What type of solution set will this have?

Answer:

[tex]\frac{3s^2-4}{s(s^2-4)}[/tex]

Step-by-step explanation:

Here, the question is to find the Laplace transformation of [tex]f(t)[/tex]

where, [tex]f(t)=(e^t-e^{-t})^2[/tex]

We know that for [tex]t>0[/tex],  [tex]\mathcal{L}\{f(t)\} =\int_0^{\infty} e^{-st}f(t)dt[/tex]

[tex]\mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{-st}e^{at}dt[/tex]

[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{(a-s)t}dt[/tex]

[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\left[\frac { e^{(a-s)}}{a-s}\right]_0^{\infty}[/tex]

[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\frac { 1}{s-a}\cdots(i)[/tex]

Here, we have [tex]f(t)=(e^t-e^{-t})^2[/tex]

[tex]\Rightarrow f(t)=(e^t)^2+(e^{-t})^2-2(e^t)(e^{-t})[/tex]

[tex]\Rightarrow f(t)=e^{2t}+e^{-2t}-2e^{0t}[/tex]

So, the laplace transformation of [tex]f(t)[/tex] is

[tex]\mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}+e^{-2t}-2e^{0t}\}[/tex]

[tex]\Rightarrow \mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}\}+\mathcal{L}\{e^{-2t}\}+\mathcal{L}\{e^{0}\}[/tex]

Now, using equation[tex](i)[/tex]

[tex]\mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s-(-2)}+\frac{1}{s-0}[/tex]

[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s+2}+\frac{1}{s}[/tex]

[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{3s^2-4}{s(s^2-4)}[/tex]

Hence, the Lapelace transformation of [tex]f(t)=(e^t-e^{-t})^2[/tex] is

[tex]\frac{3s^2-4}{s(s^2-4)}[/tex].

l = 16 feet

w = 3 feet

A = l×w

l = 10+2w

48 = (10 + 2w)w

48 = 10w + 2w² | : 2

24 = 5w + w²

w² + 5w - 24 = 0

w² + 8w - 3w - 24 = 0

w(w + 8) - 3(w + 8) = 0

(w - 3)(w + 8) = 0

w - 3 = 0 => w = 3 feet

w + 8 = 0 => w = - 8 ∉ N

l = 10 + 2w

l = 10 + 6

l = 16 feet

A = l×w = 16ft×3ft = 48ft²

Answer:

Option B.

Step-by-step explanation:

The given equation is

[tex]17h+6=40[/tex]

We need to find the property of equality to move the constant term to the right side of the equation.

In the given equation 6 is the constant term on the left side.

Using subtraction property of equality, subtract 6 from both sides.

[tex]17h+6-6=40-6[/tex]

[tex]17h=34[/tex]

So, the appropriate property of equality to move the constant term to the right side of the equation is Subtraction Property of Equality.

Therefore, the correct option is B.

Answer: [tex]\chi^2[/tex] test statistic.

Step-by-step explanation:

The chi-square ([tex]\chi^2[/tex]  ) test is a non-parametric statistical test(also known as Goodness of fit test) which is used to determine if a distribution of observed frequencies differs from the expected frequencies.

Chi-square statistic uses either nominal (categorical) or ordinal level data.

Hence, When determining how well an observed set of frequencies fits an expected set of frequencies, the test statistic is [tex]\chi^2[/tex] test statistic.

Answer:

3

Step-by-step explanation:

The number line is showing x>3.

If the circle were closed it would be x≥3.

Answer:

3.

Step-by-step explanation:

Answer:

I am almost positive it is 9.729

Step-by-step explanation:

my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.

Answer: 9.729

Step-by-step explanation:

my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.

Answer:

x = 145

Step-by-step explanation:

If we look at the right triangle with sides of 24 and 30, we can find the missing leg using the Pythagorean Theorem. If we look carefully, we notice that 18:24:30 is basically the 3:4:5 Pythagorean Triple multiplied by 6, so the missing side is 18. If we look at the right triangle with sides of x and 24, we can find the missing side by calculating 161 - 18 = 143. Using the Pythagorean Theorem, we know that 143² + 24² = x² so x = 145.

