To find the Laplace transform ℒ{f(t)} of the function f(t) = (et − e^(-t))^2, we can use Theorem 7.1.1, which states that ℒ{t^n} = n! / s^(n+1), where n is a non-negative integer.
Using this theorem, we can simplify the function as follows:
f(t) = (et − e^(-t))^2
= e^2t - 2e^t * e^(-t) + e^(-2t)
= e^2t - 2 + e^(-2t)
Now, let's apply the Laplace transform:
ℒ{f(t)} = ℒ{e^2t - 2 + e^(-2t)}
Using the linearity property of the Laplace transform, we can compute the transform of each term separately:
ℒ{e^2t} = 1 / (s - 2) (using ℒ{e^at} = 1 / (s - a))
ℒ{-2} = -2 / s (using ℒ{1} = 1 / s)
ℒ{e^(-2t)} = 1 / (s + 2) (using ℒ{e^(-at)} = 1 / (s + a))
Now, combining the individual transforms, we have:
ℒ{f(t)} = 1 / (s - 2) - 2 / s + 1 / (s + 2)
Therefore, the Laplace transform of f(t) is ℒ{f(t)} = 1 / (s - 2) - 2 / s + 1 / (s + 2), expressed as a function of s.
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3x^2 - 5x -1 =0
Quadratic Equation
please explain step by step
Answer:
Step-by-step explanation:
Solving 3x2-5x-1 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C number, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -5
C = -1
B2 - 4AC =
25 - (-12) =
37
Applying the quadratic formula :
5 ± √ 37
x = —————
6
√ 37, rounded to 4 decimal digits, is 6.0828
So now we are looking at:
x = ( 5 ± 6.083 ) / 6
Two solutions:
x =(5+√37)/6= 1.847
x =(5-√37)/6=-0.180
Alice and Bob each arrive at a party at a random time between $1:00$ and $2:00$. If Alice arrives after Bob, what is the probability that Bob arrived before $1:30$
The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
According to the question,
Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.
In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.
Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.
s = {(x, y) /1≤x≤2 and 1≤y≤2}
In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.
Formula for Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]
= 1/2
Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
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Lukas paid for a pair of shoes with a $50 bill. After the clerk added 9% tax to the purchase, Lukas received $17.30 in change. What was the price of the shoes, not including the tax?
Answer:
$29.75
Step-by-step explanation:
If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757
Create a linear equation for the following data:
Answer:
[tex]y = -3x+4[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
Step 1: Rate of ChangeA linear equation means that the y value changes at a constant rate as x increases by 1.
To find the rate of change you need to plug 2 ordered pairs into the formula:
[tex]\frac{y1-y2}{x1-x2}[/tex]
(x1,y1) can be any data point on this table. To make it easy, we will make it (2,-2).
(x2,y2) can be any data point other than the previously chosen point. So, we will choose (-1,7).
If we substitute this into the formula, previously mentioned, we get:
[tex]\frac{-2-7}{2-(-1)}[/tex]
When we solve this, we get the rate of change as -3.
This will be the "m" value in the linear equation format:
"y = mx+b"
The b value is the y-value of the data when x = 0.
So to get the b-value, you need to plug in one ordered pair into the "y=mx +b" equation.
"m" was the rate of change, which we found in the previous step.
Let's use (2,-2) as the chosen ordered pair.
By substitution, we end up with:
[tex]-2=-3(2)+b[/tex]
If we solve this out, we get:
[tex]b = 4[/tex]
m was -3 and b is now 4.
So, putting this into the equation "y = mx+b"
We get our answer as [tex]y=-3x+4[/tex].
ASAP help me 30 points
Answer:
large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la
or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues
Identify the root tissues. Record your answer under "Slide 5" on your lab report.
What is the perimeter of the contest area on the judo mat?
(please be quick)
If 5/6 is 180, what is 1/6?
(please answer and explain pls)
[tex] \frac{5}{6} \: of \: a \: number \: is \: 180[/tex]
[tex] \frac{1}{6} \: is \: 5 \: times \: less \: than \: \frac{5}{6} \\ \frac{1}{6} = \frac{180}{5} = 36[/tex]
Two people can paint a house in 14 hours. Working individually one of the people takes 2 hours more than it takes the other person to paint the house. How long would it take each person working individually to paint the house?
