what is the form of the particular solution for the given differential equation y'' 4y =e^2x

The option that is the better deal between both deals for apples, is 8 apples for $9.25.

The better deal on the apples would be the deal that gives the lower amount per apple. This means that the deal that leads to each individual apple having a lower price is the deal that should be considered best.

To find the price of an apple, you would need to divide the price of the deal given, by the number of apples in the deal.

The first deal would therefore have a per apple price of :

= Price of deal / Number of apples

= 6. 25 / 5 apples

= $ 1. 25 per apple

The second deal would be :

= Price of deal / Number of apples

= 9. 25 / 8 apples

= $ 1. 16 per apple

The better deal is therefore 8 apples for $9.25.

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The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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The mean of the sampling distribution of means is always is d. equal to the population mean.

The mean of the sampling distribution of means is equal to the population mean. This is known as the Central Limit Theorem (CLT). According to the CLT, as the sample size increases, the sampling distribution of means approaches a normal distribution with a mean equal to the population mean.

To understand this concept, let's consider a scenario where we have a population with a certain mean and we take multiple samples from that population, each with the same sample size. We calculate the mean of each sample and create a distribution of those sample means. The mean of this distribution of sample means will be equal to the population mean.

The CLT states that regardless of the shape of the population distribution, as long as the sample size is large enough, the distribution of sample means will be approximately normally distributed. Additionally, the standard deviation of the sampling distribution of means, known as the standard error, is equal to the population standard deviation divided by the square root of the sample size (N).

So, while the standard error is equal to the population standard deviation divided by the square root of N (option b), the mean of the sampling distribution of means is always equal to the population mean (option d).

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The classification of the shapes have been done below based on 2D and 3D.

None of the given terms are three-dimensional figures

Non-polygon:

None of the given terms are non-polygons

A quadrilateral is a polygon with four sides. A rectangle is a specific type of quadrilateral with four right angles. Both quadrilaterals and rectangles are two-dimensional figures.

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Answer:

yo no se pero ahorita yo te ayudo

Answer:

Step-by-step explanation:

3.46...

6 is repeating

Answer:

181/13 =w

Step-by-step explanation:

2w+2019 = 15w + 1838

Subtract 2w from each side

2w-2w+2019 = 15w-2w + 1838

2019 = 13w + 1838

Subtract 1838 from each side

2019 -1838 = 13w

181 = 13w

Divide each side by 13w

181/13 = 13w/13

181/13 =w

Answer: 3

Step-by-step explanation:

      First, we will write a mathematical equation for the phrase given.

-> Let n be "a number"

             four subtracted from twice a number is two

             four subtracted from twice a number = 2

             (twice a number) - 4 = 2

             2n - 4 = 2

      Now, we will solve this equation by isolating the variable.

             2n - 4 = 2

             2n = 6

             n = 3

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Answer:

5/48

Step-by-step explanation:

the first thing you would do is change 6 into the reciprocal, which is 1/6. After, you multiply the fractions just like that.

hope this helps!! :3

Answer:

a) y = 0.55x + 75

b) $108

Step-by-step explanation:

a) to find the equation represent the sequence use the y=mx+b formula

y = total price

m = cost per mile

x = miles driven

b = flat fee

Therefore y = 0.55x+75

b) To figure out the cost of driving 60 miles you use the equation y = 0.55x + 75

y = 0.55 X 60 + 75

= 108

Therefore the cost of renting the truck and driving 60 miles is $108

If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.

To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.

To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.

Therefore, the number of ways to form the line is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).

Therefore, the total number of ways to form the line is:

2 x 10! = 2 * 10!

Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.

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Answer:

\( \frac{1 \\ }{3125} \)

Answer:

x = 9

Step-by-step explanation:

        \(\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}\)

\(\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}\)

Base are same. Compare the exponents.

 x - 14 = -5

        x = -5 + 14    {Addition property of equality}

        x = 9

We can prove that the argument is valid.

In order to prove that Dodec(c) is true given the premises

Small(a) ↔ Tet(a),

Tet(a) ∨ Cube(b), ¬Cube(b),

Small(a) → Dodec(c),

we need to use Fitch notation.

Fitch notation is a popular tool for creating formal proofs.

Fitch notation is a type of proof system that can be used to prove the validity of arguments.

It uses a set of rules and logical symbols to represent propositions, inferences, and deductions.

Step 1: Begin by setting up the premises in the Fitch system. It is recommended that you put each premise on a separate line, like so:

Small(a) ↔ Tet(a)Tet(a) ∨ Cube(b)¬Cube(b)Small(a) → Dodec(c)

Step 2: Use the premises to make inferences and deductions.

Using the premises, we can see that Small(a) → Dodec(c) must be true.

We can use this to make the following deduction:

Small(a) → Dodec(c)Tet(a) ∨ Cube(b)¬Cube(b)

Therefore, Dodec(c)

Step 3: Check the result. We have now proved that Dodec(c) is true, given the premises

Small(a) ↔ Tet(a), Tet(a) ∨ Cube(b), ¬Cube(b), Small(a) → Dodec(c).

This means that we can be sure that the argument is valid.

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Answer:

no

Step-by-step explanation:

bc the  x intercept is repeating when 100 is going to two numbers.A WAY easier (and faster), way to know if it is a function is to see if there are two of the same x-intercept (which make a vertical line). If there is, then it is NOT a function.

i hope this helps

To find the equation of the tangent line to the curve y = tan²(2x) at x = π/4, we need to determine the slope of the tangent line at that point and then use the point-slope form of a line to write the equation.

First, let's find the derivative of y with respect to x. Using the chain rule, we have:

dy/dx = 2tan(2x) sec²(2x).

