The Laplace transform table contains properties and formulas for common transforms, as well as the inverse Laplace transform and the shift theorem. It also includes properties such as linearity, scaling, and time shifting.
The Laplace transform table is an important tool for solving linear differential equations. It contains information about common transformations and their associated formulas, as well as the inverse Laplace transform and the shift theorem. The table also includes properties such as linearity, scaling, and time shifting. Linearity states that if a function f(t) is a linear combination of two functions f1(t) and f2(t), then its Laplace transform F(s) is the sum of the Laplace transforms of f1(t) and f2(t). Scaling states that if a function f(t) is multiplied by constant k, then its Laplace transform F(s) is divided by k. Time shifting states that if a function f(t) is shifted by x units in time, then its Laplace transform F(s) is multiplied by [tex]e^(-sx)[/tex]. These properties can be used to simplify Laplace transforms and to solve linear differential equations. The Laplace transform table is a useful tool for engineers and physicists who use linear differential equations in their work.
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how much 10 ml in teaspoon?
There are approximately 1 teaspoon in 5 milliliters. Therefore, in 10 milliliters we have 2 teaspoons approximately.
When converting between milliliters and teaspoons, it's important to know that 1 teaspoon is equal to approximately 5 milliliters. Therefore, to convert 10 milliliters to teaspoons, you would divide 10 by 5, which gives you 2. This means that there are approximately 2 teaspoons in 10 milliliters. It's worth noting that while teaspoons are commonly used in the United States and other countries that use the imperial system of measurement, most countries use the metric system, which uses milliliters as the standard unit of volume. Therefore, it can be helpful to know how to convert between these units of measurement, particularly if you're following a recipe or taking medication that uses a different system than what you're used to.
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Students make a big mess in the cafeteria at lunch. 9 students had 30 minutes to clean up the mess.They got mad and named 3 others that were guilty. The principal added their names to the clean up crew and changed the time limit. How much time should she give them to complete the job?
Answer:
22.5 minutes
Step-by-step explanation:
Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.
After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.
Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:
9 · 30 = 12 · t
Solving for "t":
270 = 12t
t = 270 / 12
t = 22.5
So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.
Write an explicit formula for a(n) the n^th term of the sequence 36,−6,1
You want to estimate the mean SAT score for a population of students with a 80% confidence interval. Assume that the population standard deviation is s = 120. If you want the margin of error to be approximately 10, you will need a sample size of_____
The sample size for the given data is 17
What is sample size?The sample size is a term used in market research for defining the number of subjects included in a sample size.
Given that, a sample size has an 80% confidence interval, the population standard deviation is s = 120, the margin of error to be approximately 10, We need to find the sample size,
Sample size = (z-score)²×SD×(1-SD) / (confidence interval)²
z-score of 80% confidence interval = 1.28
Sample size = (1.28)²×0.12(1-0.12)/0.10²
= 1.6384×0.12×0.88/0.01
= 17.30
Hence, the sample size for the given data is 17
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The slope, a, of the inverse function is , and the x-intercept of the inverse function is at x =.
The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.
FunctionThe sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Each element of X receives exactly one element of Y when a function from one set to the other is used.
According to the question,
f (x) = 1/3x - 2
now to find inverse ,
Add 2 to x term and then divide by 1/3 so, we get,
f⁻¹(x) = (x + 2) / 1/3
f⁻¹(x) = 3(x + 2)
now, compare with f⁻¹(x) = a (x + 2)
a = 3
Calculate the x-intercept by putting f(x) = 0
0 = x + 2
x = -2
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(asap help!)
Explain step by step please
The inequality form is 4/3<x<11.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
The given inequality is log₂(3x-4)<log₂(2x+7)
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: 4/3<x<11
Interval Notation:(4/3,11)
Therefore, the inequality form is 4/3<x<11.
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19. The total number of students T who traveled for spring break
consists of two groups: students who flew to their destinations F and students who
drove to their destination D. The number (in thousands) of students who flew and
the total number of students who flew or drove can be modeled by the following
equations, where n is the number of years since 1995.
T = 14n + 21
F = 8n + 7
a. Write an equation that models the number of students who drove to their
destination for this time period. /
b. Predict the number of students who will drive to their destination in 2012.
c. How many students will drive or fly to their destination in 2015?
