The inverse Laplace transform of F(s) is 65t * e^(-2t).
The inverse Laplace transform of F(s) can be found by using the table of Laplace transforms or applying the properties of Laplace transforms. In this case, we have F(s) = 65 / (s^2 + 8s + 4).
To find the inverse Laplace transform, we need to express F(s) in a form that matches a known transform pair. Notice that the denominator can be factored as (s + 2)^2.
We can rewrite F(s) as follows:
F(s) = 65 / ((s + 2)^2)
Now, referring to the table of Laplace transforms, the transform pair for 1/(s + a)^2 is t * e^(-at). Therefore, we can apply this transform pair to find the inverse Laplace transform of F(s).
Using the transform pair, we have:
L^(-1)[F(s)] = L^(-1)[65 / ((s + 2)^2)]
= 65 * t * e^(-2t)
Therefore, the inverse Laplace transform of F(s) is 65t * e^(-2t).
None of the given options match this inverse Laplace transform.
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_______divisible by both 2 and 5
Step-by-step explanation:
____2__divisible by both 2 and 5
Help me get the possible point, no link or virus please.
Answer:
k(x) = -40
i(x) = -15
n(x) = 71
d(x) = 17
Step-by-step explanation:
This is exactly the same deal as the most recent question you asked.
"Evaluate each function for x = 8". In other words, this is saying, calculate the result for each function, replace x with 8. So, that means for every function, you are going to replace x with 8.
k(x) = -5x turns into k(x) = -5(8)
Then you just solve, -5(8) = -40
Since I have answered this question similarly, I ask that you go back to the answer and detailed explanation I gave you earlier.
How to solve M+4=-12
Answer:m=16
Step-by-step explanation:
A binder is 9 inches wide, 12 inches long and 1.5 inch thick. what is the volume of documents the binder can hold?
Answer:
162 square inches
Step-by-step explanation:
9*12*1.5
Answer:
162 cubic inches
Step-by-step explanation:
9 times 12 times 1.5
an engineering research center claims that through the use of a new computer control system, automo- biles should achieve, on average, an additional 3 miles per gallon of gas. a random sample of 100 automo- biles was used to evaluate this product. the sample mean increase in miles per gallon achieved was 2.4, and the sample standard deviation was 1.8 miles per gallon. test the hypothesis that the population mean is at least 3 miles per gallon. find the p-value of this test, and interpret your findings.
The test is proved that hypothesis that the population mean is atleast 3-miles per gallon.
What is hypothesis?A hypothesis is the proposed explanation for any kind of phenomenon.
So here are the values of X BAR i=2.4. S is 1.8.
Our sample n =100.
The null hypothesis here is that mu is greater than or equal to 3.
Against the alternative hypothesis that is less than three. Now the calculated value for the test statistic is going to be the equal to X bar is in (-) knots. That's 2.4 -3. divided by S over 2^2 of end. So 1.8 divided by the square root of the 100 gives us negative 3.33. So we can refer to that box of the T distribution and we are get the value. The p value for the test is going to be less than 0.5. Therefore we have the strong evidence that the not hypothesis is going to be the read checked it. So therefore we can reject to the null hypothesis and then it can accept the alternative by the hypothesis that is less than three. Where it is here is the mean of the population, the noting the average increase per gallon.
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Find inverse of 2x^2-2
Answer:
\(The \: inverse \: of \: the \: function \\ y = 2 {x}^{2} + 2 is {f - }^{1} (x) = √(x - 2) / √2\)
How can you tell from the vertex form y=a(x- h2) + k whether a quadratic function has no real zeros? Choose the correct answer below. A. The quadratic function has no real zeros if a <0, k = 0 and h70. B. The quadratic function has no real zeros if a>0, k = 0 and h#0. C. The quadratic function has no real zeros if a>0 and k = 0 or a <0 and k = 0. D. The quadratic function has no real zeros if a > 0 and k>0 or a < 0 and k<0.
