the point estimate of the proportion and the margin of error.

The lower limit of the proportion interval is calculated by subtracting the margin of error from the point estimate, and the upper limit is calculated by adding the margin of error to the point estimate.

Lower limit = point estimate - margin of error

Upper limit = point estimate + margin of error

In this case, the point estimate is 23% and the margin of error is ±4%.

Lower limit = 23% - 4% = 19%

Upper limit = 23% + 4% = 27%

Therefore, the proportion interval is [19%, 27%], which means that we can be 90% confident that the true proportion of the population lies within this range.

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Answer:

Step-by-step explanation:

What is the least number and greatest number of shells he would need

The measure of sinx from the trigonometry is 7/25

Given the following trigonometry

tan x = 7/24

Since tan theta = opposite/adjacent

Determine the hypotenuse

h^2 = 7^2 + 24^2

h^2 = 49 + 576
h^2 = 625

h = 25

The value of sin x will be given as:

sinx = opposite/hypotenuse

sinx = 7/25

Hence the exact value of sinx where sinx>0 is 7/25

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The total weight of the bottles the truck carries is 6020 ounces.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

Example:

2 + 1x + 4y = 7 is an expression.

3 + 3x + 3 = 7 is an expression.

We have,

Number of bottles the truck carries = 430

One bottle weight = 14 ounces

Now,

The total weight of the bottles.

= Number of bottles x Weight of one bottle

= 430 x 14

= 6020 ounces

Thus,

The total weight of the bottles the truck carries is 6020 ounces.

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Answer: x ≅ 11.2

Step-by-step explanation:

We can set up two equations:

Let y = measure of <BAD = measure of <CAD

then:

sin y = x/23

sin y = (20-x)/18

Since both of these are sin y, we can set them equal to each other:

x/23 = (20-x)/18

.: 18x = 460 - 23x

41x = 460

.: x ≅ 11.2

Answer:

x = 11.2

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

Use angle bisector theorem. It states that:

Apply this to the given triangle:

Cross-multiply and solve for x:

The graph of the quadratic function y = -2x² + 1 is given by the image presented at the end of the answer.

The parent quadratic function is given as follows:

y = x².

The transformed quadratic function is given as follows:

y = -2x² + 1.

The transformations are given as follows:

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The solution to the inequality are the region in the shaded area

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

y < 3x+3

3x-y ≤ 4

Represent properly

y < 3x + 3

3x - y ≤ 4

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)

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The vertical axis of the scatter plot is the height; on the other hand, if the sphere is 6 inches, the height is closer to 5 inches than to 11 inches.

In this scatter plot, the horizontal axis is the width; however, we know the second variable is the height and this should be in the vertical axis.

Following the trend of the graph, it can be concluded the height if the width is six inches is approximately 5 rather than 11 inches.

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If the shortest leg of the small triangle is 4 in and the hypotenuse is 12 in and the shortest leg of the large triangle 8 in, then the length of the hypotenuse of the large triangle is 24 inches.

We know that two triangles are proportional if their corresponding sides are in proportion to each other. That is, the ratio of the lengths of the corresponding sides is the same for both triangles.

Let's denote the length of the hypotenuse of the large triangle by "h". We can set up a proportion using the given information:

shortest leg of small triangle / hypotenuse of small triangle = shortest leg of large triangle / hypotenuse of large triangle

Plugging in the values we get:

4/12 = 8/h

Simplifying the equation we get:

h = (12*8)/4 = 24

To explain the solution, we used the fact that similar triangles have proportional sides. We then used the given information about the lengths of the sides of the small and large triangles to set up a proportion and solve for the unknown length of the hypotenuse of the large triangle.

The key to this problem was recognizing the relationship between similar triangles and using that relationship to set up and solve a proportion.

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Answer:

The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).

Answer:

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

Step-by-step explanation:

[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

The value of the limit of the rational function evaluated x = - 5 is equal to - 6.