7. A 16-inch pizza is cut into 8 equal slices. If
Thomas ate 3 slices, approximately how
many square inches of pizza did she eat?
Answer: 6 square inches
Step-by-step explanation:
Since the pizza is 16 inches and there is 8 slices divide.
16 inches ÷ 8 slices = 2 inches per slice
Each slice is 2 inches.
Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.
2 inches per slice x 3 slices = 6 square inches
Therefore she ate 6 square inches of pizza.
A kaleidoscope shaped like the prism below has mirrors covering the lateral surfaces. The bases are equilateral triangles. Find the total
square centimeters of mirrors covering the lateral surfaces.
The total square centimeters of mirrors covering the lateral surfaces is
171.5 cm².
What is surface area?
The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Given:
Perpendicular height = 14.3
So, the Surface area of Prism is
= 5 x 10 x 3 + 1/2 x 5 x 4.3 x 2
= 150 + 21.5
= 171.5
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What is 20% of 10? Because I can’t do it
Answer:
2
Step-by-step explanation:
20% = 0.2
What is 20% of 10?
We take
10 times 0.2 = 2
So, 20% of 10 is 2.
A school orchestra has 60 members 20%of the members are percussionists,how many orchestra members are percussionist
Answer:
12
Step-by-step explanation:
10% * 60 = 6
20% * 60 = 12
Write some examples of quadrilaterals
A two-dimensional form having four sides, four vertices, and four angles is referred to as a quadrilateral. Examples are: Trapezium, Parallelogram, Rectangle, Rhombus, Square and Kite.
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals. Hence a Quadrilateral is of 4 sides, vertices and angles. It consists of 360 degrees.
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There are 128 teams in a softball tournament. In each
round, half of the teams are eliminated. Which function
can be used to find the number of teams remaining in
the tournament after x rounds?
We can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
The usual way to refer to a function is as f(x), where x is the input.
One function, many. function onto (Surjective Function) into perform.
The function of a polynomial.
So, by observation we can find out the function:
y = 128(0.5)ˣ
Assume the teams after 1st round:
y = 128(0.5)ˣ
y = 128(0.5)¹
y = 128*0.5
y = 64 (Half od 128)
Therefore, we can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.
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Convert 8400 kilograms into tons. Round your answer to the nearest hundredth.
Answer:
9.26 tons
Step-by-step explanation:
8400 kilograms is 9.259415 tons and when you round to the nearest hundredth it is 9.26.
please answer this for me
Answer:
Step-by-step explanation:
where is the equation?
Answer:
Step-by-step explanation:
Multiply 4.75 by 2 to find out how much money Maurice gets when finishing 2 chores. $4.75 x 2 = $9.50. So, write $9.50 under 2. For three chores, multiply $4.75 by 3. $4.75 x 3 = $14.25. Write $14.25 under 3.
What does the size of stiffness matrix depend on?
the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.
In structural mechanics and engineering, the stiffness matrix is a mathematical representation of the stiffness of a structure, which relates the forces and displacements of the structure. The size of the stiffness matrix depends on several factors, including the number of degrees of freedom and the type of elements used in the analysis. The number of degrees of freedom (DOF) in the system determines the size of the stiffness matrix. DOF refers to the number of independent displacements or rotations that a structure can undergo in response to external forces. For example, a simple beam structure might have two DOF (vertical displacement and rotation), while a more complex structure such as a truss or frame might have many more DOF. The size of the stiffness matrix also depends on the type of elements used in the analysis. Different types of elements have different degrees of freedom and stiffness properties, which affect the size and shape of the stiffness matrix. For example, a truss element has two DOF and a constant axial stiffness, while a beam element has four or six DOF and variable stiffness properties that depend on its geometry and material properties.
In summary, the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.
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ASAP
will give brainliest to correct answer
20pts
Answer:
5, 18 and 7 respectively
Step-by-step explanation:
4+9+5=18
18+7=35
Answer:The top box is 11 making the middle boxes 15 20
Step-by-step explanation:
4 11 9
4+11 11+9
15 20
15+20
35
1. A number is less than one-fourth the sum of eight times the number and four.
We can write the inequality as -
{x} < (1/4){8x + 4}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement as -
"A number is less than one-fourth the sum of eight times the number and four"
We can write the statement as follows.
