help please kylie solved the following problem incorrectly

Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.

[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]

Integrate by parts with

[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]

By substitution,

[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]

so that for [tex]k=n[/tex], we end up with

[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]

We then have the inverse transform relation

[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]

and so

[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]

Answer:

Not linear

Step-by-step explanation:

Can be written into the form of [tex]y=mx+b\\[/tex].

The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.

An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.

Since the sum of supplementary angles is 180 degrees, hence;

<1 + <3 = 180 degrees

Also <1 + <2 = 180 degrees (sum of angles on a straight line)

<1 = 180 - <3

<1 = 180 - <2

Equate

180 - <3 = 180 - <2

-<3 = -<2

<2 = <3 (corresponding angle)

Since <2 is equivalent to <3, hence the line a is parallel to b

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Answer:

y=4x+9

Step-by-step explanation:

y-Y1= m× x-X1

Y-1 = 4×X+2

y-1 = 4x+8

y=4x+9

Answer:

11

Step-by-step explanation:

A whole number is an integer greater than 0.

-76 , -34 , -57 are all negative so they are not whole numbers.

0 is too small so it also is not a whole number.

By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.

Answer:

0 and 11

Step-by-step explanation:

Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.

Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.

well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]

Answer:

‎

4 + (-125)‎

= 4 - 125‎

= -121‎

‎

Answer:

43°

Step-by-step explanation:

Alternate interior angle are congruent.

The function F(20) is 50

The most common symbols for a function are the letters f, g, and h. A function's value at an element of its domain x is denoted by the notation f(x), and the numerical value obtained from the function evaluation at a specific input value is denoted by substituting that value for x. For instance, the value of f at x = 4 is denoted by the notation f(x) (4). When a function isn't given a name and is instead represented by the expression E, the value of the function at, say, x = 4 may be shown by the notation E|x=4.

Given that :f(x) = 2x + 10

f(x) = 2x + 10

F(20)= 2(20) + 10

F(20)= 40 + 10

F(20)= 50

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Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The equation is given in its point slope form :

[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]

And the general equation in point slope form is :

[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]

by comparing these two, we can get

And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Based on the results of Mean and Median, we can say that Mean is larger than median in value .

Mean of n observations can be calculated using the formula

Mean = (sum of all observations)/(number of observations) .

After arranging the data in ascending or descending order , the middle value can be called as Median .

In the question ,

the set of numbers is given as 4, 5, 11, 12, 5, 38, 44

rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44   .

the sum of all the number = 4+5+5+11+12+38+44

                                           = 119

number of observations = 7

hence the mean = 119/7 = 17

So, mean = 17

from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that

the middle value of the set of numbers is 11 .

So , median = 11 .

On comparing the mean = 17  and the median = 11 ,

we can say that the mean is greater than median.

Therefore , based on the results of Mean and Median, we can say that

Mean is larger than median in value .

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Answer:

yes

Step-by-step explanation:

Answer:

the answer you are looking for is D

Hence the average rate of change, in simplest form is -10 .

What is average rate of change?

Using the coordinate points from the table  ( 4,53) ( 8, 13 )

Substitute the coordinate into the expression

Average rate of change  = y₂ - y₁/x₂ - x₁

                                         = 13 - 53/8 - 4                    

                                         = -  4 0/4 ⇒ -10

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Answer:

a) the answer it 10 so no

b) the answer is −39 so nah

c) the answer is 48, nope

d) the answer is  34, did you mean to write 34 instead of 24?

Step-by-step explanation:

Answer: yes, the value of x is 4 and angle HEB is 36 degrees

Step-by-step explanation:

1a. Find the value of angle CEB

Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees

2a.set up an equation

After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2

3a. Solve the equation

13x+9x+2=90

22x+2=90 | combine like terms

22x=88 | subtract 2 from both sides

x=4 | divide by 22 on both sides

1b. Set up equation

Knowing x=4 and that angle HEB is 9x the equation is 9(4)

2b. Solve the equation

9(4)

36

The value of of slope of is 1/4.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.