In this problem we find the limit of rational function evaluated at a given value. According to the statement, there is apparently a discontinuity at x = 5. The expression can be simplified by algebra properties:

[tex]\lim_{x \to - 5} \frac{x^{2} + 4 \cdot x - 5}{x + 5}[/tex]

[tex]\lim_{x \to -5} \frac{(x + 5)\cdot (x - 1)}{(x + 5)}[/tex]

[tex]\lim_{x \to - 5} (x - 1)[/tex]

Then, we can complete the table by means of the following expression:

f(x) = x - 1

x = - 5.01

f(- 5.01) = - 5.01 - 1

f(- 5.01) = - 6.01

x = - 5.001

f(- 5.001) = - 5.001 - 1

f(- 5.001) = - 6.001

x = - 5.0001

f(- 5.0001) = - 5.0001 - 1

f(- 5.0001) = - 6.0001

x = - 5

f(- 5) = - 5 - 1

f(- 5) = - 6

x = - 4.9999

f(- 4.9999) = - 4.9999 - 1

f(- 4.9999) = - 5.9999

x = - 4.999

f(- 4.999) = - 4.999 - 1

f(- 4.999) = - 5.999

x = - 4.99

f(- 4.99) = - 4.99 - 1

f(- 4.99) = - 5.99

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Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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You have to  spend $26,500 over the course of the first year with rent and equipment.

To calculate how much money you will spend over the course of the first year with rent and equipment, you need to add the cost of rent to the cost of equipment.

In a hypothetical scenario, Let's assume that the cost of rent for the first year is $1,500 per month.

To calculate the total cost of rent for the first year, you can multiply the monthly rent by the number of months in a year:

$1,500/month x 12 months = $18,000

So the total cost of rent for the first year is $18,000.

To calculate the total cost of equipment, you can take the average cost of the equipment (i.e., the midpoint of the given range) and assume that you will spend that amount:

($7,000 + $10,000) / 2 = $8,500

So the total cost of equipment is $8,500.

To calculate the total cost of rent and equipment for the first year, you can add the two costs together:

$18,000 + $8,500 = $26,500

Therefore, you will spend $26,500 over the course of the first year with rent and equipment.

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Using the a pair of adjacent angles, we will see that:

Z° = 137°

When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.

Then here we can write a linear equation for z.

z + 43 = 180

Solving that for z, we will get:

z = 180 - 43

z = 137

That is the measure of the angle.

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Answer:

5

Step-by-step explanation:

The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:

2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)

So, 5^2.5^0 = 5^1 = 5

Therefore, the answer is 5.

The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5

The formula to calculate average speed is:

Average speed = distance traveled / time taken

In this problem, Yusef drove 130 miles in 2.5 hours.

So, we can substitute the values in the formula:

Average speed = 130 miles / 2.5 hours

Simplifying this expression, we get:

Average speed = 52 miles per hour

Therefore, the correct equation to calculate the average speed at which Yusef drove is:

r = 130/2.5 or r = 52

Option C matches this equation, so the answer is C.

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45 and 27.6 degrees are the two complementary angles.

The various angles or measurements include:

Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.

The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:

x + 17.4 = 90 - x + 17.4

When we simplify and find x, we obtain:

2x = 55.2

x = 27.6

The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.

The two complementary angles are 27.6 and 45 degrees as a result.

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The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.

The figure is given below.

From the figure, we can see that the sides of a triangle at the top and bottom are the same.

So the triangle cut from the bottom is placed at the top of the figure.

When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.

So the area of the given composite figure is the same as the area of the rectangle.

The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²

Therefore the area of the given composite figure is 158.2 mm².

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Answer: (a) -6x²y

Step-by-step explanation:

[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:

[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)

The coordinates of point H' will be: H'(3, 9)

We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.

The original object's dimensions, orientation, or shape are unaffected by translation.

