The inverse Laplace transform of X(s) = [tex]1/s^7[/tex] is f(t) =[tex]t^6.[/tex]
To locate the inverse Laplace rework of X(s) =[tex]1/(s^7[/tex]), we are able to use algebraic manipulation and the inverse Laplace transform assets said in Theorem 7.2.1, which permits us to discover the original characteristic while given its Laplace rework.
Using the assets of the Laplace transform, we will rewrite the given expression as:
X(s) = [tex]x^-1(1/s^7) = (1/s^7)[/tex]
We need to locate the feature f(t) such that its Laplace transform is X(s) = [tex]1/s^7[/tex]. By making use of Theorem 7.2.1, we understand that the inverse Laplace remodels of X(s) will give us f(t).
Now, we need to find a characteristic f(t) that has a Laplace transform [tex]1/s^7[/tex]. By examining the Laplace transform a desk or the usage of regarded formulas, we will decide that the Laplace remodel of [tex]t^n[/tex](wherein n is a high-quality integer) is given by means of[tex]n!/s^(n+1).[/tex]
In our case, we're looking for a function whose Laplace remodel is[tex]1/s^7.[/tex]Comparing this with the Laplace transform formulation cited earlier, we see that the exponent within the denominator of sought to be [tex]8 ^(7+1).[/tex]
Hence, f(t) must be t^6 (given that 6+1 = 7), and its Laplace remodel maybe [tex]6!/s^7 = 720/s^7.[/tex]
Therefore, the inverse Laplace transform of X(s) = [tex]1/s^7 is f(t) = t^6.[/tex]
In precis, by applying algebraic manipulation and making use of the inverse Laplace rework assets, we determined that the inverse Laplace transform of [tex]1/s^7 is f(t) = t^6[/tex]. This approach that a unique feature corresponding to the given Laplace rework is [tex]t^6.[/tex].
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If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent. True or False?
The statement "If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent" is true.
Let's understand why?
Explanation:
An argument with a tautology conclusion is an argument that arrives at a conclusion that is always true, regardless of the truth values of the premises. In other words, it is impossible for the premises to be true while the conclusion is false.
This means that any attempt to find a counterexample that disproves the conclusion will always fail, as there is no possible scenario in which the conclusion is false.
The counterexample set of an argument is the set of all possible scenarios in which the premises are true but the conclusion is false. If the conclusion is a tautology, then there is no possible scenario in which the conclusion is false, and thus the counterexample set is empty. An empty counterexample set is equivalent to an inconsistent counterexample set, as it means that there is no consistent scenario in which the conclusion is false.
Therefore, if the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent.
Hence, the statement is true.
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In a study by a researcher, the Poisson distribution was used to model the number of patients per month referrea to an oncologist. The researchers use a rate of 16 patients per month that are referred to the oncologist. Calculate the probability that in a month:
a) exactly 10 patients are referred to an oncologist. -
b) between five and 15 inclusive are referred to an oncologist.
c) more than 10 are referred to an oncologist
The probability that exactly 10 patients are referred to an oncologist in a month is 0.036
The probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.
The probability that more than 10 patients are referred to an oncologist in a month is 0.873
Given:
A researcher used Poisson distribution to model the number of patients per month referred to an oncologist. The researcher uses a rate of 16 patients per month. We have to find the probabilities for different conditions:
a) The probability of exactly 10 patients are referred to an oncologist.
b) The probability that between five and 15 inclusive are referred to an oncologist.
c) The probability that more than 10 are referred to an oncologist.
Solution:
a) The number of patients referred to an oncologist per month follows Poisson distribution with parameter λ = 16.
The probability of exactly 10 patients are referred to an oncologist is:
`P(X = 10) = e^(-λ) * (λ^x) / x!` = `e^(-16) * (16^10) / 10! = 0.036`
Therefore, the probability that exactly 10 patients are referred to an oncologist in a month is 0.036.
b) The probability that between five and 15 inclusive are referred to an oncologist is:
`P(5 ≤ X ≤ 15) = P(X ≤ 15) - P(X ≤ 4)``= ∑_(x=0)^4 (e^(-16) * (16^x) / x!) + ∑_(x=5)^15 (e^(-16) * (16^x) / x!)`≈ 0.98
Therefore, the probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.
c) The probability that more than 10 are referred to an oncologist is:
`P(X > 10) = 1 - P(X ≤ 10)` `= 1 - ∑_(x=0)^10 (e^(-16) * (16^x) / x!)` ≈ 0.873
Therefore, the probability that more than 10 patients are referred to an oncologist in a month is 0.873.