The correct answer is D. The quadratic function has no real zeros if a > 0 and k>0 or a < 0 and k<0. This is because in the vertex form y=a(x- h2) + k, the value of k determines the vertical shift of the graph, and the value of a determines the direction of the graph. If a>0 and k>0, the graph will be shifted up and open upward, meaning it will not cross the x-axis and therefore have no real zeros.
Similarly, if a<0 and k<0, the graph will be shifted down and open downward, also not crossing the x-axis and having no real zeros. The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. The value of a determines the shape of the parabola: if a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.
For a quadratic function to have no real zeros, it must not intersect the x-axis. This means that the vertex of the parabola must be above or below the x-axis, depending on the direction of the opening.
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3. If the geometric mean of a and 25 is 20,
find the value of a.
Answer:
Value of a is 16.
Step-by-step explanation:
Solution Given:
we know that
Geometric mean=\(\sqrt{a*b}\)
By using this formula
20=\(\sqrt{a*25}\)
20=5\(\sqrt{a}\)
dividing both side by 5, we get
20/5=5/5* \(\sqrt{a}\)
4=\(\sqrt{a}\)
squaring both side
4²=a
:. a=16
Five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the regional science fair. Their names are placed in a hat, and four names are chosen at random to decide who attends the fair. What is the theoretical probability that chandra will be chosen as one of the science fair participants?.
The theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.
What is theoretical probability?Theoretical probability of an event is the ratio of number of favourable outcome to the total expected number of outcome of that event.
Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair.
Their names are placed in a hat, and four names are chosen at random to decide who attends the fair.
The total number of names are 5.The total number of names chosen are 4.The total number of ways 4 names can be taken out from 5 names is,
\(^5C_4\).
Here one spot needs to be fixed for Chandra. Now the total number of outcome remain 4 and favourable outcome remain 3.
Thus, the number of ways 4 names can be taken out such that it contains the name Chandra is
\(^4C_3\).
The theoretical probability that Chandra will be chosen as one of the science fair participants is,
\(P=\dfrac{^4C3}{^5C4}\\P=\dfrac{4}{5}\\P=0.8\\P=80\%\)
Thus, the theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.
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A convention center is in the shape of a rectangular pyramid with a height of 332 m. Its base measures 475 m by 571 m. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
The convention centre has a volume of approximately 30,085,616.8 cubic metres as a result.
What is the formula for volume?As opposed to length, width, and height for a rectangle's surface, the basic formula for volumes is length, breadth, and height. It doesn't matter how you refer to the different dimensions; for example, using "depth" instead of "height" wouldn't affect the calculation.
V = base area ×height (1/3)
The pyramid's height is disclosed to be 332 meters. We multiply the base's length and width to determine the base area:
Base area = 475 m × 571 m = 271525 m²
We can now enter the values into to the formula as follows:
V = (1/3) × 271525 m² × 332 m
V = 30085616.7 m³
This is rounding up to the closest tenth, giving us:
V ≈ 30085616.7 ≈ 30085616.8 m³
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The following are the last 10 run scores colin got in cricket: 16, 11, 25, 27, 11, 25, 20, 26, 29, 35 a) work out colin's mean score. b) colin plays cricket again on sunday. he gets 6 runs. what is his new mean score? give your answers as decimals.
Colin's new mean score, after getting 6 runs on Sunday, is approximately 20.09.
To calculate Colin's mean score, we need to sum up all his scores and divide by the number of scores.
a) Mean score:
16 + 11 + 25 + 27 + 11 + 25 + 20 + 26 + 29 + 35 = 215
Total scores: 10
Mean score = 215 / 10 = 21.5
Colin's mean score is 21.5.
b) To calculate his new mean score after getting 6 runs on Sunday, we need to add the new score to the previous total and divide by the new number of scores.
