find the laplace transform f(s)=l{f(t)} of the function f(t)=e2t−8h(t−4), defined on the interval t≥0. here, h(t) is the unit step function (heaviside).
Answers
The Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).
We can split the function into two parts:
f(t) = e^(2t) - 8h(t-4)
Taking the Laplace transform of each part separately, we get:
L{e^(2t)} = ∫_0^∞ e^(-st) e^(2t) dt = ∫_0^∞ e^(t(2-s)) dt = 1/(s-2) (by using the Laplace transform formula for e^(at))
L{8h(t-4)} = 8 e^(-4s) (by using the formula for the Laplace transform of the unit step function h(t-a))
Thus, the Laplace transform of f(t) is:
f(s) = L{f(t)} = L{e^(2t)} - L{8h(t-4)} = 1/(s-2) - 8 e^(-4s)
Therefore, the Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).
To know more about Laplace transform refer here:
https://brainly.com/question/31481915
#SPJ11
Related Questions
Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 60 seconds. Calculate the probability a customer waits:
Answers
The probability that a customer waits less than or equal to 90 seconds is approximately 0.7769, or 77.69%.
To calculate the probability that a customer waits a certain amount of time at the local Subway sandwich shop, we can use the exponential distribution formula:
\(P(X > t) = e^{(-t/u)}\)
Where:
P(X > t) is the probability that the waiting time (X) is greater than a specific value (t).
e is the base of the natural logarithm (approximately 2.71828).
t is the specific value of waiting time.
μ is the mean of the exponential distribution.
In this case, the mean waiting time (μ) is given as 60 seconds. Let's calculate the probability of a customer waiting less than or equal to a specific time, which is the complement of waiting longer than that time:
P(X ≤ t) = 1 - P(X > t)
For example, to calculate the probability a customer waits less than or equal to 90 seconds, we have:
P(X ≤ 90) = 1 - P(X > 90)
\(= 1 - e^{(-90/60)}\\= 1 - e^{(-1.5)}\)
≈ 1 - 0.2231
≈ 0.7769
To know more about probability,
https://brainly.com/question/29511543
#SPJ11
The probability that a customer waits less than 30 seconds is approximately 0.3935, or 39.35%.
The probability that a customer waits less than a certain amount of time can be calculated using the exponential distribution. In this case, the mean waiting time is given as 60 seconds.
To calculate the probability that a customer waits less than a specific time, we can use the formula for the cumulative distribution function (CDF) of the exponential distribution.
Let's say we want to calculate the probability that a customer waits less than 30 seconds. We can plug the values into the formula:
\(P(X < 30) = 1 - e^(-λt)\)
Where λ is the rate parameter, which is the reciprocal of the mean (λ = 1/60), and t is the desired time (30 seconds).
\(P(X < 30) = 1 - e^(-1/60 * 30) = 1 - e^(-1/2) ≈ 0.3935\)
Therefore, the probability that a customer waits less than 30 seconds is approximately 0.3935, or 39.35%.
Similarly, we can calculate the probability for other desired waiting times by plugging in the appropriate values into the formula.
Keep in mind that this calculation assumes that the waiting times follow an exponential distribution with a mean of 60 seconds.
Learn more about probability:
brainly.com/question/31120123
#SPJ11
which of the following is equal to sin(300)
Answers
Sin(300°) = -√3 / 2 .
Research about 5 monuments around the world where Roman numerals are used to depict the year in which they were built explain in 5 sentences about the monument and stick pictures of the same also write the Hindu Arabic form of the Year they were built.
Answers
Answer:
Modern uses. Roman numerals are still used today and can be found in many places. They are still used in almost all cases for the copyright date on films, television programmes, and videos - for example MCMLXXXVI for 1986.
Five monuments around the world where Roman numerals are used to depict the year in which they were built are indicated below.
What are the Roman Monuments and the dates they were built?The roman monuments and the dates they were built are:
Learn more about Roman Monuments at:
https://brainly.com/question/15786258
#SPJ2
if 5 builders take 5 days to make 5 walls, how long would it take 100 builders to make 100 walls? days
Answers
To approach this type of problem, you have to make a couple of reasonable assumptions - first, that each worker works at the same pace, and second, that the effort to build each wall is the same.