Let the number be {x}. Then, we can write the inequality as -
{x} < (1/4){8x + 4}
Therefore, we can write the inequality as -
{x} < (1/4){8x + 4}
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If a system graphs as parallel lines, the system would have how many solutions?
Answer:
zero
Step-by-step explanation:
If a system of equations is graphed as 2 lines, then if the lines intersect, they intersect at one single point, and that point is the solution. There is one solution.
If the lines are parallel and do not intersect, then there is no solution. The number of solutions is zero.
Answer: zero
Tyler is working two summer jobs, making $25 per hour tutoring and making $9 per
hour clearing tables. In a given week, he can work no more than 18 total hours and
must earn a minimum of $270. If a represents the number of hours tutoring and y
represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
One possible solution is to tutor for 11 hours and clear tables for 5 hours
How to write and solve a system of inequalities graphicallyFrom the question, we have the following parameters that can be used in our computation:
$25 per hour tutoring and making $9 per hour clearing tables. He can work no more than 18 total hours and must earn a minimum of $270Using the above as a guide, we have the following:
25x + 9y ≥ 270
x + y ≤ 18
Where
x = hours tutoring
y = hours cleaning tables
Next, we plot the graph (see attachment)
One solution from the graph is (11, 5)
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When creating a serial dilution from 1/10 to 1/1000, the first dilution will be [a] part sample and [b] parts diluent (what you dilute the sample in). The second dilution will be one part [c] and nine parts [d]. The final dilution will be one part [e] and nine parts diluent.
The answer is: 1 part sample, 9 parts diluent, 1 part of the first dilution, 9 parts diluent, 1 part of the second dilution, 9 parts diluent
When creating a serial dilution, the starting concentration is typically given as a ratio of sample to diluent. For example, a 1/10 dilution would mean that there is one part of sample and nine parts of diluent.
Now when we create a serial dilution from 1/10 to 1/1000, the first dilution will be 1 part sample and 9 parts diluent. The second dilution will be one part of the first dilution and nine parts diluent. The final dilution will be one part of the second dilution and nine parts diluent.
Thus, the answer is:
1 part sample
9 parts diluent
1 part of the first dilution
9 parts diluent
1 part of the second dilution
9 parts diluent
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____ The given question is incorrect, the correct question is given below:
When creating a serial dilution from 1/10 to 1/1000, the first dilution will be _______ part sample and ______ parts diluent. The second dilution will be one part ____ and nine parts _____. The final dilution will be one part _____ and nine parts diluent.
Choices:
1(one)
9(nine)
1/10 dilution
1/100 dilution
1/1000 dilution
diluent
divide 3x^3-2x^2+4x-3 by x^2+3x+3
On dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is to divide (3x³ - 2x² +4x - 3) by (x² + 3x + 3).
Let us assume that -
f(x) = (3x³ - 2x² + 4x - 3)
g(x) = (x² + 3x + 3)
We can write -
h(x) = f(x)/g(x)
h(x) = (3x³ - 2x² + 4x - 3)/(x² + 3x + 3)
h(x) = 3x + {(- 11x² - 5x - 3)/(x² + 3x + 3)}
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}
Therefore, on dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -
h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.
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Graph and find the area of the figure with vertices (-3,-2),(-2,-),(1,1), (0,-2) NEED help pls
Answer: The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Plugging in the given coordinates, the area of the triangle is:
A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))
A = 1/2(-3)(-2)+(-2)(3)+1(-3)
A = -9+6-3
A = 4
Step-by-step explanation: Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).
Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).
Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).
Step 4: Solve the equation: A = -9+6-3.
Step 5: Find the area of the triangle: A = 4.
The regular price on a pair of jeans is $54. The store advertises a back to school sale at 40% of the regular price of the jeans. Two weeks later, the store advertises a sale at an additional 20% off the sale price of the jeans. Two friends decided to purchase the jeans. Shannon says these jeans are now 60% of the regular price. Mary disagrees because she figures that the total discount is less than 60%. What is the cost of the jeans at the 40% off back-to-school sale. What is the cost of the jeans during the additional 20% off sale
Answer:
See explanation
Step-by-step explanation:
40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.
