please help im so confused ):

Answer:

x  ⪯ 7

Step-by-step explanation:

5 + 2 = 7

The solution to the given differential equation is L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

To solve the differential equation using the convolution theorem, we'll follow these steps:

Take the Laplace transform of both sides of the differential equation.

Use the convolution theorem to simplify the resulting expression.

Take the inverse Laplace transform to obtain the solution in the time domain.

Let's start with step 1:

Given differential equation: d²y/dt² - 4y = t cos 2t

Taking the Laplace transform of both sides, we get:

s²Y(s) - sy(0) - y'(0) - 4Y(s) = L{t cos 2t}

Where Y(s) represents the Laplace transform of y(t), y(0) is the initial condition for y(t) at t = 0, and y'(0) is the initial condition for dy/dt at t = 0.

The Laplace transform of t cos 2t can be found using the Laplace transform table:

L{t cos 2t} = -Im{d/ds[1 / (s² - (2i)²)]}

= -Im{d/ds[1 / (s² + 4)]}

= -Im{(-2s) / [(s² + 4)²]}

= 2Im{(s) / [(s² + 4)²]}

Now let's simplify the expression using the convolution theorem:

The Laplace transform of the convolution of two functions, f(t) and g(t), is given by the product of their individual Laplace transforms:

L{f * g} = F(s) G(s)

In our case, f(t) = y(t) and g(t) = 2Im{(s) / [(s² + 4)²]}.

Therefore, F(s) = Y(s) and G(s) = 2Im{(s) / [(s² + 4)²]}.

Multiplying F(s) and G(s), we get:

Y(s) G(s) = Y(s) 2Im{(s) / [(s² + 4)²]}

Now, we can rewrite the left-hand side of the equation using the convolution theorem:

Y(s) * 2Im{(s) / [(s² + 4)²]} = L{t cos 2t}

Taking the inverse Laplace transform of both sides, we have:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{L{t cos 2t}}

Simplifying the right-hand side using the inverse Laplace transform table, we get:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = t sin 2t / 4

Now, we can apply the convolution theorem to the left-hand side of the equation:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{Y(s)} * L⁻¹{2Im{(s) / [(s² + 4)²]}}

The inverse Laplace transform of 2Im{(s) / [(s² + 4)²]} can be found using the inverse Laplace transform table:

L⁻¹{2Im{(s) / [(s² + 4)²]}} = 1 / 2b³ (sin bt - bt cos bt)

Therefore, we have:

L⁻¹{Y(s)} * 1 / 2b³ (sin bt - bt cos bt) = t sin 2t / 4

From this, we can deduce the inverse Laplace transform of Y(s):

L⁻¹{Y(s)} = (t sin 2t / 4) / (1 / 2b³ (sin bt - bt cos bt))

Simplifying further:

L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

This is the solution to the given differential equation.

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Step-by-step explanation:

X - 4 = 0

X = 4

X - 2 = 0

X = 2

So the values of x are 2 and 4

Therefore, the probability that at least half of them must wait for more than 10 minutes is approximately \(1.137 x 10^-13.\)

Additionally, using relevant terms from the question in the answer is helpful.

Explanation:Given that waiting times at a service counter in a pharmacy are exponentially distributed with a mean of 10 minutes, we are to approximate the probability that at least half of the 100 customers must wait for more than 10 minutes.P(X > 10) is the probability of a customer waiting for more than 10 minutes.\(P(X > 10) = 1 - P(X < 10)P(X < 10) = 1 - P(X > 10) = 1 - e^(-10/10) = 1 - e^-1 = 0.632\)

Therefore, \(P(X > 10) = 1 - 0.632 = 0.368\)Thus, P(at least 50 customers wait for more than 10 minutes) =

\(P(X > 10)50 = 0.368^50 = 1.137 x 10^-13.\)

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The capacity of the mug is given by M = 1 7/8 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the amount of mug filled = ( 1/5 ) of the full amount M

Now , the mug contains 3/8 of a cup of water

So , the equation is

( 1/5 )M = ( 3/8 ) of a cup

Multiply by 5 on both sides , we get

M = 15/8 of a cups

M = 1 7/8 cups

Hence , the capacity of the mug is 1 7/8 cups

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Answer:

24

Step-by-step explanation:

16 +8 = 24  I got this answer by  4  X 4 = 16 +8 So Ms.Dantes  has 24 brownies now.