Next, figure out how much effort is required to build one wall. The effort is measured in “working days”. So, how many days does one worker need to build one wall, or how many workers would be required to build one wall in one day? We can calculate this by dividing the 25 worker days used to build five walls by the number of walls (5). So we need five worker days per wall.
(5 workers) x (5 days) = 25 worker-days;
25 worker days/5 walls = 5 worker days per wall.
With 100 workers, it will take five days to build 100 walls. Each worker will build one wall in 5 days. So it will also take 5 days for all 100 workers to build all 100 walls.
100 x 5 = 500 worker days;
500 worker-days / 100 workers = 5 days (answer)
finding the missing digits on this photo PLS
Answers
The diameter of a circular pool is 18 feet, how much land does the pool take up?
PLEASE HELP ME
Answers
Work Shown:
d = 18 = diameter
r = d/2 = 18/2 = 9 = radius
A = area of a circle of radius r
A = pi*r^2
A = 3.14*9^2
A = 254.34
The pool takes up approximately 254.34 square feet of area. Use more decimal digits of pi to get a more accurate answer.
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: 5
Step-by-step explanation:
explain in words what this problem is asking you to do 3(×+2)
Answers
Step-by-step explanation:
You simply have to multiply 3 by all what is in the bracket forinstance
3x+6 , this is so because 3 is multiplied by x and also multiplied by 2
If you ask survey respondents to respond to questions with a limited choice of answers, you are asking what type of questions
Answers
If you ask survey respondents to respond to questions with a limited choice of answers, you are asking closed-ended questions.
Closed-ended questions are used in surveys to elicit specific information from survey respondents. In this type of question, respondents are asked to select an answer from a list of options provided by the surveyor, such as yes/no, multiple choice, or rating scale questions.
The major advantage of using closed-ended questions is that they are easy to answer and analyze, and the answers obtained can be quantified. Closed-ended questions also require less time and effort from the respondents. They are particularly useful for large-scale studies involving a large number of respondents as they allow for quick data collection.
However, closed-ended questions can be limiting as they restrict the respondents' ability to provide in-depth information about their experiences or feelings.
The number of possible responses or answer options in a closed-ended question is known as the number of terms. For instance, if a question has three possible answers (yes, no, and not sure), it has three terms. If a question has ten possible responses (1-10 rating scale), it has ten terms. Therefore, a question with 150 possible responses (such as a Likert scale with 150 points) would have 150 terms.
Learn more about closed-ended questions here:
https://brainly.com/question/30553280
#SPJ11
Consider the parametric curve given by the equations x(t) = t² + 23t +47 y(t) = t² + 23t + 44 Determine the length of the portion of the curve from t = 0 to t = 7.
Answers
To find the length of the portion of the parametric curve from t = 0 to t = 7, we can use the arc length formula for parametric curves. The arc length formula is given by:
L = ∫(a to b) √[x'(t)² + y'(t)²] dt
where a and b are the starting and ending values of t, and x'(t) and y'(t) are the derivatives of x(t) and y(t) with respect to t, respectively.
First, let's find the derivatives of x(t) and y(t). Taking the derivatives, we get:
x'(t) = 2t + 23
y'(t) = 2t + 23
Next, we can plug these derivatives into the arc length formula and integrate from t = 0 to t = 7:
L = ∫(0 to 7) √[(2t + 23)² + (2t + 23)²] dt
Simplifying under the square root, we have:
L = ∫(0 to 7) √[(4t² + 92t + 529) + (4t² + 92t + 529)] dt
L = ∫(0 to 7) √[8t² + 184t + 1058] dt
Integrating this expression may require advanced techniques such as numerical integration or approximation methods. By evaluating this integral, you can find the length of the portion of the curve from t = 0 to t = 7.