20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.
[tex]\lim_{x\to \023}[/tex][tex]\sqrt{x+2}-5/x-23[/tex]
The limit of the expression [tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex] when evaluated is -18.22
What is a Limit?Limit is a value that a function approaches the output for the given input values.
How to determine the limit of the expressionFrom the question, we have the following limit expression that can be used in our computation:
[tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex]
To find the limit tends to 23, we substitute 23 for x in the above equation
So, we have the following representation
[tex]\lim_{x \to \223} \sqrt{23+2} -\frac{5\\}{23} -23[/tex]
Evaluate the sum in the expression
[tex]\lim_{x \to \223} \sqrt{25} -\frac{5\\}{23} -23[/tex]
Evaluate the exponent and the fractions
Limit = 5 -5/23 -23
When the expression is evaluated, we have
Limit = -18.2173913043
Approximate
Limit = -18.22
Hence, the solution is -18.22
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PLS HELP...... 4. John and Carol have both set up a proportion to solve for x in the diagram below.
John :
Carol:
Who is correct? Then solve for x.
Naomi has taken six science tests so far this year. The tests are out of 100 points, and she has gotten the following scores.
64, 88, 92, 86, 81, 92
What is the median of her scores?
no median
83.8
92
87
I don’t get this math problem4/5 + 3/4
Answer:
AS a fraction: 1[tex]\frac{11}{20}[/tex]
AS a decimal: 1.55
Step-by-step explanation:
4/5 + 3/4
least common multiple of 5 and 4 is 20. Conver [tex]\frac{4}{5}[/tex] and [tex]\frac{3}{4}[/tex] to fractions with denominator 20.
16/20 + 15/20
since [tex]\frac{16}{20} and \frac{15}{20}[/tex] have the same denominator, add them by adding their numerators.
[tex]\frac{16 + 15}{20}[/tex]
Add 16 and 15 to get 31.
[tex]\frac{31}{20}[/tex]
[tex]\frac{31}{2^{2}x5 } = 1\frac{11}{20}[/tex]
Hope that helps and have a great day! =) ~sunshine~
You want to purchase
a pair of shoes for the
summer. Normally
they cost $79.99.
They are on sale for
15% off, or you also
have a $10 off
coupon. Including
sales tax at 10.3%,
what is the total
savings between
using the coupon and
taking the discount?
Answer:
$2.21
Step-by-step explanation:
You want to know the savings between using a $10 off coupon and taking a 15% discount, if the tax rate is 10.3%.
CouponThe price with the coupon is ...
$79.99 -10.00 = $69.99
When tax is added, the total becomes ...
$69.99 × 1.103 ≈ $77.20
DiscountThe price with the discount is ...
$79.99 × (1 -0.15) ≈ $67.99
When tax is added, the total becomes ...
$67.99 × 1.103 ≈ $74.99
SavingsThe savings by making use of the discount is ...
$77.20 -74.99 = $2.21
The total savings between the coupon and the discount is $2.21. That is, you save $2.21 more by using the discount instead of the coupon.
__
Additional comment
The question seems a bit ambiguous. The word "or" suggests you cannot use both discounts. If you do, the total amount saved will depend on the order in which they are applied.
You get the best result by taking the $10 off the sale price. Doing that gives you a total savings of about $24.27 off the normal price with tax.
How many ways can
4 candy bars be chosen
from a store that sells 30 candy bars?
Permutation or combination?
The count of the ways in which to chose 4 candies from a store that sells 30 candy bars, obtained by the combination formula, are 27405 ways
What is a combination in mathematics?A mathematical combination, is the ways in which a number of items can be chosen from a set of items, excluding a reference to the order in which the items are selected.
The number of ways k items can be chosen from n items, can be found by using the following combinations formula;
[tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]
Therefore, the number of ways 4 candies can be chosen from a store that sells 30 candy bars can be found by plugging in k = 4, and n = 30 as follows;
[tex]\binom{30}{4} = \frac{30!}{4!\cdot (30-4)!} = 27405[/tex]
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