New total scores = 215 + 6 = 221
New number of scores = 10 + 1 = 11
New mean score = 221 / 11 = 20.09 (rounded to two decimal places)
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a sample that was obtained from a continuous variable consists of the following scores: 2, 5, 8, and 9. the range of these scores is 7. True or false?
True.The range is a measure of dispersion that represents the difference between the highest and lowest scores in a dataset. In this case, the highest score is 9 and the lowest score is 2, so the range is simply 9-2=7.
It is important to note that the range only considers the extreme values in the dataset and does not take into account the distribution of the scores. Therefore, it should be used in conjunction with other measures of dispersion, such as the standard deviation, to fully understand the variability of the dataset.the range refers to the difference between the largest and smallest values in a set of data. It is a measure of dispersion that helps to provide an idea of how much variation exists in the dataset. To calculate the range, one simply subtracts the smallest value from the largest value
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Find the exact volume of the cylinder. 8mm. 8mm
Answer:
V≈2.14×106
Step-by-step explanation:
i looked up volume of a cylinder, do the same.
Hellp me plz now yeyeyey
Answer:
step two
explanation:
the first 17.8 (-17.8) he was supposed to use was negative but the 17.8 (17.8) he used was not
Which is the better buy? 5-pack of toaster pastries for $4.13 or 9-pack of toaster pastries for $7.56
Answer: The answer is 9-pack of toaster pastries for $7.56
Step-by-step explanation:
Basicly it would be more expensive if you bought 9 for the first option but less for the other.
311/500 write each fraction or mixed numbers as a decimals
-7x+2+5-4x= blank x +6
If the equation -7x+2+5-4x = x +6, then the solution for x is x = 1/12.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To solve for x, we need to simplify and isolate the variable on one side of the equation.
Starting with the given equation:
-7x + 2 + 5 - 4x = x + 6
We can first combine like terms on the left side:
-11x + 7 = x + 6
Next, we can isolate the variable terms on one side and the constant terms on the other side:
-11x - x = 6 - 7
Simplifying both sides, we get:
-12x = -1
Finally, we can solve for x by dividing both sides by -12:
x = (-1)/(-12) = 1/12
Therefore, the solution for x is x = 1/12.
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11 What is the value of k if the mid-point of the line joining (1 – k, 4) and (2, k + 1) is (-k, k)?
Answer:
k = -3
Step-by-step explanation:
Given
(-k, k) is the midpoint of the line joining (2, k + 1) and (1 - k, 4)Solving
Equate the midpoint and endpoints using the Midpoint FormulaLet's equate the x parts-k = 2 + 1 - k / 2-2k = 3 - k-k = 3k = -3Which of the following number lines shows the solution to the compound inequality given below?
-2<3r+4<13
Answer:
We get -2 < r < 3
Corresponding to the fourth choice
The fourth number line is the correct option
Step-by-step explanation:
-2 < 3r+4 < 13
We have to isolate r,
subtracting 4 from each term,
-2-4< 3r + 4 - 4 < 13 - 4
-6 < 3r < 9
divding each term by 3,
-6/3 < r < 9/3
-2 < r < 3
so, the interval is (-2,3)
or, -2 < r < 3
this corresponds to
The fourth choice (since there is no equality sign)
You push a 20 kg crate with a force of 10 N. What is the crate's acceleration
Answer:
0.5kg/m
Step-by-step explanation:
The formula for acceleration is f/m = a
10/20 = a
0.5 = a
Best of Luck!
If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
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⚠️PLEASE HELP DUE SOON⚠️
if y=2x-3/3, then x=?
Answer:
Now, find the point where these two lines meet—that is the point with ... We just used them to help us locate the point \left(1,3\right) . ... Since x=2 , the point is to the right of the y-axis. Since y=-3 , the point is below the x-axis. ... Can you tell just by looking at the coordinates in which quadrant the point \left(-2 ... \left(3,-3\right)
Answer:
x = y/2+1/2
Step-by-step explanation:
Simplify the equation, leaving X on one side, giving you x=y/2+1/2.
the area under the entire probability density curve is equal to ____
The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.
