Someone help and plz make sure it’s right :)

We used Laplace transform to solve the given initial-value problem y' + 6y = e5t, y(0) = 2.

Using Laplace transform, we have:

Let a=5t

L{y'} + 6L{y} = L{eᵃ}

sY(s) - y(0) + 6Y(s) = 1/(s-5)

Substituting y(0) = 2 and solving for Y(s), we get:

Y(s) = 1/(s-5) + (2s + 5)/(s+6)(s-5)

Using partial fraction decomposition, we can simplify this to:

Y(s) = (1/11)(1/(s-5)) + (5/11)(1/(s+6))

Taking the inverse Laplace transform of Y(s), we get:
Let-6t=n
y(t) = (1/11)e^(5t) + (5/11)eⁿ

Therefore, the solution to the initial-value problem is:

y(t) = (1/11)eᵃ + (5/11)eⁿ   answer in 100 words



In conclusion, we used Laplace transform to solve the given initial-value problem y' + 6y = e5t, y(0) = 2. After applying the Laplace transform and solving for Y(s), we simplified it using partial fraction decomposition. Taking the inverse Laplace transform of Y(s) gave us the solution y(t) = (1/11)eᵃ + (5/11)eⁿ

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9514 1404 393

Answer:

  62°

Step-by-step explanation:

The measure of the external angle where the secants meet is half the difference of the arcs they subtend.

  ∠A = (DE - BC)/2

  2×∠A = DE -BC

  DE = BC + 2×∠A

  DE = 38° +2(12°)

  arc DE = 62°

(a) The solutions to the equation a(a + 4) = 3a + 1 are a = (-1 + √5) / 2 and a = (-1 - √5) / 2.

(b) The solutions to the equation (b+1)² = 7b are b = (5 + √29) / 2 and b = (5 - √29) / 2.

(c) The solutions to the equation (c-2)(c+5) = c are c = -2 and c = 5.

(d) The solution to the equation d(d - 4) = 2(d+7) is d = 9.

(a) To solve the equation a(a + 4) = 3a + 1:

Expanding the left side of the equation, we get:

a^2 + 4a = 3a + 1

Bringing all terms to one side of the equation:

a^2 + 4a - 3a - 1 = 0

Combining like terms:

a^2 + a - 1 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

a = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = 1, and c = -1. Substituting these values, we have:

a = (-1 ± √(1^2 - 4(1)(-1))) / (2(1))

a = (-1 ± √(1 + 4)) / 2

a = (-1 ± √5) / 2

Therefore, the solutions to the equation are:

a = (-1 + √5) / 2 and a = (-1 - √5) / 2

(b) To solve the equation (b+1)² = 7b:

Expanding the left side of the equation, we get:

b^2 + 2b + 1 = 7b

Bringing all terms to one side of the equation:

b^2 + 2b - 7b - 1 = 0

Combining like terms:

b^2 - 5b - 1 = 0

This is a quadratic equation, and we can solve it using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

b = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -5, and c = -1. Substituting these values, we have:

b = (-(-5) ± √((-5)^2 - 4(1)(-1))) / (2(1))

b = (5 ± √(25 + 4)) / 2

b = (5 ± √29) / 2

Therefore, the solutions to the equation are:

b = (5 + √29) / 2 and b = (5 - √29) / 2

(c) To solve the equation (c-2)(c+5) = c:

Expanding the left side of the equation, we get:

c^2 + 5c - 2c - 10 = c

Combining like terms:

c^2 + 3c - 10 = c

Bringing all terms to one side of the equation:

c^2 + 3c - c - 10 = 0

Combining like terms again:

c^2 + 2c - 10 = 0

This is a quadratic equation, and we can solve it using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

c = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = 2, and c = -10. Substituting these values, we have:

c = (-(2) ± √((2)^2 - 4(1)(-10))) / (2(1))

c = (-2 ± √(4 + 40)) / 2

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Answer:

The answer is 78 blue jelly beans.

Step-by-step explanation:

Since the ratio is 4:13, and there are 24 green jelly beans, 4 times 6 equals 24. If you do 13 times 6, it equals 78. Hope this helped!

