Which sentence is Correct and please take your time !!!

The solution of the given differential equation using the Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Given differential equation is y″−2y = eˣ, y(0) = 0, y′(0) = 0. We will solve it using Laplace transforms.

To solve the given differential equation using the Laplace transform, take the Laplace transform of each term of the differential equation. Then solve for Y(s) and find y(t) by taking the inverse Laplace transform.

Here, we take L{y} for Y(s) and L{y''} and L{y'} for s²Y(s) and sY(s) respectively.

L[y′′] − 2L[y] = L[eˣ] s²Y(s) − s⋅y(0) − y′(0) − 2Y(s)

= 1s − 1.0 − 0 − 2Y(s)

= 1s − 1 

We have to rearrange the terms of the above equation in order to get Y(s) on one side.

Y(s) = 1s(s−2)(s−1) = As+Bs−2+Cs−1.

Using partial fraction expansion, A=1, B=1, and C=−2.

So,Y(s) = 1s+(1s−2)−2s−1.

We can write Y(s) as follows.Y(s) = 1s−(1s−2)+2s−1.

Then find the inverse Laplace transform of Y(s) to get the solution y(t).

y(t) = L − 1{Y(s)} = L − 1{1s} − L − 1{1s−2} + L − 1{2s−1}

= 1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Therefore, the solution of the given differential equation using Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

To know more about Laplace Transform,

https://brainly.com/question/30401252

#SPJ11

Answer:

Step-by-step explanation:

If you have $2250 as against an inflation rate of 2% every year, this then means that after the first year, the value of your money becomes

2250 * 2% =

2250 * 0.02 = 45

2250 - 45 = $2205

At the end second year

$2205 * 2% =

$2205 * 0.02 = 44.1

$2205 - 44.1 = 2160.9

At end of the third year

$2160.9 - 2% =

$2160.9 * 0.02 = 43.218

$2117.682

And so on, and so forth

Answer:

100

Step-by-step explanation:

Add all of the inches together including the parts you don't see.

one side is 9 inches. there are 8 sides. so 9x8. One side in the box is 7 inches. there are 4 sides. so 7x4.  9x8 + 7x4 is equal to 72 + 28.

72 + 28=100

The probability of a vanilla taffy is given as follows:

P(vanilla) = 0.31.

Hence the probability of a vanilla or banana taffy is given as follows:

P(vanilla or banana) = 0.52.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

When we are given the relative frequencies, we must simply identify the desired outcomes, as follows:

Hence the probability is given as follows:

P(vanilla or banana) = P(vanilla) + P(banana) = 0.52.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

3/5

Step-by-step explanation:

Use Pythagorean  to figure out that the  is 100. Then do 60/100 and simplify

theoremhypotenuse

By using the basic comparison test and limit comparison test for the series: 3Σn=1 to ∞ a₁n³e⁻ⁿ², The number π²/2 is a finite number, and the series 3Σn=1 to ∞ a₁n³e⁻ⁿ² is convergent.

Part 1: We need to identify whether the given series is converging or diverging.

Part II: We can use the basic comparison test to test the convergence of the given series. Let's compare the given series with another series that is easily recognizable and convergent. For

n ≥ 1, a₁n³e⁻ⁿ² > 0

We know that the series Σ a₁n³e⁻ⁿ² is convergent, which means that the sequence of terms must be converging to zero as well. This can be shown using the following limit statement.

lim n→∞ a₁n³e⁻ⁿ² = 0.

By comparing the series with a simpler convergent series, we can prove that the series is convergent. The simpler convergent series can be represented by the expression 3Σn=1 to ∞ 1/n². This series is known as the p-series with p = 2. We can use this series to perform a comparison test.

Let Sn be the nth partial sum of the given series. Thus,

3Σn=1 to ∞ a₁n³e⁻ⁿ² ≤ 3Σn=1 to ∞ 1/n²

Let's evaluate the second series using the formula for the sum of a p-series:

Σn=1 to ∞ 1/n² = π²/6

Thus, 3Σn=1 to ∞ a₁n³e⁻ⁿ² ≤ 3 x π²/6

You can learn more about Convergent at: brainly.com/question/31756849

#SPJ11

If f(5) = 11, f ′ is cοntinuοus, and 6 5 f ′(x) dx = 19, then f(6) = 30.