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JK and LM are perpendicular diameters of a circle. They are each 12 inches long. What is the approximate length of chord LK? With Explanation Please
Answer:
8.5 inches
Step-by-step explanation:
Let the center of the circle = C
Now CK = CL = 6
Using Pythagoras theorem
LK^2 = CL^2 + CK^2
= 6^2 +6^2
= 36 + 36
= 72
LK = 72 ^1/2
= ( 36*2)^1/2
= 6(2)^1/2
= 8.5 inches
Which digit in 12,345 has the same place value as 6 in 67.89
Answer:
4
Step-by-step explanation:
Line up the numbers at the decimal point and then find the number the same number of spaces away from the decimal point.
12,345.00
00067.89
please help me .......
A zoo keeper measured the length of two baby alligators. The first one was 12 inches. The other was 5/6 of that length. How long was the second baby alligator?
Answer:
10 inches
Step-by-step explanation:
5/6*12
5*2 (since 12/6=2)
10 inches long!
hope it helps you!
Answer:
It would be 10 inches
Step-by-step explanation:
The 5/6 of 12 is 10 since(or you can simply say that we just subtract 2, I don't really know how to explain my work)
25 points. Get it before the mod sees it!
gogogogo lol
Answer:
yy
Step-by-step explanation:
bi
Please help me with the question please ASAP I’ll mark u as a brnlist
*2 questions
Answer:
First answer is 76.50 and the second one is scale factor of 1/2
Step-by-step explanation: Mark brainlist or im deleting my answer :)
Answer:
scale factor = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{WX}{AB}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]
------------------------------------------
1 pizza costs $12.75 and feeds 4
To feed 24 students he needs 24 ÷ 4 = 6 pizzas , then
6 cost = 6 × $12.75 = $76.50
is (x 7) a factor of f(x) = x3 − 3x2 2x − 8? explain your reasoning.
(x + 7) is a factor of f(x) = x^3 - 3x^2 + 2x - 8. By using synthetic division, we find that the remainder is 0.
To determine if (x + 7) is a factor of the polynomial f(x) = x^3 - 3x^2 + 2x - 8, we can use synthetic division.
Performing synthetic division with the divisor (x + 7), we set up the division as follows:
-7 | 1 -3 2 -8
|_________________
1 -10 72 -520
The numbers in the bottom row of the synthetic division represent the coefficients of the quotient polynomial. In this case, the quotient polynomial is 1x^2 - 10x + 72, and the remainder is -520.
Since the remainder is not zero, (x + 7) is not a factor of f(x). If (x + 7) were a factor, the remainder would be zero.
Therefore, (x + 7) is not a factor of f(x) = x^3 - 3x^2 + 2x - 8.
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Find the least squares straight line y = mx + b to fit the data points: (0,3), (2, 1), (3, 1). Compute the minimum square error.
The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
Given data points are (0, 3), (2, 1), (3, 1).
To find the least square straight line, y = mx + b.
The line that fits these points will have the minimum square error.(0,3) y = mx + b; 3 = 0 + b; b = 3(2,1)
y = mx + b; 1 = 2m + b; b = 1 - 2m(3,1)
y = mx + b; 1 = 3m + b; b = 1 - 3m
Substitute the value of b in (2) and (3)1 - 2m = 3 - 3m; m = -2y = mx + b;
y = -2x + 3
The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found.
Now, we need to compute the minimum square error.
Square error of each point: Point 1 (0, 3): Square error = (3 - 3)² = 0
Point 2 (2, 1): Square error = (1 - (-4))² = 25
Point 3 (3, 1): Square error = (1 - (-5))² = 36
The minimum square error is the sum of the square error of all the points, Minimum square error = 0 + 25 + 36 = 61
Therefore, the least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
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find the solution to mx cx kx=f(t) for an arbitrary function f(t), x(0)=0, x'(0)=0
Step-by-step explanation:
The given equation `mx cx kx=f(t)` is a second-order linear differential equation with constant coefficients. The general solution to this type of equation is given by the sum of the complementary solution `x_c(t)` and the particular solution `x_p(t)`.
The complementary solution x_c(t) is the solution to the associated homogeneous equation mx cx kx=0. The characteristic equation for this homogeneous equation is mr^2 + cr + k = 0. Solving this quadratic equation gives two roots r_1 and r_2. The complementary solution can then be written as x_c(t) = C_1e^(r_1t) + C_2e^(r_2t).
The particular solution x_p(t) depends on the form of the function f(t). There are several methods for finding the particular solution, such as undetermined coefficients or variation of parameters.
Once the complementary and particular solutions are found, the general solution to the given differential equation is given by x(t) = x_c(t) + x_p(t). The constants C_1 and C_2 can then be determined using the initial conditions x(0)=0 and x'(0)=0.