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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Answer:

57 1 and 91 3

Step-by-step explanation:

because there's the number 57 once and 91 3 times

Answer:

\(f=\frac{3+4d}{3+d}\)

Step-by-step explanation:

\(d= \frac{3(1-f)}{(f-4)} \\(f-4)d=3-3f\\f-4=\frac{3-3f}{d} \\f=\frac{3-3f+4d}{d} \\f+\frac{3f}{d} =\frac{3+4d}{d} \\fd+3f=3+4d\\f(d+3)=3+4d\\f=\frac{3+4d}{3+d}\)

Answer:

43 Sets for 650

Step-by-step explanation:

Just do division.

Hope this helps :-)

Answer:

ok

Step-by-step explanation:

12

2

2

2

2

2

3

The circled section represents the outliers in the data.

In the context of the given information, the circled section represents data points that deviate significantly from the majority of the data. Outliers are observations that lie far away from the central tendency of the dataset, and they can have a notable impact on statistical analysis.

In this case, the child who solved the Rubik's Cube in 21.7 seconds is an outlier as their time is significantly lower than the other children. Similarly, the child who took 72 seconds to solve the cube is also an outlier, as their time is much higher than the majority of the children who completed it in around 7 seconds. Outliers can provide valuable insights into the distribution and behavior of the data, and they are often examined separately due to their unique characteristics.

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Simpson's Paradox makes this claim possible.

The phenomenon whereby particular trends are prevalent in small data portions but are not evident or an inverse trend is observed when the portions are joined together is known as Simpson's paradox.

Whereby the data for calculating the batting averages as found online are given as follows:

Season                      Derek Jeter                           David Justice

1995                           12/48 = 0.250                         104/411 ≈ 0.253

1996                           183/582 ≈ 0.314                      45/140 ≈ 0.321

The overall hits to the overall bat's ratio are:

(183 + 12)/(582 + 48) ≈0.310   (104+45)/(411+140) = 0.27

This shows that  Derek Jeter's overall average was better than Justice's average.

Thus, Simpson's Paradox makes this claim possible.

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As per the given average, the team statistician claims Jeter's overall average was better than Justice's average is 0.27

Here we have given that the following table of data is presented

Time,                       Score of Derek Jeter               Score of David Justice

At 1995,                         ≈  0.250                                     ≈ 0.253

At 1996,                          ≈ 0.314                                      ≈ 0.321

Then the overall score for Derek Jeter is calculated by

=>  (183 + 12)/(582 + 48) ≈0.310  

And the overall score for  David Justice is calculated as

=> (104+45)/(411+140) = 0.27

Here the resulting values shows that  Derek Jeter's overall average was better than Justice's average  

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The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

4 / 3

Step-by-step explanation:

tan x = opposite / adjacent

tan x = AB / AC

tan x = 4 / 3

{ x = theta ]

9514 1404 393

Answer:

  tan(θ) = 4/3

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

Then ...

  tan(θ) = AB/AC

  tan(θ) = 4/3

Using calculator, the value of  the angle 5 sin (20 +10°) -4 = 0​ where 0 <x<90 is 17.5 degrees

You should understand that the sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle

The given angle is 5 sin (20 +10°) -4 = 0

To find the angle, first open the bracket to have

5sin(30) - 4 = 0

Collecting like terms to have

5 sin 30 = 4

Dividing both sides by 5 we have

5 sin30/5 = 4/5

This means that sin30 = 0.8

⇒sin30 - 0.8 = 0

⇒ 0.5 -0.8 = 0

-0.3

Therefore sin⁻-0.3 = 17.5⁰

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Answer:

Convenience sample

Step-by-step explanation:

Getting paid to respond

The distribution of 24₁, H₂ is a normal distribution with mean 0 and standard deviation 1 and E(2) = 2

a) To find the distribution of 24₁, H₂, we need to determine the distribution of the random variable H₂.

The random variable H₂ is given as B ~ N(0,1), which means it follows a standard normal distribution.

The random variable 24₁ represents 24 independent and identically distributed standard normal random variables.