Tο find the value οf f(6), we can use the Fundamental Theοrem οf Calculus. Accοrding tο the theοrem, if f(x) is cοntinuοus οn an interval [a, b] and F(x) is an antiderivative οf f(x) οn that interval, then the definite integral οf f(x) frοm a tο b is equal tο F(b) - F(a).

Given that f'(x) is cοntinuοus, we can apply the theοrem tο the integral:

∫₅₆ f'(x) dx = f(6) - f(5)

We are given that ∫₅₆ f'(x) dx = 19, and f(5) = 11. Plugging in these values, we have:

19 = f(6) - 11

Tο sοlve fοr f(6), we add 11 tο bοth sides:

f(6) = 19 + 11

f(6) = 30

Therefοre, the value οf f(6) is 30.

To know more about continuous, refer here:

https://brainly.com/question/31523914

#SPJ4

Answer:

x - 12 = 20

Step-by-step explanation:

If I'm wrong do x = 12 - 20

Answer:

this is not a right triangle

Step-by-step explanation:

^  = squared

The formula forthe Pythagorean theorem is    a^+ b^   = c^

If this is a right triangle this must be true

6^ +    8^   =   14^

36 + 64 =  196

100  is not equal to 196

So this is not a right triangle

(a) Approximately 40.13 percent of offices have more than 45 bilingual employees.

(b) Approximately 37.07% of offices have less than 38 bilingual employees.

(c) Approximately 16.55% of offices have between 40 and 45 bilingual employees

Mean (μ) = 42

Standard deviation (σ) = 12

(a) The percentage of offices with more than 45 bilingual employees, we need to calculate the area under the Normal curve to the right of 45.

Z-score for 45 using the formula

Z = (X - μ) / σ

Z = (45 - 42) / 12 Z = 0.25

The Z-score in the Z-table (or use a calculator) to find the corresponding area. The Z-table gives the area to the left of the Z-score, so we need to subtract it from 1 to get the area to the right.

From the Z-table, the area to the left of 0.25 is approximately 0.5987. Therefore, the area to the right of 0.25 is 1 - 0.5987 = 0.4013.

So, approximately 40.13% of offices have more than 45 bilingual employees.

(b) The percentage of offices with less than 38 bilingual employees, we need to calculate the area under the Normal curve to the left of 38.

The Z-score for 38 using the formula

Z = (X - μ) / σ

Z = (38 - 42) / 12 Z = -0.3333

The Z-score in the Z-table to find the corresponding area.

From the Z-table, the area to the left of -0.3333 is approximately 0.3707.

So, approximately 37.07% of offices have less than 38 bilingual employees.

(c) The percentage of offices with between 40 and 45 bilingual employees, we need to calculate the area under the Normal curve between these two values.

The Z-scores for 40 and 45 using the formula

Z1 = (X1 - μ) / σ

Z2 = (X2 - μ) / σ

Z1 = (40 - 42) / 12

Z1 = -0.1667

Z2 = (45 - 42) / 12

Z2 = 0.25

The Z-scores in the Z-table to find the corresponding areas.

From the Z-table, the area to the left of -0.1667 is approximately 0.4332. From the Z-table, the area to the left of 0.25 is approximately 0.5987.

The area between these two Z-scores, we subtract the smaller area from the larger area: 0.5987 - 0.4332 = 0.1655

So, approximately 16.55% of offices have between 40 and 45 bilingual employees.

To know more about percent click here :

https://brainly.com/question/5983152

#SPJ4

False. Type II error and power are complementary probabilities. The power of a statistical test is the probability of rejecting the null hypothesis when it is false (i.e., correctly detecting a significant effect or difference).

On the other hand, the type II error is the probability of failing to reject the null hypothesis when it is false (i.e., failing to detect a significant effect or difference).

Therefore, if the probability of committing a type II error is 0.20, then the power of the test is 1 - 0.20 = 0.80. This means that there is an 80% chance of correctly detecting a significant effect or difference.

However, we cannot determine the power of a statistical test from the probability of committing a type II error alone. We would need additional information such as the sample size, effect size, alpha level, and variability to calculate the power of the test.

Learn more about power are complementary probabilities  from

https://brainly.com/question/30664353

#SPJ11

Answer:

13 hypotenuse

12 adjacent

5 opposite

Answer:

im guessing 6 is your base and your height is 15 3/4.