To learn more about Parametric curve - brainly.com/question/15585522
#SPJ11
for what value of 'a' the number 7/a is not a rational number
Answers
Answer:
0
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction of two integers q/p where p, the denominator is not a 0. Therefore if a is 0 then it isn't a rational number
Answer:
0 must be the value of 'a' the number 7/a is not a rational number
Step-by-step explanation:
7/0=infinity
I need to know the amount of football helmets in this shed. It’s 20 x 10 ft and the helmet is 9.5 inches tall. I need an approximate and accurate answer,
Answers
Answer:
my guess is about 76
Step-by-step explanation:
iI counted the top 2 layers and assuming that there is about 1 or 2 that is around 28 helmets, added to the 48 currently seen in the picture.But, it is just an estimate. Thanks for the 100 points!!!
Multiply. Show your work.
42.7 x 0.8 show your work tell me how u got the answer
Answers
Answer:
34.16
Step-by-step explanation:
42.7
x 0.8
-------
34.16
Answer:
34.16
Step-by-step explanation:
2 5
42.7
x
0.8
=
43.16
Find the indicated probability. In a survey of 300 college graduates, 56% reported that they entered a profession closely related to their college major. If 8 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major?
Answers
16.22% probability that 3 of them entered a profession closely related to their college major explanation: For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major,
6/15=3/x.
I'm going insane
Answers
Answer:
x = 7.5
Step-by-step explanation:
\( \frac{6}{15} = \frac{3}{x} \)
cross multiply expressions
6x = 45 divide both sides by 6
x = 7.5
The field just outside a 3.00 cm radius metal ball is 3.05×102N/Cand point towards the ball. What charge resides on the ball
Answers
The field just outside a 3.00 cm radius metal ball is '3.05×102N/Cand point' towards the ball, the charge that resides on the ball is 3.06×10⁻⁹ C.
To find the charge that resides on the ball, we can use the equation for electric field, E = kQ/r², where E is the electric field, k is the Coulomb constant, Q is the charge, and r is the radius. Rearranging the equation to solve for Q, we get Q = Er²/k.
Plugging in the given values, we get:
Q = (3.05×10² N/C)(0.03 m)²/(8.99×10⁹ Nm²/C²)
Q = 3.06×10⁻⁹ C
Therefore, 33.06×10⁻⁹C of charge is present on the ball.
You can learn more about charge at
https://brainly.com/question/18102056
#SPJ11
A cylindrical soup can has a diameter of 3in. and volume of 33.91 n.3. Find the height of the can.
Answers
mark looked at the statistics for his favorite baseball player, jose bautista. mark looked at seasons when bautista played 100 or more games and found that bautista's probability of hitting a home run in a game is 0.173. if mark uses the normal approximation of the binomial distribution, what will be the variance of the number of home runs bautista is projected to hit in 100 games? answer choices are rounded to the tenths place.
Answers
14.3 is probability of the variance of the number of home runs bautista is projected to hit in 100 games.
How does probability explain work?
Probability measures how probable something is to occur.We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.Statistics is the study of events subject to probability.Given: n = 100
p = 0.173
Variance = np(1-p)
= 100*0.173*0.827
= 14.3071
Therefore, the variance to two decimal places is
= 14.3.
Learn more about probability
brainly.com/question/11234923
#SPJ4
if a sample of shoppers showed stating that the supermarket brand was as good as the national brand, what is the p-value (to decimals)?
Answers
The p-value is 0.046, or 4.6% if a sample of shoppers showed stating that the supermarket brand was as good as the national brand.
To calculate the p-value, we use null and alternative hypotheses, as well as the test statistic and its distribution under the null hypothesis.
By the null hypothesis, we can say that supermarket brands are as good as national brands, and by the alternative hypothesis, we can say that supermarket brands are not as good as national brands.
This hypothesis can be tested by performing a two-tailed z-test for proportions.
In a sample of n shoppers, say that x shoppers say that supermarket brands are as good as domestic brands. The sample percentage can be calculated as follows:
p hat = x/n
in the null hypothesis, the sample proportion is equal to the hypothesized proportion, that is 0.5
The test statistic for a two-sided z-test for proportions is given by:
z = (p-hat - p0) / sqrt(p0(1-p0)/n)
where p0 is the hypothesized proportion under the null hypothesis.