Translating a point P(x, y) 1 unit up means we need to add to use P'(x, y+1), that is adding 1 unit to the y-coordinate of the point P'(x, y).

Now we have to translate the triangle 1 unit up. So, use the formula

P(x, y) → P'(x, y + 1)

Thus, the coordinates of point H' will be:

H( 3, 8) → H'( 3, 8+1) → H'(3, 9)

Therefore, the coordinates of point H' will be: A'(3, 9).

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The meaning of 5 = f(I) is that the 5% have an income of $6000

The average rate is that %0.054 per thousand of dollars

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

The graph

The equation is given as

5 = f(I)

This means that:

We find x when f(I) = 5

Using the graph, we have

x = 6

This means that the income is $6000

This is calculated as

Rate = (f(x2) - f(x1))/(x2 - x1)

Substitute the known values in the above equation, so, we have the following representation

Rate = (1.8 - 4.5)/(10 - 60)

Evaluate

Rate = 0.054

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Answer:

Step-by-step explanation:

The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.

The total number of arrangements of the eight letters is 8!:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

The number of arrangements of H's is 2!:

2! = 2 x 1 = 2

The number of arrangements of E's is 3!:

3! = 3 x 2 x 1 = 6

So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:

40320 / (2 x 6) = 40320 / 12 = 3360.

Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".

Answer:

The company must make $450.

If the company must pay $300, then you will take 300, and since they want to make a profit, which means 1500 dollars more once they pay the 300, the you will add that to 300.

300 + 150 = 450

Now to find how many weeks it will take, you will divide 450 by 60:

450/60 = 7.5

It will take 7 1/2 (or round it to 8)weeks to gain $450, which is enough money to pay the bank $300, and make a profit of $150.

Step-by-step explanation:

Hope it helps! =D

7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.

When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470

The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.

"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.

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According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)

According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.

In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.

Note: This question is incomplete. Here is the complete information:

Image attached

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The amount after 35% off on a 85 dollar item will be $55.25

Percentage is a way to express a number as a fraction of hundred. It is often used to represent proportions  and  ratios in a more convenient and understandable form, especially in financial  statistical and financial  contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To find the sale price of an item that has a discount, you can use the following formula:

Sale price = Original price - (Discount percent × Original price)

In this case, the discount is 35% off of an $85 item. So we have:

Discount percent = 35%

Original price = $85

Substituting these values into the formula, we get:

Sale price = $85 - (35% × $85)

Sale price = $85 - $29.75

Sale price = $55.25

Therefore, the sale price of the item after a 35% discount is $55.25.

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The future value is 6,495,554.308.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

Compound interest can be calculated in math in a variety of ways depending on the circumstances. To make the calculations simpler, we can use the compound interest formula. We need to know the amount and the principal in order to calculate compound interest. The distinction is between the amount and the principal.

Given that  $12,000 is invested in a project at 7% for 9 years.

The formula of compound interest is

A = P(1+r/n)^nt

A = amount

P = principal

r = rate of interest

t = time

n =  number of compound interest per annum

For the given problem:

P =12,000, r = 7%, t = 9, n = 365:

The amount after 9 years will be:

A = 12,000(1+0.07/365)^(365×9)

A = 6,495,554.308

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According to the given function net change and average rate of change between the given values of the variable.

A. 2

B. 2/a

A rate of change's integral is taken into account by the net change theorem. According to this, a quantity's new value equals its initial value plus the integral of its rate of change whenever it changes. There are two methods to formulate the equation. The second is more widely known and is just the definite integral.

The (definite) integral of a function's derivative, in other words, represents the overall change in a function. In specifically, the integral of velocity is the net distance travelled (final position minus initial position). The integral of acceleration is the difference between the final velocity and the starting velocity.

g(x) =2/x

x = 1

x = a

A.

g(x) =2/x

g(1) =2/x

g(1) =2

B.

g(x) =2/x

g(a) =2/x

g(a) =2/a

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