Formula of a triangle we must remember:

BH x 1/2 (basically dividing by 2)

94.5 (fraction form will be: 94 1/2)

94.5 divided by 2 = 47.25 <---------- decimal form

94 1/2 divided by 2 = 47 1/4 <------- fraction form

The given identities can be verified using basic rules of exponentials and algebra. Here are the steps to verify the given identities:

(a) 1 = ∑_(n=1) ^∞▒〖10^(x)+2(-1) ^nln⁡(x)〗0

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n. ∑_(n=1)^∞▒10^(x) = 10^x+10^x+...= (2/3) (10^x) (odd terms only)∑_(n=1)^∞▒〖(-1)^nln⁡(x)〗= ln(x)-ln(x)+ln(x)-ln(x)+...= (0) (even terms only)

Thus, we have 1= (2/3) (10^x) + (0) = (2/3) (10^x) (b) e^x = ∑_(n=1) ^∞▒〖10^x+2n(x)〗

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.

∑_(n=1) ^∞▒10^(x) = 10^x+10^x+...= (1/2) (10^x) (even terms only) ∑_(n=1) ^∞▒〖2n(x)〗= 2(x)+2(2x) +2(3x) +...= 2x (1+2+3+...) = -x/(-1) ^2= -x

Thus, we have e^x= (1/2) (10^x) - x(c) e^(-x) = ∑_(n=1) ^∞▒〖10^x+2(-1) ^nln⁡(x)〗0

We can use the same series from part (a) with x replaced by -x.

Thus, we have e^(-x) = (2/3) (10^(-x)) + (0) = (2/3) (1/10^x)

Similarly, e^x= (2/3) (10^x) Subtracting these two equations, we get: e^x - e^(-x) = (2/3) (10^x + 1/10^x) (answer) (d)

Cosh x = ∑_(n=0) ^∞▒〖10^x+2n(x)〗

Similar to part (b), we have two series, one for even values of n, and one for odd values of n.∑_(n=0)^∞▒10^(x) = 1+10^x+10^x+...= (1/2) (10^x) (even terms only)∑_(n=0)^∞▒〖2n(x)〗= 0+2x+2(2x)+2(3x)+...= 2x (1+2+3+...)= 2x(1/(-1)^2)= 2xThus, we have Cosh(x) = 1 + (1/2) (10^x) + 2x (e^x)(e^x - e^(-x)) / 2= 1 + (1/2) (10^x) + 2x (1 + (2/3) (10^x + 1/10^x)) (answer)(e) Sinh x = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗

Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x+2^3x+2^5x+...= 2x(1+2^2+2^4+...)= 2x(2^0+2^2+2^4+...)= 2x(1/ (1-2^2))= -2x/3Thus, we have Sinh(x) = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x/3 (answer)

To know more about exponentials refer to:

https://brainly.com/question/12626186

#SPJ11

Answer:

12 feet

Step-by-step explanation:

Answer:

The answer is 25 i got it right!!!

There are 20 red tickets Jeanette drew on each attempt.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

There are 50 tickets in a jar.

And, Each ticket is either red or blue.

Here, Jeanette randomly draws 10 tickets from the jar, counts the number of red tickets, and then replaces the tickets.

She does this 8 times.

Hence, We get;

Mean = 3 + 4 + 6 + 7 + 3 + 4 + 2 + 3 / 8

         = 32 / 8

         = 4

The ratio of the red tickets = 4 / 10 = 2 / 5

Now, Let number of red tickets = x

Hence,

⇒ x / 50 = 2 / 5

⇒ x = 20

Thus, There are 20 red tickets Jeanette drew on each attempt.

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ3

The value of x at which the slope of the tangent line to the given function is equal to 5 is 4. Thus, the correct answer is option (b).

The incline of the digression line to the capability y=x²-3x+2 at some random point (x₀, y₀) on the bend is given by the subordinate of the capability by then. To find the worth of x for which the slant of the digression line is equivalent to 5, we want to separate the given capability and set it equivalent to 5 and afterward tackle for x.

Therefore, let's distinguish the function from x: dy/dx = 2x - 3 Now, we need to set this derivative to 5: 2x - 3 = 5. If we solve for x, we get: 2x = 8x = 4. This means that the value of x at which the tangent line to the given function is equal to 5 is 4. Accordingly, the right response is choice (b).