Answer:

the error is ( 4-17) is equal -13 not 13

so if she used - 13 the right answer is 17/34

Step-by-step explanation:

see attached

hope it helps

The values of the samples are:

a.) P(y₁<=3/4, y₂<=3/4) = 7/8

b.) P(y₁<=1/2, y₂<=1/2) = 1/2

For this case we have two random variables Y1 and Y2, the joint density function is given by:

f(y₁,y₂(=2, ≤ y₁ ≤ 1, 0 ≤ y₂ ≤y₂, 0 ≤ y₁+y₂ ≤1

And 0 for other case.

We know that Y₁+Y₂≤1

Let Y1 =X and Y2 =Y we can plot the joint density function. First we need to solve the slope line equation from the condition y₁+y₂≤1

And we got that y₂≤1 - y₁ or equivalently in our notation y ≤ 1-x . And we know that the two random variables are between 0 and 1. So then the joint density plot would be given on the figure attached.

Part a

In order to find the probability that:

P(Y₁<=3/4, Y₂<=3/4) we can use the second figure attached.

We see that we have two triangles with the same Area, on this case  

A = bh/2 = 1/4×1/4/2 and then the total area for both triangles is

At = 2 ×1/4×1/4/2

Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :

Vt = 2 ×  2 ×1/4×1/4/2

And then we can find the probability like this:

P(Y₁<=3/4, Y₂<=3/4) = 1 -  2 ×  2 ×1/4×1/4/2

= 7/8

Part b

For this case w want this probability:

P(Y₁<=1/2, Y₂<=1/2)  we can use the third figure attached.

We see that we have two triangles with the same Area, on this case  

A = bh/2 = 1/2×1/2/2 and then the total area for both triangles is

At = 2 ×1/2×1/2/2

Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :

Vt = 2 ×  2 ×1/2×1/2/2

And then we can find the probability like this:

P(Y₁<=1/2, Y₂<=1/2) = 1 -  2 ×  2 ×1/2×1/2/2

= 1/2

Hence we get the required answer.

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Answer:

14/3

Step-by-step explanation:

3 1/3 x 1 2/5 = 10/3 x 7/5

10/3 x 7/5 = 70/15, which simplifies to 14/3.

The point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Let’s plot the given points E, F and G on the graph and try to find the missing point H:

Now, the length of the side EF will be:

EF = √((3-1)² + (5-5)²)EF = 2 units

The length of the side FG will be:

FG = √((6-3)² + (1-5)²)FG = √10 units

The length of the side EG will be:

EG = √((6-1)² + (1-5)²)EG = √26 units

Therefore, the total length of the three sides of the fence will be:2 + √10 + √26 units

Now, the perimeter of the fenced area with 4 sides EFGH is:16 = 2 + √10 + √26 + EHThe length of EH will be:

EH = 16 - 2 - √10 - √26EH = 11.60 units

We need to plot the missing point H which is at a distance of 11.60 units from point E along the line passing through points E and F.

Using the slope formula we find that the slope of the line passing through points E and F is: m = (y2 - y1)/(x2 - x1) = (5 - 5)/(3 - 1) = 0Therefore the line passing through E and F is a horizontal line as it has zero slope.