Answer:

Step-by-step explanation:

Given the amount invested for a particular period of time at an interest rate, the equation that can model the Interest achieved on investment is expressed using the simple interest formula as shown;

Simple Interest = PRT/100 where;

P is the principal (amount invested)

R is the rate (in %)

T is the time (in years)

From the equation I = PRT/100, we need to express tht time T as a function of the rest of the variable as shown;

I = PRT/100

cross multiply

100I = PRT

Divide both sides by PR

100I/PR = PRT/PR

100I/PR = T

Hence the the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is expressed as

T = 100I/PR

Answer:

4

Step-by-step explanation:

Easiest way to remember absolute value is the number always comes out positive.

l-4l=4

Answer:

the answer is 4

Step-by-step explanation:

the absolute value means it doesn't consists of any sign (neither positive nor negative)

Answer:

B.  7

Step-by-step explanation:

|3x – 1| =

= |3(-2) - 1|

= |-6 - 1|

= |-7|

= 7

Answer: B.   7

Answer:

The answer is B (60)

Step-by-step explanation:

The formula for area is L x W, since they claim the base is 12in and even state teh length is 10in all that is needed is to multiply 12 x 10 to get 120. The area of the window is 120 inches. and half of 120 is 60 Area articulates  the space occupied by a flat shape or the surface of an object. The answer is B

The area of the window will be 60 square inches. Then the correct option is B.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.

A small window in a barn is shaped like a parallelogram. The height of the window is half the length of the base of the window.

The formula for area is L x W, since they claim the base is 12in and even state the length is 10 in all that is needed is to multiply 12 x 10 to get 120.

The area of the window is 120 inches and half of 120 is 60 Area articulates the space occupied by a flat shape or the surface of an object.

The area of the window will be 60 square inches. Then the correct option is B.

More about the parallelogram link is given below.

https://brainly.com/question/1563728

#SPJ2

Answer:

x = -3

Step-by-step explanation:

16x − 4 + 5x = -67

Combine like terms

21x -4 = -67

Add 4 to each side

21x-4+4 = -67+4

21x = -63

Divide each side by 21

21x/21 = -63/21

x = -3

Answer:

[tex]\huge \boxed{x = -3}[/tex]

Step-by-step explanation:

[tex]16x - 4 + 5x = -67[/tex]

Combine like terms.

[tex]21x - 4 = -67[/tex]

Add 4 to both sides.

[tex]21x = -63[/tex]

Divide both sides by 21.

[tex]x = -3[/tex]

Answer:

Hey there!

For the first one:

Chips: x

Pretzels: 3x

Nachos: 3x-2

Total snacks: x+3x+3x-2=7x-2

For the second one:

In the equation, 150+5d, 150 represents the starting amount of money, in this case, 150 dollars. 5d means that for every day, five dollars get put into his account.

For the third one:

In this equation, 1.50 represents to initial fee, and 2.25m represents the cost per mile. Dividing by 2 gives us what each person in the cab pays.

Let me know if this helps :)

Answer:

The answer is nonexistent

Step-by-step explanation:

Answer:

The probability that a randomly selected day in April will be rainy or windy is 0.62 or 62%.

Step-by-step explanation:

We are given that the probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%.

And we have to find the probability that a randomly selected day in April will be rainy or windy.

Let the probability of rain on any day in the month of April = P(A) = 0.34

The probability of windy on any day in the month of April = P(W) = 0.38

The probability of both windy and rainy on any day in the month of April = P(R [tex]\bigcap[/tex] W) = 0.10

Now, the probability that a randomly selected day in April will be rainy or windy is given by = P(R [tex]\bigcup[/tex] W)

        P(R [tex]\bigcup[/tex] W) = P(R) + P(W) - P(R [tex]\bigcap[/tex] W)

                        = 0.34 + 0.38 - 0.10

                        = 0.62 or 62%

So, the probability that a randomly selected day in April will be rainy or windy is 62%.

Answer:

p: x = 4  

q: y = -2

If p happens then q will also happen

Step-by-step explanation:

Given two propositions, we want to rearrange them in a conditional statement.

The correct answer is:

p → q

First, a conditional statement is something of the form:

If [Hypothesis] then [Conclusion]

So, if the first part is true, then the second part must be true.

Now, here we have two propositions:

p: "x  = 4"

q: "y = -2"

We want to write:

"if x = 4, then y = -2"

this is just written as: "p implies q" or:

p → q

Where "→" means "then", and the initial "if" is tacit.