( You are supposed to get a quadratic equation and then solve that, but I don't know how to get to it.)
Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, we have that the rates are given as follows:
The together rate is 1/14.The separate rates are 1/d and 1/(d-2).Hence:
[tex]\frac{1}{d} + \frac{1}{d - 2} = \frac{1}{14}[/tex]
[tex]\frac{d - 2 + d}{d(d - 2)} = \frac{1}{14}[/tex]
d² - 2d = 28d - 28.
d² - 30d + 28 = 0
(d - 29)(d - 0.96) = 0.
Both d and d - 2 have to be positive, hence the solution is d = 29, and it would take each person working individually 27 and 29 hours to paint the house.
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n a chemical plant, 24 holding tanks are used for final product storage. Four tanks areselected at random and without replacement. Suppose that six of the tanks contain material inwhich the viscosity exceeds the customer requirements.(a) What is the probability that exactly one tank in the sample contains high-viscosity material
The probability that exactly one tank in the sample contains high-viscosity material is P(A) = 0,4607 or P(A) = 46,07 %
The probability of an event (A) is for definition:-The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring. In the very simplest cases, the probability of a particular event A occurring from an experiment is obtained from the number of ways that A can occur divided by the total number of possible outcomes.P(A) = Number of favorable events/ Total number of events FE/TE
If A and B are complementary events ( the sum of them is equal to 1) then:
P(A) = 1 - P(B)
The total number of events is:
C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!
C ( 24,4) = 24*23*22*21*20! / 4! * 20!
C ( 24,4) = 24*23*22*21/4*3*2C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626
TE = 10626
Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v
we get that total number of favorable events is the product of:
FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!
FE = 4896
Then P(A) ( 1 tank in the sample contains h-v material is:
P(A) = 4896/10626
P(A) = 0,4607 or P(A) = 46,07 %
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which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities
The multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.
What is the multiplicative rule?The multiplication rule is a method for calculating the likelihood of two events occurring at the same time (this is also one of the AP Statistics formulas). There are two rules for multiplication. P(A B) = P(A) P(B|A) is the general multiplication rule formula, while P(A B) is the specific multiplication rule (A and B).The multiplication rule is the multiplication of one event's probability by the likelihood of another occurrence. The law of independent assortment, Mendel's second law, stipulates that alleles of one gene segregate into gametes independently of alleles of another gene.Therefore, the multiplicative rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their probabilities.
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determine whether the following pairs of line will be parallel perpendicular or neither x=y ;x=y+1
Answer:
parallel because they have the same slope
Step-by-step explanation:
pls help me on 109 I got it wrong :c
Answer:
30
Step-by-step explanation:
Let's start by multiplying the equation through bt the least common denominator so that we can clear the denominator:
[tex]\frac{2}{5}x+\frac{1}{3}y=1[/tex]
The least common of 3 and 5 is 15, so we can multiply through by 15:
[tex]15(\frac{2}{5}x+\frac{1}{3}y)=15(1)\\6x+5y=15[/tex]
We want the left side of the equation to be 12x + 10y. We can get this if we multiply the expression we currently have (6x + 5y) by 2. However, if we multiply the left side by 2, we must also multiply the right side by 2 to balance out the equation. If we do this, we will get our answer:
[tex]2(6x+5y)=2(15)\\12x+10y=30[/tex]
On the right side, we get 30. Therefore, the answer is 30
Marge conducted a survey by asking 350 citizens whether they frequent the city public parks. of the citizens surveyed, 240 responded favorably. what is the approximate margin of error for each confidence level in this situation?
Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate are given by:
[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]
Hence the margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]
M = 0.0486 = 4.86%.
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Answer:
99% - 0.06
95% - 0.05
90% - 0.04
Step-by-step explanation: i got it right
There are 25 students in a class. How many ways can the teacher (randomly) pick two students for the lead roles in the class play?