The distance between points E and H is 11.60 units and point H will be on the same horizontal line passing through E and F.Therefore, the x-coordinate of point H will be:

EH = √((x2-x1)² + (y2-y1)²)11.60 = √((x-1)² + (5-5)²)

Solving the above equation:

(x-1)² = 134.56(x-1)

= ±√134.56x

= 1 + √134.56 or x = 1 - √134.56

Therefore, the point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

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Answer:

1.15 miles

Step-by-step explanation:

Answer:

<A obtuse

<B acute

<C obtuse

<D right

Step-by-step explanation:

22) The volume of the cylinder in terms of π is: 243π ft³

23) The area of the shaded segment is: 22cm²

22) The volume of the cylinder is given by the formula:

V = πr²h

where:

r is radius

h is height

From the attached image, we can say that the volume of the cylinder is:

V = π(4.5)² * 12

V = 243π ft³

23) The area of the shaded segment is:

A = r²/2(π/180 * D - sin(D))

Thus:

A = 6²/2(π/180 * 120 - sin(120))

A = 22cm²

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Answer: a. (-2, -2)

Step-by-step explanation:

The point at which the two lines intersects is at (-2, -2), which is the solution.

Answer:

The value is -10

Step-by-step explanation:

Based on the information given the required production is 13,000 units.

Using this formula

Required production=Budgeted sales units+Ending inventory units-Beginning inventory units

Let plug in the formula

Required production=10,000 units+5,000 units-2,000 units

Required production=13,000 units

Inconclusion the required production is 13,000 units.

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Answer:

Last option) 3

Step-by-step explanation:

For having no real solutions, discriminant of this equation must be be less than 0.

D=\(\sqrt{b^{2}-4ac }<0\)

b²-4ac<0

b²<4ac

b²/4a<c

c>b²/4a

c>\(\frac{(-4^{2} )}{8}\)

c>16/8

c>2

Answer:

t=-3

Step-by-step explanation:

2x²-4x-t=0

disc=b²-4ac=(-4)²-4×2×(-t)=16+8t

it has no solution if 16+8t<0

8t<-16

t<-2

so t=-3

2.

\(\sqrt{x-a} =x-4\\if a=2\\\sqrt{x-2} =x-4\\squaring\\x-2=x^2-8x+16\\x^2-9x+18=0\\\)

x²-6x-3x+18=0

x(x-6)-3(x-6)=0

(x-6)(x-3)=0

x=6,3

when x=6

√(6-2)=6-4

√4=2

2=2

when x=3

√(3-2)=3-4

√1=-1

1=-1

which is not true.

Hence x=3 is an extraneous solution.

x=6 is real solution.

Answer:

$18

Step-by-step explanation:

You Should Divide The Total Miles (300) Needed To Drive by 20 which is the miles per gallon number. You would get 15. You would then multiply 15 by 1.2 or $1.20 TO GET $18.

HOPE THIS IS HELPFUL✔

Answer: 360 dollars for 300 miles

Answer:

bvs rverve wber

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The number of ways of 3 volumes chosen at random is 455.

The number of ways that will include volume 1 and volume 2 is 13 and

The number of ways that will include volume 1 but not volume 2 is 156

Permutation and combination

In Mathematics, Permutation and combination are the ways of representing a group of objects by selecting from a set and forming subsets. These define the different types of ways to arrange a certain group of data.

When we select objects from a group, it is said to be permutations, whereas the combination is a way of selecting items, here the order of selection does not matter.

The formula for the combination of x things from a set of n things without replacement is given by

Here we have,

Number of volumes of  an encyclopedia = 15

Number volumes were chosen at a time = 3

From above formula

The number of ways of 3 volumes is chosen at random is

¹⁵C₃ = 15!/3!(15 - 3)!  

= 15!/3!(12)!  

= 15 × 14 × 13 × 12! / 6 (12!)

= 455  

(b) Including volume 1 and volume 2

To Include volume 1 and volume 2 in the set, first, we choose volume 1 and volume 2, and then we must choose the 3rd volume from the remaining volumes from 3 to 15 volumes [total 13 volumes].