Without more information about the function f(t), it is not possible to find a more specific solution to the given differential equation.
anybody can help me with this
Answer:
the answer is a/ 21 kilometers
calculate the value of x for the following polygon
(answers me or i'll throw oli london at you )
Answer:
X = 60 degrees
Answer
80°
Step by Explanation:
the angle right to 60°= 180-60 (linear pair)
= 120°
total angle of 5 sided polygon= 540°
540° = x + 110° + 130° + 100° + 120°
540° = x + 460°
x= 540° - 460°
x = 80°
Franco Co-operation makes iron benches, they want to move their production unit to a new location. The new production plant will cost SAR 200000 to construct Variable costs of production of each bench are SAR 200 and the selling price of each bench is SAR 250. Determine the break-even point for bench production at the new plant?
The break-even point for bench production at the new plant is 4000 units.
The new production plant of Franco Cooperation will cost SAR 200000 to construct.
The variable costs of production of each bench are SAR 200. The selling price of each bench is SAR 250. We can find out the break-even point of bench production at the new plant by using the break-even formula.
Break-even point (in units) = Fixed costs / Contribution margin per unitWhere,
F = Fixed costs
P = Price per unit
V = Variable cost per unit
Contribution margin per unit = Price per unit - Variable cost per unit
First, let's calculate the contribution margin per unit.
P = Selling price of each bench = SAR 250V = Variable cost per unit = SAR 200
Contribution margin per unit = P - V= SAR 250 - SAR 200= SAR 50
Now, let's calculate the break-even point.
Fixed costs (F) = Cost of constructing the new plant= SAR 200000
Contribution margin per unit = SAR 50
Break-even point (in units) = F / Contribution margin per unit= SAR 200000 / SAR 50= 4000.
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The break-even point for bench production at the new plant can be found by dividing the fixed costs by the contribution margin per unit.
The break-even point for bench production at the new plant is 4000 benches.
To determine the break-even point, we need to calculate the contribution margin per unit. Contribution margin per unit is the amount left over after deducting the variable costs from the selling price. It is also called unit contribution margin. Therefore, the contribution margin per unit = Selling price per unit - Variable cost per unit
= SAR 250 - SAR 200
= SAR 50
Now, we can use the formula to calculate the break-even point:
Break-even point = Fixed costs / Contribution margin per unit
Fixed costs = cost of new production plant
= SAR 200000
Contribution margin per unit = SAR 50
Therefore, Break-even point = SAR 200000 / SAR 50
= 4000 benches
The break-even point for bench production at the new plant is 4000 benches.
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Jerry ordered 4 items online. He is charged $2.91 per pound for shipping. The items weighed 4.3 pounds, 2 pounds, 3.8 pounds, and 5.9 pounds. How much will he be charged for shipping? (Round to the nearest cent).
Answer:
46.56 pounds
Step-by-step explanation:
Given data
4.3 pounds
2 pounds
3.8 pounds, and
5.9 pounds
Let us find the total weight of all the items
=4.3+2+3.8+5.9
=16 pounds
We are told that he is charged $2.91 per pound for shipping
Hence the cost of shipping 16 pounds is
=2.91*16
=46.56 pounds
someone helpp!!!!!!!
Answer:
the rate of change is 3
Step-by-step explanation:
if im wrong im sorry but if im right give me brainliest
Ali travelled 75% of her journey to work by taxi. If his total journey is 12km, what distance did she travel by taxi? don't send in file please
7. The short sides of a parallelogram are both 12.0 cm. The acute angles
of the parallelogram are 65°, and the short diagonal is 15.0 cm.
Determine the length of the long sides of the parallelogram. Round
your answer to the nearest tenth of a centimetre.
Please help explain this question
The length of the longest side of the parallelogram is 14.7 cm.
We have,
Let's denote the length of the long sides of the parallelogram as L.
In a parallelogram, the opposite sides are congruent, so both long sides have the same length.
The Law of Cosines states:
c² = a² + b² - 2ab cos(C)
Where:
c is the length of the side opposite the angle C,
a and b are the lengths of the other two sides,
C is the measure of the angle opposite side c.
The short sides of the parallelogram are 12.0 cm, and the acute angle is 65°.
Applying the Law of Cosines to find the length of the long side:
[tex]L^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(65)\\L^2 = 144 + 144 - 288 * cos(65)\\L^2 = 288 - 288 * cos(65)\\L = \sqrt{(288 - 288 * cos(65))}\\L = 14.7 cm[/tex]
(rounded to the nearest tenth of a centimeter)
Thus,
The length of the longest side of the parallelogram is 14.7 cm.
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A rectangular garden has a width of 7x -2 and a length of 3x +10. Find the perimeter.