Answer:
300
Step-by-step explanation:
25 choose 2 (exactly how it sounds like)
= (25*24)/(2*1)=600/2=300
How many 2 digit numbers are the product of two different primes
Answer:
30.
Step-by-step explanation:
2 digit Numbers which have factor of 2:
2*3, 2*5, 2*7, 2*11, 2*13, 2*17, 2*19, 2*23, 2*29, 2*31, 2*37, 2*41, 2*43, 2*47.
That's 14.
Then there are the ones with factor 3:
3*5 ....... 3*31 = 9 numbers.
Then
5*7 to 5*19 = 5 numbers.
7*11 , 7*13 = 2 numbers.
Total is 14 + 9 + 5 + 2
= 30.
There are 30 2-digit numbers that are the product of two different primes.
To determine the number of 2-digit numbers that are the product of two different primes, we first need to identify the primes within the range of 10 to 99. The prime numbers within this range are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
To find the count of 2-digit numbers that are the product of two different primes, we can consider all possible pairs of these primes.
The numbers that yield 2-digit numbers with a multiple of 2 are:
(2, 5), (2, 7), (2, 11), (2, 13), (2, 17), (2, 19), (2, 23), (2, 29), (2, 31), (2, 37), (2, 39), (2, 41), (2, 43), (2, 47).
Total = 14
The numbers that yield 2-digit numbers with a multiple of 3 are:
(3, 5), (3, 7), (3, 11), (3, 13), (3, 17), (3, 19), (3, 23), (3, 29), (3, 31).
Total = 9
The numbers that yield 2-digit numbers with a multiple of 5 are:
distinct: (5, 7), (5, 11), (5, 13), (5, 17), (5, 19).
Total = 5
The numbers that yield 2-digit numbers with a multiple of 7 are:
Distincts: (7, 11), (7, 13)
Total = 2
Therefore, the total numbers of pairs are 14 + 9 + 5 + 2 = 30.
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24 people go out for a meal.
13 have a starter, 15 have a pudding and 7 have both a starter and a pudding.
Show this information on a Venn diagram.
Answer:
see image
Step-by-step explanation:
The two circles will represent "starter" or "pudding" people and the overlap are both, but also don't forget people who chose neither. There must be 3-neither people. Because 6+7+8 only add to 21 and the question said there were 24 people.
A man left savings of the 2 50,000 to his wife, 2 daughters and a son. find the value of the shares that each received.q
Answer:
62,500
Step-by-step explanation:
250,000 ÷ 4 = 62,500
∴ Each member would receive 62,500.
I NEED IT NOW
Owen made 60% of the shots he attempted during his hockey practice. He made 18 shots. How many shots did Owen attempt during his hockey practice?
Through how many radians does the minute hand of a clock turn during a 3-minute period?
pi/5.
Think of a clock as a circle. The minute hand when it moves around the clock will have traveled 360 degrees or 2*pi radians, traveling 2*pi radians in 60 minutes. So3 minutes out of 60 minutes is 1/10. So the minute hand travels 1/10 of 2*pi radians (multiply 1/10 and 2*pi to get your answer).
Therefore your answer is pi/5 which is the letter a.
Well, a Radian, simply put, is a unit of measure for angles that is based on the radius of a circle. What this means is that if we imagine taking the length of the radius and wrapping it around a circle, the angle that is formed at the center of the circle by this arc is equal to 1 Radian.
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(Determine the net change between the indicated points on the graph.
Answer: 4
Step-by-step explanation:
The points are (-1, 1) and (5, 5).
So, the difference in the y coordinates is [tex]5-1=4[/tex].
The net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.
The coordinates from the given graph are (5, 5) and (-1, 1).
What is the net change between the coordinate points?Given two points, (a, f(a)) and (b, f(b)) on the graph of f(x), the net change is the difference between the two f(x) values. Thus, net change is given by f(b)−f(a).
Here, the change in x-coordinates is 5-(-1) = 6
The change in y-coordinates is 5-1 = 4
Therefore, the net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.
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What is the point slope equation of a line with slope -3 that contains the point (-8,-4)?