Any two distinct places along the line can be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the "vertical change" to the "horizontal change" in each case. The difference between the line's y and x coordinate changes is known as the slope of the line. Net changes in the y and x coordinates are as follows: y = y and x = x.

m = [tex]y_{2} - y_{1} /x_{2} x_{1}[/tex]

m = 1/4

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The measure of each angle is 34.1° and 55.9°

complementary angles are angles that gives 90° when added to together.

if the first angle is x and the other complementary angle is y,

then x+y=90

x= y-21.8

representing y-21.8 for x in equation x+y=90

y+ y-21.8= 90°

2y= 111.8

y= 55.9°

and x= 34.1°

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Answer:

Step-by-step explanation:

8(2+3)

She buy 48 inches of ribbon to have the exact amount that she needs.

Given,

Area of the ribbon = 144 sq. inches

and, We know the formula for side of square is =[tex]\sqrt{Area of a square }[/tex]

Plug the value of area of square in above formula

Side of a Square = [tex]\sqrt{144}[/tex] = 12 inches

Now, we get the side of a square i.e., 12 inches

According to the question:

Sonya wants to sew ribbon along each side of a square pillow.

So, we need to find the perimeter of the square pillow.

and, Perimeter of a square is = 4 x side

=> Perimeter = 4 x 12 = 48 inches.

Therefore, She buy 48 inches of ribbon to have the exact amount that she needs.

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Given,

f(x) = 1x + 12

expression to be in form of h

To find on the interval: [9, 9 + h]

∵ Average rate of change of f(x) on interval (a,b) is

A = f(b) - f(a) / b - a

⇒ f(9) = 1 x 9 + 12 = 21

⇒ f(9 + h) = 9 +h + 12 = 21 + h

⇒ f(b) - f(a) = 21 + h - 21 = h

⇒ (b-a) = 9 + h - 9 = h

∴ Average rate of change = h / h

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The probability of a lizard living for more than 2.5 years is 16%.

The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.

Average lizard u = 3.1,

standard deviation σ = 0.6

To calculate the likelihood of a lizard living for more than 2.5 years;

p(X<2.5)

μ + aσ = 2.5

3.1 + a(0.6) = 2.5

a(0.6) = −0.6

a = −1

To calculate the probability, apply the empirical rule.

The total area = 100% (since total probability always is 1)

Area from  μ to ∞  =  p(X > μ)  = 50%

Area between  (μ−σ)  and  (μ+σ)  = 68%  

Area between  (μ−σ)  and  μ  is  p((μ−σ) < X < μ)  =34%  

Thus,

p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))

                  = 1 − (0.34 + 0.5)

p(X< (μ−σ)) = 0.16  

Therefore, the probability that a lizard will live longer than 2.5 years 16%.

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Answer:

45 levels

Step-by-step explanation:

60% of 75 is 45 i think

Answer:

54 cm

Step-by-step explanation:

A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.

a = edge

Area = 6a to the power of 2

The coordinates of a centroid of a triangle with vertices  [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex]  are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].

Centroid of a triangle

For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.

Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.

Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”

As D is the midpoint of the side LM, we can write,

D = ((x2+x3)/2, (y2+y3)/2)

Now, we know that, G intersects AD in the ratio 2:1 , we get

Hence, using section formula we can write,

The x-coordinates of G will be:-

x = (2(x2+x3)/2 + 1.x1 )/ (2+1) =  (x2+x3+x1)/3  = (x1+x2+x3)/3

The y-coordinates of G will be :-

y =(2(y2+y3)/2 + 1.y1 )/ (2+1) =  (y2+y3+y1)/3 =  (y1+y2+y3)/3

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Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Answer:

Subtract 66.5 from Devon's total to find how much he has left