To know more about tangent line  refer to

https://brainly.com/question/23416900

#SPJ11

Answer & Explanation:

Gross income is the total pay you earn before any reduction and adjustments (taxes, mortgage, etc.).

Net income is the amount of pay you get after taxes and other reductions are taken out of your gross income; it's the money that you "actually get to take home in your pocket with" on the payday.

Answer:

43.5

divide 174 ÷ 4 and you get 43.5

Answer:

Length=45 inches, width=15 inches

Step-by-step explanation:

Length=3w

Width=w

Can be written as 3w+w+3w+w

Combine like terms to get 8w

120/8=15

w=15

Width=15 inches

Length=3(15)=45

Length=45 inches

Answer:

(Refer below:)

Step-by-step explanation:

Because there is no image, here's what I'm going to assume: there are multiple scenarios. Refer to each one below:

1) Where r = 6 and h = 7:

V = Bh

V = (π r²) (h)

V = (6² π) (7)

V = 36π (7)

V = 252π

2) Where r = 7 and h = 6:

V = Bh

V = (π r²) (h)

V = (7² π) (6)

V = 49π (6)

V = 294π

3) Where d = 6 and h = 7:

d = 2r = 6

r = 3

V = Bh

V = (π r²) (h)

V = (3² π) (7)

V = 9π (7)

V = 63π

4) Where d = 7 and h = 6:

d = 2r = 7

r = 3.5

V = Bh

V = (π r²) (h)

V = (3.5² π) (7)

V = 12.25π (7)

V = 87.75π ≈ 269.39

Answer:

27

Step-by-step explanation:

54/27=2

81/27=3

135/27=5

Answer:

Q7  0.2

Q8  0.17

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen when added to the probability that it will not happen is 1

Given that the probability that the bulb will grow is 0.8, the probability it would not grow

= 1 - 0.8

= 0.2

A match may be won lost or drawn

Given that the probability of a win is 0.28 and that of a draw is 0.55, the probability of  a loss

= 1 - (0.28 + 0.55)

= 0.17

Answer:

y1=4

x2=7

y2=-3

The given differential equation is not exact. To determine if a differential equation is exact, we need to check if its partial derivatives satisfy a specific condition.

In this case, the given equation is dy/dx = 9xe^x – y + 6x^2. Let's find the partial derivatives of the expression on the right-hand side with respect to y and x.∂/∂y (9xe^x – y + 6x^2) = -1∂/∂x (9xe^x – y + 6x^2) = 9e^x + 12x

The condition for exactness is that these partial derivatives are equal: ∂/∂y (∂/∂x) = ∂/∂x (∂/∂y). However, in this case, we have -1 ≠ 9e^x + 12x, which means the equation is not exact.As the equation is not exact, we cannot directly solve it by finding a potential function. Other methods, such as using integrating factors or applying specific techniques for solving non-exact equations, may be required.

Learn more about  partial derivatives click here: brainly.com/question/32554860

#SPJ11

Answer:

20 x 4 = 60

Step-by-step explanation:

because it's says how many

Answer:

18 maybe

Step-by-step explanation:

it's either 20,19,or 18

but the secretary is the third to be elected so the answer is 18 maybe and if that doesn't work try one of the others trust me it's one of them.

hope this helps

Answer:

True

Step-by-step explanation:

That graph below is a parabola that can be a function for example f(x)=x^2+3x-12 is a graph of a parabola

Hope that helps :)

Answer: [tex]4\times 3.5\ ft^2[/tex]

Step-by-step explanation:

Given

area of the rectangle is [tex]A=14\ ft^2[/tex]

Suppose width is given by w

So, length is [tex]l=2w-3[/tex]

The area of a rectangle is [tex]A=l\times w[/tex]

putting values

[tex]\Rightarrow A=(2w-3)w\\\Rightarrow 14=2w^2-3w\\\Rightarrow 2w^2-3w-14=0\\\Rightarrow 2w^2-7w+4w-14=0\\\Rightarrow w(2w-7)+2(2w-7)=0\\\Rightarrow (2w-7)(w+2)=0\\\\\Rightarrow w=\dfrac{7}{2}\ ft[/tex]

length is [tex]l=4\ ft[/tex]