Answer:
y = -3x - 28
Step-by-step explanation:
y = mx + b is the slope-intercept of a line. To write an equation in this form. I need to find the slope (m) and the y-intercept (b). Yay! They gave us the slope (m). It is -3. Now we just need to figure out the y. We can do that by plugging in the slope (-3) and using the x (-8) and the y (-4) that they gave us from the point to solve for b.
y = mx + b
-4 = -3(-8) + b Multiple -3(-8) Remember a negative times a negative is a positive.
-4 = 24 + b Now subtract 24 from both side of the equation
-28 = b Now we can write the equation
y = mx + b
y = -3x + (-28) or y = -3x -28. Adding a negative is the same as subtracting a positive.
Roselyn is driving to visit her family, who live 150150150 kilometers away. Her average speed is 606060 kilometers per hour. The car's tank has 202020 liters of fuel at the beginning of the drive, and its fuel efficiency is 666 kilometers per liter. Fuel costs 0.600.600, point, 60 dollars per liter.
What is the price for the amount of fuel that Roselyn will use for the entire drive?
Answer:
Step-by-step explanation:
150 kilometers
60 kph
tank is 20 liters
6 km/l
150/6 = 25 liters needed
$60/l
5 more liters of fuel
total cost 25 x .60 = $15
the eccentricity of the conic section below is
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The eccentricity of the conic section below is 1, since the given conic section is a parabola, and any parabola's eccentricity is 1.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]
what is the slope is the line that passes through the points (-1,6) and (14,3)? Write your answer in simplest form.
Answer:
m= -1/5
Step-by-step explanation:
slope formula to find it ^^
If 3 cups of flour are needed to make 60 biscuits, how much flour is needed to make 95 of the same kind of biscuits
Answer:
3 cups for 60 biscuits
60/3=20
1 cup for 20 biscuits
95/20=4.75
4.75 cups of flour
Hope This Helps!!!
Answer:4.75
Step-by-step explanation: If 3 cups equals 60 biscuits then how much with you need for 95 biscuits
60/3 equals 20 95/20 equals 4.75 just to make sure lets multiply
475x20 equals 9500 now put the decimal back in place 95.00
Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer
The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively
What is a kite?A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
The given figure is a kite with two intersecting lines that are perpendicular to each other.
Since the lines are perpendicular to each other, hence;
m<1 = 90 degrees
For the measure of m<2
m<2 + 90 + 27 =180
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63degrees
Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees
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This graph represents a quadratic function. An upward parabola on a coordinate plane vertex at (minus 2, 2) and passes through (minus 3, 5) and (minus 1, 5). What is the value of a in the function’s equation? A. 3 B. 2 C. -3 D. -2
The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:
y = ax² + bx + c
The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.
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Answer:
The correct answer is A:3
Step-by-step explanation:
A man leaves home at 22:15 hours and reaches his destination at 04:00 hours on the following day. how many hours did the journey take?
Answer,
Leaves from home=22:15hour
get to destination=4:00hour
time taken on a journey,
from time 22:15hour to 24:00hour=2:45hour and,
time is taken form 22:00hour to 4:00hour=4:00hour
So, the total time taken to reach the destination is 2:45+4:00=6:45hour
Using the net below, find the surface area
of the triangular prism.
7 cm
5 cm
15 cm
4 cm
Surface Area =
5 cm
7 cm
[?] cm²
Enter
The Surface area of the triangular prism with the net shown below is 106 cm²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²
The Surface area of the triangular prism with the net shown below is 106 cm²
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Can someone help? ASAP
[tex]\tan 45^{\circ}=\frac{x}{2\sqrt{10}}\\\\1=\frac{x}{2\sqrt{10}}\\\\\boxed{x=2\sqrt{10}}\\\\\\\\\sin 45^{\circ}=\frac{2\sqrt{10}}{y}\\\\\frac{1}{\sqrt{2}}=\frac{2\sqrt{10}}{y}\\\\y=2\sqrt[20}\\\\\boxed{y=4\sqrt{5}}[/tex]