A car was bought a year ago for £2375. It is now worth £1729. What percentage of the cost of the car is the car worth now?

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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Therefore, we have indirectly proven that if n is an odd number, and its negation is false, then the original statement "if n is an odd number" is true.

To construct an indirect proof of the statement "if n is an odd number," we assume the negation of the statement, which is "n is not an odd number" or "n is an even number."

In an indirect proof, we aim to derive a contradiction from this assumption. Therefore, we will show that assuming n is an even number leads to a contradiction.

Assume n is an even number. By definition, an even number can be written as 2k, where k is an integer.

Since n is an even number, we can write it as n = 2k for some integer k.

Now, we can consider the parity of n. If n is an even number, it can be divided by 2 without a remainder, which means n is divisible by 2.

However, this contradicts the initial assumption that n is an odd number. By definition, an odd number cannot be divided by 2 without a remainder.

Since assuming n is an even number leads to a contradiction, we can conclude that the negation of the statement "n is not an odd number" is false.

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Answer:

i think your answer would be $38.60

Step-by-step explanation:

i hope its right

Answer:

0.3144654088

Step-by-step explanation:

6/19.08=0.3144654088

Answer:

Least Common Multiple (LCM) of 28,42,63 is 252 ∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 3 = 252

Step-by-step explanation:

Answer:

252 is the answer

Step-by-step explanation:

find the multiples of all of them ( and make sure it is the least. )

28:

28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308

42:

42, 84, 126, 168, 210, 252, 294, 336

63:

63, 126, 189, 252, 315, 378

bolded + undurlined is the answer

you see that 252 is the answer

252 is the answer

Answer:

4/3

Step-by-step explanation:

You can simplify the exponent expression using exponent rules. The rules are:

A positive exponent is the number of times the base multiplies by itself.

A negative exponent is the number of times the base divides itself.

Multiplying same bases with exponents is simplified by adding the exponents.

Dividing same bases with exponents is simplified by subtracting the exponents.

A zero exponent always evaluates as 1.

The expression \frac{4^{-3}3^44^2}{3^54^{-2}}

3

5

4

−2

4

−3

3

4

4

2

can be simplified first using the negative exponent rule to move base with negative exponent to the other part of the fraction.

\frac{4^{-3}3^44^2}{3^54^{-2}} = \frac{4^{2}3^44^2}{3^54^{3}}

3

5

4

−2

4

−3

3

4

4

2

=

3

5

4

3

4

2

3

4

4

2

Now use the multiplication rule to simplify numerator and denominator.

\frac{4^{2}3^44^2}{3^54^{3}} = \frac{4^{2+2}3^4}{3^54^{3}} = \frac{4^{4}3^4}{3^54^{3}}

3

5

4

3

4

2

3

4

4

2

=

3

5

4

3

4

2+2

3

4

=

3

5

4

3

4

4

3

4

Finally, use the division rule to reduce the fraction.

\frac{4^{4}3^4}{3^54^{3}}= 4^{4-3} 3^{4-5} = 4*3^{-1} = \frac{4}{3}

3

5

4

3

4

4

3

4

=4

4−3

3

4−5

=4∗3

−1

=

3

4

The "hypothesis of no change," "status quo," and "conventional wisdom" are all alternative names for the null hypothesis. Unless there is overwhelming evidence to the contrary, the null hypothesis is assumed to be correct.

H0: u = 1: u ≠ 1,400

When testing hypotheses with the P value, the null hypothesis is rejected if?

The evidence against the null hypothesis is stronger when the p-value is smaller (closer to 0).If the p-esteem is not exactly or equivalent to the predetermined importance level α, the invalid speculation is dismissed;The null hypothesis is not rejected otherwise.

A statement of expectation or prediction that will be tested by research is called a research hypothesis. Read up on the subject that interests you before coming up with your research hypothesis.

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The value of y obtained after solving the given equation will be equal to 11/3 or 3 2/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

3/4y + 1/2 = 3 1/4

Firstly, write the equation in a simplified way,

3/4y + 1/2 = 13/4

3/4y = 13/4 - 1/2

3/4y = (13 - 2)/4

3/4y = 11/4

Now, solve the equation for y,

y = (11 × 4)/(4 × 3)

y = 11/3

In mixed fraction form, it can be written as 3 2/3.