Now, let's substitute x = π/4 into the derivative:

dy/dx = 2tan(2(π/4)) * sec²(2(π/4))

      = 2tan(π/2) * sec²(π/2)

      = 2(∞) * 1

      = ∞.

The derivative at x = π/4 is undefined, indicating that the tangent line at that point is vertical. Therefore, the equation of the tangent line is x = π/4. Note that the equation y = 2/tan(2x) (sec²(2x) + 1/2) is not the equation of the tangent line, but rather the equation of the curve itself. The tangent line, in this case, is vertical.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

Step-by-step explanation:

Answer:

y = 4/3 x - 4

Step-by-step explanation:

The slope-intercept form of the equation of a line

The equation of a line can be expressed in several forms. One of them is the slope-intercept form:

y = mx + b

Where

m = slope

b = y-intercept

We are required to convert the equation of the line:

4x - 3y = 12

It can be done by solving for y.

Subtracting 4x:

- 3y = - 4x + 12

Dividing by -3;

y = 4/3 x - 4

The four integers are 3, 6, 6, and 13.

Since the median of the four integers is 6, the two middle integers are 6. Let the other two integers be x and y.

Since the mean of the four integers is 7,

the sum of the four integers is 4*7=28.

The sum of the two middle integers, 6 and 6, is 12,

so the sum of x and y is 28-12=16.

Since the range of the four integers is 10, the difference between the maximum and minimum integers is 10. Since the maximum integer is either x or y and the minimum integer is either x or y, the difference between x and y is 10.

If x>y, then x=y+10. If y>x, then y=x+10. Since the sum of x and y is 16, we can set up the following system of equations:

x+(x+10)=16

2x+10=16

2x=6

x=3

y=x+10

3+10=13

y=12

Therefore, the four integers are 3, 6, 6, and 13. The mode of the four integers is 6.

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Answer:

bottom right 8 x 10^1

Step-by-step explanation:

multiply the numbers (2x4 is 8)

add the exponents of 10 (-3+4 is 1)

so the answer is the bottom right 8 x 10^1

Answer:

B

Step-by-step explanation:

Alright, to start off... we need to find a range of value that sqr 74 is between.

To do that, we can check by just trying some random numbers.

Let's try 8 -- 8^2 is 64. Let's try 9 -- 9^2 is 81. So the sqr 64 is 8 and sqr 81 is 9.

sqr 74 is between sqr 64 and sqr 81, so the statement is true. However, the multiple-choice has decimal numbers, meaning that they want us to be more specific.

First, we can cross out 9.5, because we don't want to expand our range, we want to keep it as accurate as possible.

That leaves us 8.5

To find if 8.5 fits the criteria, meaning that it can't be larger than sqr 74, we can use two methods.

The first method is preferred, you simply need to multiply them. I hope you know how to do that by hand. We get 72.25

The second method is less preferred but works. We need to approximate the value by finding the mean of 64 and 81, because 8.5 is the mean of 8 and 9. The approximate value should be very close to the true value. By doing (81+64)/2, we get 72.5

Now, double-check: is the 74 between 72.25 and 81? Yes, it is!
Hence, that gives us the answer that sqr74 is between 8.5 (sqr 72.25) and 9 (sqr 81)

a) the inverse function is:

f-1(y) = (y-b)/a

b) f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

First, let's answer the first part of the question:

To determine whether the function f(x) = ar+b is one-to-one, we need to check if different inputs produce different outputs. Let's suppose that f(x1) = f(x2), where x1 and x2 are distinct inputs. Then, we have:

ar+b = f(x1) = f(x2) = ar+b

Subtracting ar+b from both sides, we get:

ar-ar+b-b = 0

Simplifying, we get:

a(x1 - x2) = 0

Since a is nonzero, this equation implies that x1 = x2, which contradicts our assumption that x1 and x2 are distinct. Therefore, the function f(x) = ar+b is one-to-one.

To find the inverse function of f(x) = ar+b, we can solve for x in terms of y:

y = ar+b

y-b = ar

r = (y-b)/a

x = (y-b)/a

Therefore, the inverse function is:

f-1(y) = (y-b)/a

Now, let's answer the second part of the question:

To find (F-1)(a) for f(x) = x2 + 2x - 1 and a = -4, we set y = -4 and solve for x:

y = x2 + 2x - 1

-4 = x2 + 2x - 1

x2 + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3 or x = 1

Since f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

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To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:

Step 1: Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1

Step 2: Combine like terms on both sides of the equation:
2w = -2

Step 3: Solve for w by dividing both sides of the equation by 2:
w = -1

Therefore, the solution for w is -1.

In HTML format, the answer would be:

<p>To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:</p>
<ol>
<li>Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1</li>
<li>Combine like terms on both sides of the equation:
2w = -2</li>
<li>Solve for w by dividing both sides of the equation by 2:
w = -1</li>
</ol>
<p>Therefore, the solution for w is -1.</p>

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Answer:

Use distributive property and multiply

Step-by-step explanation:

then you will get your polynomial

Answer:

if you needed it simplify its 4x^2-6x-4

Answer:

B has greater intercept

Step-by-step explanation:

function B has greater intercept.

Function B has x-intercept =2

Function A has x x-intercept = -2

So, function B has greater intercept.

Answer:

B has greater intercept

Step-by-step explanation:

Function B has x-intercept =2

Function A has x x-intercept = -2

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

124 students

Step-by-step explanation:

let number of boys be 11x and girls be 9x.

A.T.Q 124 more boys than girls

equation=

11x = 9x + 124

11x- 9x = 124

2x = 124

x = 124/2 = 62

boys= 62 * 11 = 682

girls= 62 * 9 = 558

total = 558+682 = 1240 students