Therefore the number of ways that will include volume 1 and volume 2

= 1 × 1 × 13 = 13  

(c) Including volume 1 but not volume 2

Here we are including volume 1 but not volume 2, for that in the first place we chose volume 1, for the second and third place we must choose from the remaining volumes 3 to 15 [total 13 volumes except 2 ]

The number of ways that will include volume 1 but not volume 2

= 1 × 13 × 12

= 156

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Answer:

  (c)  the converse of the original conditional statement

Step-by-step explanation:

If a conditional statement is described by p→q, you want to know what is represented by q→p.

For the conditional p→q, the variations are ...

As you can see from this list, ...

  the converse of the original conditional statement is represented by q→p, matching choice C.

__

Additional comment

If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.

<95141404393>

Answer: variable x = -36

Step-by-step explanation:

Given that \(- 1 = 5 + \frac{x}{6}\), we can get \(5+\frac{x}{6} =-1\)

Subtract 5 from both sides: \(\frac{x}{6} =-6\)

Multiply both sides by 6: x=  -36

So the variable x equals - 36.

Translation, rotation, and reflection are three of the fundamental transformations.

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Answer: The solution for w, expressed as a natural logarithm, is:

w = ln(88/3) / 5

Step-by-step explanation: Starting with the given equation:

-3e^(5w) = -88

Dividing both sides by -3:

e^(5w) = 88/3

Taking the natural logarithm of both sides:

ln(e^(5w)) = ln(88/3)

Using the property that ln(e^x) = x:

5w = ln(88/3)

Finally, solving for w by dividing both sides by 5:

w = (1/5)ln(88/3)

So the solution for w, expressed as a natural logarithm, is:

w = ln(88/3) / 5

Answer:

y = -3/4x + 36

Step-by-step explanation:

In slope-intercept form, (y = mx + b), m is the slope and b is the y intercept. The slope is the rise/run. You can count from one point to another that you move down 3 and to the right 4. So your rise/run is -3/4.

The y-intercept is 36, because that is where the line crosses the y-axis.

So you can substitute the values into the equation:

y = mx + b

y = (-3/4x) + (36)

y = -3/4x + 36

Answer:

see graph

Step-by-step explanation:

The function that is shown below is the graph of the given function \(y = log_{4}(x+3)\) .

"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."

The given function is:

\(y = log_{4}(x+3)\)

For \(x = -2\), \(y = log_{4}(-2+3) = log_{4}1 = 0\)

For \(x = -1\), \(y = log_{4}(-1+3) = log_{4}2 = 0.5\)

For \(x = 0\), \(y = log_{4}(0+3) = log_{4}3 = 0.793\)

For \(x = 1\), \(y = log_{4}(1+3) = log_{4}4 = 1\)

For \(x = 2\), \(y = log_{4}(2+3) = log_{4}5 = 1.161\)

By putting the values of (x, y) in the graph, we get the graph of \(y = log_{4}(x+3)\).

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Binary integer variables are variables whose values consist of two values, 0 and 1.

Correct answer will be :- b. Variables with values 0 and 1.

These values are also known as bits, which are represented as 0 and 1 in computers. Binary integer variables are used in computing as a way to represent numbers, characters, and instructions. Binary integer variables are used to represent information in digital systems, because they can be used to represent any value with a single bit.

For example, a single bit can represent a number, letter, or instruction. Binary integer variables are also used in computer programming, as they can be used to represent boolean values, such as true and false. Additionally, they can be used to represent various types of data, such as numbers, characters, and images.

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Answer: B

in three ways we have;

Explanation:

We want to write the ratio of the situation in three ways, comparing the first quantity to the second quantity.

Given that;

A zoo has 17 monkeys and 12 chimpanzees

so, we want to compare the number of Monkeys to the number of Chimpanzees.

There are 17 Monkeys to 12 Chimpanzees.

Writing in other ways, we have;

and lastly in fraction;

Therefore, in three ways we have;