In this case, we have:
p-hat = 0.5
p0 = 0.5
n = sample size
The null hypothesis states that the supermarket brand is as good as the national brand, so we would expect the proportion of shoppers who state this to be 0.5.
If the test statistic z falls in the rejection region (i.e., if |z| > 1.96 for a significance level of 0.05),
we would reject the null hypothesis and conclude that there is evidence to suggest that the supermarket brand is not as good as the national brand.
If the test statistic falls in the non-rejection region (i.e., if |z| <= 1.96 for a significance level of 0.05),
we would fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the supermarket brand is not as good as the national brand.
To calculate the p-value, we need to find the probability of getting a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true.
For a two-tailed test, the p-value is twice the observed area of the tails above the absolute value of the test statistic.
Assuming the sample size is large enough, the distribution of the test statistic can be approximated as a standard normal distribution under the null hypothesis.
Suppose in a sample of 100 shoppers, 50 said that supermarket brands are as good as domestic brands. after that:
p hat = 0.5
p0 = 0.5
n=100
The test statistic is:
z = (p hat - p0) / sqrt(p0(1-p0)/n) = 0 / sqrt(0.5 * 0.5 / 100) = 0
The p-value is the probability that the test statistic is extreme or more extreme than 0. This is the probability of getting further away from the 50/100 ratio or 0.5 in either direction.
p-value = P(p hat <= 0.4 or p hat >= 0.6) = 2 * P(p hat <= 0.4) = 2 * P(Z <= ( 0.4 - 0.5) / sqrt (0.5 * 0.5 / 100) ) = 2 * P(Z <= -2) ≈ 0.046
where Z is a standard normal random variable.
Therefore, the p-value is approximately 0.046, or 4.6%.
learn more about probability
brainly.com/question/29381779
#SPJ4
please helpppppp!!!!!
Answers
9514 1404 393
Answer:
A + 2×BD - 2×CStep-by-step explanation:
The shaded area contains area A and two of area B. The expression for that area can be written ...
Area of trapezoid = A + 2×B
__
The overall rectangle has an area of D. The areas labeled C can be subtracted from that to leave the shaded area. The expression for that is ...
Area of trapezoid = D - 2×C
Makes the equation 6x – 14 + 3(2x – 1) = 5 – 2(x – 10) true? *
Answers
Bodmas 6x+14= 9x -14×1x=14-10=4 x=10
What is the slope on graph
what is the y intercept of the graph what is the equation of graph
Answers
Answer:The solution is in the attached file
Step-by-step explanation:
Answer:
\(y = -1x + 4\)
Step-by-step explanation:
Hello!
The equation of a line is written in slope-intercept form.
Slope - Intercept Form: \(y = mx + b\)
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how much the y-values change as x-values change.
Slope is calculated by the Rise of the graph divided by the Run of the graph. Rise is how much the graph goes up or down between 2 points, while Run is how much the graph goes left or right between 2 points.
Points: (0,4) and (4,0)
Calculate:
\(Rise \div Run\)\(-4\div 4\)\(-1\)The slope is -1.
Y-interceptThe y-intercept is where the graph intersects the y-axis (x = 0).
The graph intersects it at (0,4), so the y-intercept is 4.
EquationWe can plug in the values for slope and y-intercept to find the equation.
Equation: \(y = -1x + 4\)
please help me solve
this!
6. Find the equation of the parabola with directrix at y = -2 and the focus is at (4,2).
Answers
To find the equation of the parabola with the given information, we can start by determining the vertex of the parabola. Since the directrix is a horizontal line at y = -2 and the focus is at (4, 2), the vertex will be at the midpoint between the directrix and the focus. Therefore, the vertex is at (4, -2).
Next, we can find the distance between the vertex and the focus, which is the same as the distance between the vertex and the directrix. This distance is known as the focal length (p).
Since the focus is at (4, 2) and the directrix is at y = -2, the distance is 2 + 2 = 4 units. Therefore, the focal length is p = 4.