For a continuous random variable X, the probability density function f(x) satisfies the following properties:
1. Non-negativity: f(x) ≥ 0 for all x.
2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:
∫[−∞, ∞] f(x) dx = 1
This integral represents the total area under the probability density curve, which must be equal to 1.
To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:
P(a ≤ X ≤ b) = ∫[a, b] f(x) dx
This integral gives the probability that X takes on a value between a and b.
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Which ordered pair is a solution to this equation? 2x + 3y = 16
(11, 1)
(7, 2)
(3, 2)
(5, 2)
Answer:
(5, 2)
Step-by-step explanation:
2(5) + 3(2) = 16
10 + 6 = 16
16 = 16
Hope this helps
Answer:
4) (5, 2)
Step-by-step explanation:
We should go through each of the coordinate pairs and substitute them into the line's equation. If the coordinate pair we checked satisfies the equation, it means the line passes through that point (which also means it's a solution to the equation).
1) (11, 1): \(2\times11+3\times1 \to 22 + 3\to25 \ne 16\)
It is not equal to 16, therefore, it does not satisfy the equation.
2) (7, 2): \(2\times7+3\times2\to14+6\to20 \ne 16\)
It is not equal to 16, therefore, it does not satisfy the equation.
3) (3, 2): \(2\times3+3\times2\to6+6\to12 \ne 16\)
It is not equal to 16, therefore, it does not satisfy the equation.
4) (5, 2): \(2\times5+3\times2\to10+6\to16=16\)
It is equal to 16, therefore, it does satisfy the equation.
4÷1.84=
what is the answer to this and explain how u got ur answer btw this is easy division but my brain cells just hate math so yeah- (btw this is in decimal form)
4÷1.84 means 4 over 1.84 (4/1.84) = 2.17
if u calculate 1.84 ÷ 4 (using calculator) the ans will be different bcauz it means 1.84 over 4 (1.84/4)
can sum1 pls help? this is geometry 10th grade.
The lateral surface area and volume of the shape will be 2405.4 square feet and 10,324.6 cubic feet, respectively.
Given information:
Base length, a = 34 ft and b = 10 ft
Height, h = 24.7 ft
Slant height, l = 27 ft
Width, w = 19 ft
The volume of the shape is calculated as,
V = 1/2 x (34 + 10) x 24.7 x 19
V = 10,324.6 cubic feet
The surface area is calculated as,
SA = 2(19 x 27) + 1/2 x (34 + 10) x 24.7 + 10 x 19 + 34 x 19
SA = 1026 + 543.4 + 190 + 646
SA = 2405.4 square feet
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h(x)=-x^2+6x. So what is the value of h(2)
✩ Answer:
✧・゚: *✧・゚:*✧・゚: *✧・゚:*✧・゚: *✧・゚:*
\(\bold{Hello!}\\\bold{Your~answer~is~below!}\)
✩ Step-by-step explanation:
✧・゚: *✧・゚:*✧・゚: *✧・゚:*✧・゚: *✧・゚:*
✺ Quadratic polynomials can be factored using the transformation \(ax^2+bx+c=a(x-x_{1})(x-x_{2} )\), where \(x_{1}\) and \(x_{2}\) are the solutions of the quadratic equation \(ax^2+bx+c=0\):
\(-x^2+6x=0\)✺ All equations of the form \(ax^2+bx+c=0\) can be solved using the quadratic formula:
\(-b=\frac{+}\\\sqrt{b^2-4ac}\\~~~~~~~~~~~~~2a\)✺ The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction:
\(x=\frac{\sqrt{-6\frac{+}\\\sqrt{6^2}}}{2(-1)}\)✺ Take the square root of \(6^2\):
\(x=\frac{\sqrt{-6\frac{+}\\{6}}}{2(-1)}\)✺ Multiply \(2\) times \(-1\):
\(x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}\)✺ Now solve the equation \(x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}\) when ± is plus. Add \(-6\) to \(6\):
\(x=\frac{0}{-2}\)✺ Divide \(0\) by \(-2\):
\(x=0\)-OR-
✺ Now solve the equation \(x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}\) when ± is minus. Subtract \(6\) from \(-6\):
\(x=\frac{-12}{-2}\)✺ Divide \(-12\) by \(-2\):
\(x=6\)✺ Optional : Factor the original expression using \(ax^2+bx+c=a(x-x_{1})(x-x_{2} )\). Substitute \(0\) for \(x_{1}\) and \(6\) for \(x_{2}\):