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Given the vectors a = [-1, -4, -5] and b = [6, 5, 4], we can perform various operations on them.

a) Rewriting vector a in terms of i, j, and k:

a = -1i - 4j - 5k

b) Calculating the magnitude of vectors a and b:

|a| = √((-1)² + (-4)² + (-5)²) = √(1 + 16 + 25) = √42

|b| = √(6² + 5² + 4²) = √(36 + 25 + 16) = √77

c) Expressing a + b and a - b in terms of i, j, and k:

a + b = (-1 + 6)i + (-4 + 5)j + (-5 + 4)k = 5i + 1j - 1k

a - b = (-1 - 6)i + (-4 - 5)j + (-5 - 4)k = -7i - 9j - 9k

d) Calculating the magnitude of a + b:

|a + b| = √(5² + 1² + (-1)²) = √(25 + 1 + 1) = √27 = 3√3

e) Showing that |a + b| ≤ |a| + |b|:

|a + b| = 3√3 ≤ √42 + √77 ≈ 6.48

f) Calculating the dot product of a and b:

a · b = (-1)(6) + (-4)(5) + (-5)(4) = -6 - 20 - 20 = -46

g) Finding the angle between vectors a and b:

cosθ = (a · b) / (|a| |b|) = -46 / (√42 √77) ≈ -0.448

θ ≈ arccos(-0.448) ≈ 116.1°

h) Calculating the projection of a onto b:

proj_b(a) = (a · b / |b|²) b = (-46 / 77) [6, 5, 4] = [-276/77, -230/77, -184/77]

i) Calculating the cross product of a and b:

a x b = [(-4)(4) - (-5)(5)]i - [(-1)(4) - (-5)(6)]j + [(-1)(5) - (-4)(6)]k

= [-9, -10, 1]

j) Evaluating the area of the parallelogram defined by a and b:

Area = |a x b| = √((-9)² + (-10)² + 1²

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Answer:

Wooden Ruler

Step-by-step explanation:

Wood is rigid and cannot bend, stretch, or be changed and adapted.

Answer:

1. La ecuación vectorial de la línea es \(\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}\)

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

\(\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}\)

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

Answer:

4ac

Step-by-step explanation:

Assuming you're referring to the equation \(ax^2+bx+c=0\).

Since the discriminant \(D=b^2-4ac\) has to be equal to 0 in order for there to be exactly one real solution, then we have the following:

\(0=b^2-4ac\\b^2=4ac\)

Therefore, b² needs to be the same value as 4ac.

Answer:

The answer should be y = -\(\frac{3}{2}\)\(x\) + 8, but its not one of the answers, so check the question again.

Step-by-step explanation:

If the second line is parallel, then the gradient will be the same:

y = -\(\frac{3}{2}\)\(x\) + c

Find what c is (y-intercept) by inputting the given point into the equation (4,2):

2 =  (-\(\frac{3}{2}\) x 4) + c

2 = -6 + c

c = 8

Answer:

B

Step-by-step explanation:

The Domain is the X- value so that makes it the domain and you have to order it correctly

Answer:

decimal

Step-by-step explanation:

Before using the rate given as a percentage in simple interest formula, you must first convert it to decimal.

 This helps in simplifying the work and help the calculation.

 Simple interest = \(\frac{PRT}{100}\)  

P is the principal

R is the rate

T is the time

  The rate is taken to decimal and inserted into the problem.

Before using it in the simple interest formula, you must first convert it to a decimal.

The following information should be considered:

Therefore we can conclude that the last option is correct.

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Answer:

m = -1/3

Step-by-step explanation:

First, write the equation in slope-intercept form:

3y = 10 - x

y = 10/3 - x/3

y = 10/3 - 1/3x

Since our slope is the coefficient of the x term, our slope is -1/3.

Answer:

$3072

Step-by-step explanation:

It is given that :

I work for 4 hours everyday, working 2 days a week.

And in 1 hour , I get $8.

Therefore,

1 hour = $8

4 hours = 4 x  8

             = $32

So, in 1 day working for 4 hours, I get $32.