For a parabola with a vertical axis, the standard equation is given as (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the focal length.
Plugging in the values, we have:
\((x - 4)^2 = 4(4)(y + 2).\)
Simplifying further:
\((x - 4)^2 = 16(y + 2).\)
Expanding the square on the left side:
\(x^2 - 8x + 16 = 16(y + 2).\)
Therefore, the equation of the parabola is:
\(x^2 - 8x + 16 = 16y + 32.\)
Rearranging the terms:
\(x^2 - 16y - 8x = 16 - 32.x^2 - 16y - 8x = -16.\)
Hence, the equation of the parabola with the given directrix and focus is \(x^2 - 16y - 8x = -16.\)
To learn more about parabola click on the link below:
brainly.com/question/11801996
#SPJ11
Some help please!!!!
Answers
Step-by-step explanation:
what do you not understand ? please let me know where you need more instructions.
the basic rule : every term of one side has to be multiplied with every term of the other side, and the results are added (by using the correct signs of the products).
remember :
+ × + = +
- × - = +
+ × - = -
- × + = -
(3x - 3)(5x - 4) = 3x × 5x + 3x × -4 + -3 × 5x + -3 × -4 =
= 15x² - 12x - 15x + 12 = 15x² - 27x + 12
simplify the following
Answers
The simplest form of the expression can be shown as;
(y - 4) (y + 1)/(y + 4) (y - 3)
What is the simplified form?Simplifying algebraic expressions involves reducing or combining like terms, applying the distributive property, and performing operations such as addition, subtraction, multiplication, and division.
Step 1;
We know that we can write the expression as shown in the form;
(y - 1) (y + 2)/ (y + 3) ( y + 4) ÷ (y + 2) (y - 5)/(y + 3) ( y - 4) * (y + 1) (y - 5)/ (y -1) (y - 3)
Step 2;
(y - 1) (y + 2)/ (y + 3) ( y + 4) * (y + 3) ( y - 4)/(y + 2) (y - 5) * (y + 1) (y - 5)/ (y -1) (y - 3)
Step 3;
The simplest form then becomes;
(y - 4) (y + 1)/(y + 4) (y - 3)
Learn more about algebraic expressions:https://brainly.com/question/28884894
#SPJ1
the sql aggregate function that gives the arithmetic mean for a specific column is _____.
Answers
The SQL aggregate function that gives the arithmetic mean for a specific column is `AVG()`.
SQL (Structured Query Language) aggregate functions are functions that operate on a set of values and return a single value as a result. These functions are used in SQL queries to perform calculations on groups of rows in a database table.
There are several common aggregate functions in SQL, including:
1. `COUNT()` - returns the number of rows in a table or the number of non-null values in a specific column.
2. `SUM()` - calculates the sum of values in a specified column.
3. `AVG()` - calculates the average value of values in a specified column.
4. `MAX()` - returns the maximum value in a specified column.
5. `MIN()` - returns the minimum value in a specified column.
Aggregate functions are typically used with the `GROUP BY` clause in SQL queries to group the data based on one or more columns and then apply the aggregate function to each group.
To know more about SQL aggregate function refer here:
https://brainly.com/question/28482003#
#SPJ11
The SQL aggregate function for calculating the arithmetic mean of a specific column is AVG.
Explanation:The SQL aggregate function that gives the arithmetic mean for a specific column is AVG.
For example, if you have a table called 'students' with a column called 'grades', you can use the AVG function in SQL to calculate the average grade:
SELECT AVG(grades) FROM students;
Learn more about SQL aggregate function for arithmetic mean here:https://brainly.com/question/32174535
#SPJ12
Halp me this question
Answers
Answer:
In 14,689, 14 is the thousands group, and 689 is the ones group.
rewrite -1-2 using addition
Answers
Answer:
Step-by-step explanation:
-1+(-2)
Find tan B. WILL MARK BRAINLIEST
Answers
Why does the test for homogeneity follow the same procedures as the test for independence?
Answers
Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.
The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.
The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.
For more information about chi-square test,visit
https://brainly.com/question/17142834
#SPJ4