Answer:
20x + 16
Step-by-step explanation:
Width (w) = 7x - 2
Length (l) = 3x + 10
Perimeter = 2*(l + w)
= 2* (3x + 10 + 7x - 2)
= 2* (3x + 7x + 10 - 2 ) {Combine like terms}
= 2* ( 10x + 8) {Use distributive property: a(b +c) =(a*b) + (a*c)}
= 2*10x + 2*8
= 20x + 16
A critical component in a circuit will work properly only if 3 other components all work properly. The probabilities of a failure for the 3 other components are 0.008, 0.015, and 0.022. Find the probability that at least 1 of these 3 components will fail.
Note: Round using three significant figures, if necessary
Answer: Probability that one of the three components will fail is about 0.045.
Step-by-step explanation:
clients with a quickbooks online plus subscription can create 400 ungrouped tags and 1000 grouped tags distributed among up to 40 tag answer
Clients with a QuickBooks Online Plus subscription have the ability to create a total of 400 ungrouped tags and 1000 grouped tags, which can be distributed among up to 40 tag categories.
QuickBooks Online Plus offers users the flexibility to categorize transactions using tags. Tags are a way to organize and track transactions based on specific criteria or categories. There are two types of tags available: ungrouped tags and grouped tags.
With a QuickBooks Online Plus subscription, clients can create a maximum of 400 ungrouped tags. These tags can be assigned to individual transactions to provide additional information or categorization. Clients can create up to 40 tag categories and distribute the 1000 grouped tags among these categories.
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David had $35 to spend at the fair. If the admission to the fair is $4.5 and the rides cost $1.50 each, what is the greatest number of rides David can go on?
Answer:
20 rides
Step-by-step explanation:
35-4.5=30.5
20*1.5=30 and 30 plus 4.5 equals 34.5
Select the function that represents the simple interest formula.
A. A) = P(1 + )- 1, where n is a positive integer
O
B. A(n) = P+ (n-1);• P, where n is a positive integer
O
C. An) = n + (-1). P, where n is a positive integer
O
D. A(n) = (1 - 1)(P:n)', where nis any real number
Answer:
B. A(n) = P + (n-1)i*P
Step-by-step explanation:
The formula to determine the simple interest formula is given below:
Simple interest = P×r × t
where
P denotes the principal
r denotes the rate of interest
And, t denotes the number of years
Now we replace i with the t
So,
SI = Pni
Now for n-1 years, the simple interest is
SI = P(n - 1)×i
So, the total amount would be
A(n) = P + (n - 1)i × P
Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid singularity statement please help
Answer:
Not similar
Step-by-step explanation:
Question 11 i’m confused
I dont know this someone please answer this and show work and FAST! My teacher will call on me soon
Answer:
I can' see this. Can you show it closer? Please!
Step-by-step explanation:
Answer:
ok maybe itll work with this???
Step-by-step explanation:
file:///C:/Users/apple/Downloads/13f2bddc55b71689635395017a167da1%20(1).pdf
I hope it workksss
Greyson and Preston have a piece of paper that is 10 inches by 9 inches. What is the area of the paper?
Answer:
90
Step-by-step explanation:
Gabe can travel 40 miles on his motorbike in the same time it takes Dena to travel 15 miles on her bicycle. If Dena rides her bicycle 20 mph slower than Gabe rides his motorbike, find
Dena's rate.
Answer:
answer is 12 miles vause he can travel faster
Step-by-step explanation:
3x ft
1.5x ft
x ft
180 ft
Which of the following statements is an example of a null hypothesis? * 2 points The average GWA of resident students is higher than the average GWA of commuter students. The average GWA of resident students is not equal the average GWA of commuter students. There is no difference between the average GWA of resident students and the average GWA of commuter students, and if there is, it is due to chance. The average GWA of resident students is lower than the average GWA of commuter students. There is a difference between the average GWA of resident students and the average GWA of commuter students.
The following statement is an example of a null hypothesis: There is no difference between the average GWA of resident students and the average GWA of commuter students, and if there is, it is due to chance.
In statistics, a null hypothesis is a statement that assumes there is no difference between the two variables being tested. The null hypothesis is the statement that the researcher is attempting to disprove in favor of the alternative hypothesis. The null hypothesis can either be rejected or not rejected by the researcher after conducting statistical analysis.
In this case, the null hypothesis states "There is no difference between the average GWA (General Weighted Average) of resident students and the average GWA of commuter students, and if there is, it is due to chance." This means that the null hypothesis assumes that there is no significant distinction in the average GWA between resident students and commuter students. Any observed differences, if they exist, are attributed to random chance rather than a systematic difference between the two groups.
When conducting hypothesis testing, we compare the observed data to the null hypothesis to determine if there is enough evidence to reject the null hypothesis in favor of an alternative hypothesis.
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