∴ Working 2 days = 32 x 2

                              = $64

In 1 month, there are 4 weeks

So, in 4 weeks (or 1 month), I work for = 4 x 2

                                                               =  8 days

Therefore, in 8 days, I get = 8 x 32

                                            = $256

Now there are 12 months in a year.

So, in 12 months , I will get = 12 x 256

                                            = $3072

Therefore, in 1 year , I will get $3072.

Answer: KVL

Step-by-step explanation:

This would be the correct name for the angle since the V needs to be in the middle of the answer. In the angle you can see L V and K all pass 5 making it the correct name for the angle

Two angles are Supplementary, when they add up to 180 degrees. Hence:

Let x and y be both angles (x is the angle we are looking for);

x + y = 180° (1)

x = 1/5y (2)

We need to solve the system of equations, as follows:

Replacing equation 2 on equation 1:

1/5y + y = 180

y = 150°

Replacing the value of y in equation 2:

x = 1/5(150)

x = 30°

ANSWER

The measurement of the angle is 30°

Answer: x < 4

Step-by-step explanation: You are trying to isolate the variable, x, so you have to subtract 1 on both sides of the inequality. Then, you are left with x < 4.

The computation shows that the number of years ruled is 41 years.

From the information, Octavian became the emperor of Rome in 27 B.C and he ruled until his death in A.D. 14.

Therefore, the number of years that he rules will be:

= 14 - (-27)

= 14 + 27

= 41

Therefore, the number of years will be 41.

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Answer:

\(x < 1\)

For any number to be less than the given number in an inequality, the number on the right side has to match up with the word problem given. The problem says the number was less than 8, and to get anything less than 8, you must multiply any number below 1 by that number.

Answer:

b

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

You should sell the perfume for at least 278.40 euros to cover the cost of ingredients and achieve a 20% profit margin.

To determine the minimum selling price for the perfume, we need to calculate the total cost of the ingredients and then add a desired profit margin.

Let's calculate the cost of each ingredient first:

Cost of essence = 1 liter × 200 euros/liter = 200 euros

Cost of alcohol = 5 liters × 6 euros/liter = 30 euros

Cost of water = 2 liters × (cost per liter in euros)

Let's assume the cost of water is 1 euro per liter. In that case, the cost of water would be:

Cost of water = 2 liters × 1 euro/liter = 2 euros

Now we can calculate the total cost of the ingredients:

Total cost = Cost of essence + Cost of alcohol + Cost of water

= 200 euros + 30 euros + 2 euros

= 232 euros

To determine the minimum selling price, you need to add a desired profit margin.

Let's assume you want a 20% profit margin.

To calculate the selling price, you would add 20% of the total cost to the total cost:

Selling price = Total cost + (Profit margin × Total cost)

= 232 euros + (0.20 × 232 euros)

= 232 euros + 46.40 euros

= 278.40 euros

Therefore, you should sell the perfume for at least 278.40 euros to cover the cost of ingredients and achieve a 20% profit margin.

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Translation :-

A PERFUME MANUFACTURER MIXES 1 LITER OF ESSENCE

WITH 5 LITERS OF ALCOHOL AND 2 LITERS OF WATER. THE ESSENCE

IT COSTS 200 EUROS / LITER, ALCOHOL 6 EUROS / LITER AND WATER

EUROS PER LITER. HOW MUCH SHOULD YOU SELL AT LEAST THE

PERFUME?

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.

Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6

of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6

of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.

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Option B is Correct. An specific place in space is called a point. A dot indicates a point.

A point in space is a location. No length, width, or thickness exist in a point. In geometry, a dot stands in for a point. We typically use a (capital) letter to name a point. The simplest basic geometric object is a point. It is named with a capital letter and symbolised by a dot.

A point has no size and solely represents position (that is, zero length, zero width, and zero height). In a line, a line segment has two distinct endpoints. The line segment's length, which is the separation of two fixed points, is constant.

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Correct Question:

An exact location in space is called a _______

A. Line

B. Point

C. Circle

D. Line segment

Answer:

\(\frac{1}{9}\) (Decimal Form: 0.111111)

Step-by-step explanation:

1) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\(\frac{1}{3^2}\)

2) Simplify \(3^2\) to 9.

\(\frac{1}{9}\)

Thanks.