Since each variable follows a standard normal distribution, their sum (H₂) will also follow a normal distribution.

Therefore, the distribution of 24₁, H₂ is a normal distribution with mean 0 and standard deviation 1.

b) To find E(2), we need to determine the expected value of the random variable 2.

The random variable 2 is a constant and does not depend on any random variables.

Therefore, the expected value of 2 is simply the value of 2 itself.

E(2) = 2

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According to the question The most appropriate distribution to model the number of hits on a personal website in a week would be the Poisson distribution.

The Poisson distribution is commonly used to model rare events that occur randomly and independently over a fixed interval of time or space. It is characterized by a single parameter, λ (lambda), which represents the average rate of occurrence of the event.

In this case, since hits on a personal website occur quite infrequently with an average of five per week, the Poisson distribution is suitable. The parameter λ would be set to 5, indicating the average rate of hits per week.

By using the Poisson distribution, you can calculate the probabilities of different numbers of hits occurring in a week and make predictions about the website's traffic patterns.

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Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

Answer:

y = -3/4x + 7

Step-by-step explanation:

ok first u need to find the slope so use the slope equation for this (x2 - x1 over y2 - y1) so

1 - 4 = -3

8 - 4 4

so the m is -3/4

now you need to find the y intercept so pick one of the points (let's do (8, 1)) and plug that into the slope intercept form (y = mx+b)

so 1 = -3/4(8) + b

1 = -6 + b

+ 6 + 6

b = 7

so the equation is y = -3/4x + 7. hope this helps

Answer:

D. right

Step-by-step explanation:

f(x) = 4*2^x

g(x) = 4*2^(x-3)

g(x) = f(x - 3), so g(x) is shifted 3 units right.

Step-by-step explanation:

total no of items (n)= 5

median (m) = (n+1)/2 th item

= (5+1)/2 th item

= 6/2 th item

= 3rd item

= 152152152

Step-by-step explanation:

all regular polygons have (n-2)*180 this formula can use here. n= no of sides

Answer:

M = (n-2)*180 degrees for polygons with n sides.

Step-by-step explanation:

As already noted, there is no description of the polygon in question.  However, the formula for the sum of the measure of the interior angles of a regular polygon is M = (n-2)•180 where n is the number of sides.  A triangle has 3 sides, so M = (3-2)*180 = 180 degrees.

A hexagon has 6 sides, so M = (6-2)*180 = 720.

A parallel line would contain the same slope and have a different y-intercept.

Using the slope of the original line you would start with:

Y = -5x + b, where b is the new y-intercept.

Using the given point replace x and y and solve for b:

-9 = -5(-4) + b

Simplify:

-9 = 20 + b

Subtract 20 from both sides

-29 = b

Now replace b in the equation to get:

Y = -5x -29

Answer: ;)

Step-by-step explanation:

    <333

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Equation of line is y = 2/3x + 2

Answer:

36 cm square will be the correct answer

The bucket number 2 will contain 45 after sorting the data.

According to the statement

we have given that the a data list which is sorted into 4 buckets then we have to find he in which the umber 45 is sorted.

So, For this purpose,

The given data list is:

76, 56, 93, 24, 45, 88, 13, 7, 37

And the data is sorted into the buckets so,it is sorted in 4 buckets. and the data contain numbers from 0 to 100.

So, let the sorting.

We know that the 100 numbers are sorted in 4 buckets then it means each bucket contain 25 numbers.

So, let us consider a

BUCKET 1 : 0 to 25

it contains the data number 7, 13,24.

Now,

BUCKET 2 : 25 to 50

it contains the data number 37,45.

Now,

BUCKET 3 : 50 to 75

it contains the data number 56.

Now,

BUCKET 4 : 75 to 100

it contains the data number 76, 88, 93.

From sorting the 45 number sort in the bucket 2.

So,The bucket number 2 will contain 45 after sorting the data.

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Answer:

Solution given:

volume of pyramid =⅓area of base×height

=⅓*1*1*1=⅓=0.33yd³

the volume of the pyramid

0.33yd³