\(-x^2+6x=-x(x-6)\)✩ Answer:
✺ Factored Form: \(x(x-6)\)
✺ Exact Form: \(x=6\)
✺ Graph Point Form: \(x=(6,0)\)
\(Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex\)
"ටᆼට"
Find an equation involving g,h, and k that makes this augmented matrix correspond to a consistent system;
⎣
⎡
1
0
−2
−4
3
5
7
−5
−9
g
h
k
⎦
⎤
To make the augmented matrix correspond to a consistent system, we need to ensure that the third row is a linear combination of the first two rows. Let's denote the entries in the third row as a, b, and c, respectively. Then, the equation involving g, h, and k that makes the matrix consistent is:
-4g + 3h + 5k = a
7g - 5h - 9k = b
In a consistent system, all rows of the augmented matrix must be linearly dependent. This means that the third row should be a linear combination of the first two rows. By equating the corresponding entries in the third row to variables, we can find an equation involving g, h, and k that satisfies this condition.
In the given augmented matrix, the third row is represented by the variables g, h, and k. We denote the entries in the third row as a, b, and c, respectively. To create a consistent system, we need to find a relationship between these variables and the entries in the first two rows.
By comparing the entries in the first and second columns, we can set up the following equations:
-4g + 3h + 5k = a (equation 1)
7g - 5h - 9k = b (equation 2)
These equations ensure that the augmented matrix corresponds to a consistent system. If we substitute the values of g, h, and k into equations 1 and 2, the resulting values in the third row will satisfy the entries a and b, respectively.
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Bonnie deposited $1000 in an investment account on the first of January in 2001. The account pays 7.2% interest compounded annually. How much is the investment worth at the end of 2005? please help, having a mental break down over my math homework <3
Answer:
About $1415.71
Step-by-step explanation:
We can use the formula for compound interest, given by:
\(\displaystyle A=P(1+\frac{r}{n})^{nt}\)
Where P is the initial amount, r is the rate, n is the number of times compounded annually, and t is the time in years.
Our initial amount is the $1000 Bonnie deposited. So, P = 1000.
Our rate is the interest, which is 7.2% of 0.072. So, r = 0.072.
Since it is compounded annually, our n = 1. So, we have:
\(A=1000(1+0.072)^t\)
We want the amount after 5 years. So, t = 5. Substitute and evaluate:
\(A=1000(1.072)^5\approx\$1415.71\)
The investment will be worth about $1415.71 after 5 years.
Answestream wonder
Step-by-step explanation:
k 9
Suppose each license plate in a certain state has three digits followed by three letters. The digits 4 and 5 are not used. So, there are 26 letters and 8 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?
The required, there are 8998912 possible license plates that can be generated using this format.
Here, we have,
There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.
Therefore, there are 8 choices for each of the three digits,
giving us 8 x 8 x 8 = 512 possible combinations for the digits.
Similarly, there are 26 letters that can be used for each of the three letters on the license plate.
Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.
Total number of license plates = number of choices for the digits x number of choices for the letters
= 512 x 17576
= 8998912
Therefore, there are 8998912 possible license plates that can be generated using this format.
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