If you want to learn more, you can read:

https://brainly.com/question/10714086

Options :

A) 50t + 60t =4002

B) (50t)2+(60t)2 = 4002

C) 50t + 60t = 400

C) 50t2 + 60t2 = 4002

Answer:

400^2 = (50*t)^2 + (60*t)^2

Step-by-step explanation:

Given the following :

Ms. Ironperson:

moves due east

Speed = 50 mph

Rate of travel = 50t

Let time taken = t ; hence Distance covered with respect to time = ( 50 * t) = 50t

Mr. Thoro

moves due South

Speed = 60 mph

Rate of travel = 60t

Let time taken = t ; hence Distance covered with respect to time = ( 60 * t) = 50t

They are moving at right angle from each other, thus, we can apply Pythagoras rule ;

The displacement between them will be = 400 miles which is the hypotenus

From Pythagoras :

Hypotenus^2 = opposite^2 + Adjacent^2

Displacement = distance 1 + distance 2

400^2 = (50*t)^2 + (60*t)^2

Answer:

55mph . None of the options are correct

Step-by-step explanation:

If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;

v is the speed

t is the time taken

Hence;

v = k/t with k being the constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:

55 = k/5

Cross multiply

k = 55*5

k = 275

Hence, to calculate the speed it will Martin to  drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t  as shownl

v = 275/5

v = 55 mph

Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.

Answer:

c

Step-by-step explanation:

Answer:

The slope is the inclination of a surface or a line with respect to the horizontal. It can be measured at an angle in degrees, radians or grades or even in percentage, that is to say according to the height to length ratio multiplied by 100.

Step-by-step explanation:

6.458 = 6 + 0.4 + 0.05 + 0.008

Each blank slot is filled with a digit from the original number. The zeros are placeholders to make sure we have the right alignment.

Answer:

Step-by-step explanation:

6.458

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

6.000

0.400

0.050

0.008

6.458 = 6.000 + 0.400 + 0.050 + 0.008

trailing zeros can be omitted

Answer:

Hey there!

There are 13 clubs in a deck of cards.

There are 4 tens.

However, the tens overlap with the clubs, so there are 16 cards to choose.

16/52=4/13

Let me know if this helps :)

The events are mutually inclusive. Option B is correct because the required probability is [tex]\dfrac{4}{13}[/tex].

Important information:

A deck of cards has total 52 cards, which includes 4 suits and each suit has 13 cards. If S be the sample space, then n(S) = 52.

Let A be the event that the card is a club card and B be the event that it is a ten card.

The number of club cards is 13. So, n(A) = 13.

There are 4 cards of 10. So, n(B) = 4.

One ten card is of club. So, [tex]n(A\cap B)=1[/tex].

Since [tex]n(A\cap B)=1\neq 0[/tex], therefore the events are mutually inclusive.

The number of club or a ten card is:

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

[tex]n(A\cup B)=13+4-1[/tex]

[tex]n(A\cup B)=16[/tex]

Now,

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]P(A\cup B)=\dfrac{16}{52}[/tex]

[tex]P(A\cup B)=\dfrac{4}{13}[/tex]

Therefore, the probability of choosing a card from a deck of cards that is a club or a ten is [tex]\dfrac{4}{13}[/tex]. Hence, option B is correct.

Find out more about 'Probability' here:

https://brainly.com/question/15944614

Answer:

  3/4

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by its reciprocal.

  [tex]\dfrac{2}{5}\times\dfrac{5}{4}\div\dfrac{2}{3}=\dfrac{2}{5}\times\dfrac{5}{4}\times\dfrac{3}{2}\\\\=\dfrac{(2)(5)(3)}{(2)(5)(4)}=\boxed{\dfrac{3}{4}}[/tex]

Answer:

1 solution; (1,4)

Step-by-step explanation:

Whenever two lines intersect, their solution is the point that the two share in common. Here, it's (1,4), so that is the answer.

Answer:

4,130

Step-by-step explanation:

4780-650=4130 ft

Greetings from Brasil...

We have to remember 2 details:

→ When X = 0, the function intersects the Y axis

→ When Y = 0, the function intersects the X axis

So

1: X = 0

Y = X + 5

Y = 0 + 5

Y = 5

X = 0 and Y = 5 ⇔ (0; 5)

2: Y = 0

Y = X + 5

0 = X + 5

X = - 5

Y = 0 and X = - 5 ⇔ (- 5; 0)

Then the point at which the graph intersects the X and Y axis will be

(0; 5) and (- 5; 0)

Answer: Choice C) 4

=========================================

Work Shown:

Set the denominator equal to zero and solve for x

4x-16 = 0

4x-16+16 = 0+16 ... add 16 to both sides

4x = 16

4x/4 = 16/4 ... divide both sides by 4

x = 4

--------

If x = 4, then the denominator is 0

4x-16 = 4(4)-16 = 16-16 = 0

So this x value is what we exclude from the domain to avoid a division by zero error.

Answer:

Step-by-step explanation:

[tex]\frac{67+72+63+77+59+75}{6} \\\\\frac{413}{6} \\\\68.833333 or 68.8[/tex]