The selling price of a car is $15000. What is its cost price if a 25% loss was made?

To find a particular solution for y'' 4y' 3y = 1/(1+e^t) using transfer functions, impulse response, and convolutions, we first need to find the homogeneous solution and then the particular solution.

The homogeneous solution is y_h = c1 e^(-t) + c2 e^(-3t), where c1 and c2 are constants. The transfer function is H(s) = 1/(s^2 + 4s + 3), and the impulse response is h(t) = e^(-t) - e^(-3t).

To find the particular solution, we need to first find the Laplace transform of the input function, which is F(s) = 1/(s+1)(1+e^(-s)). We can then use the convolution theorem to find the output function in the Laplace domain, which is Y(s) = H(s) F(s). Simplifying this expression using partial fraction decomposition and inverse Laplace transform, we get the particular solution y_p = (e^(-t) - e^(-3t)) / (2 - e^(-t)). Therefore, the general solution for the differential equation is y = y_h + y_p, where y_h is the homogeneous solution and y_p is the particular solution.

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The range of the function f (x) = - 3x² + 5 is,

⇒ (- ∞, 5]

⇒ All real numbers less than or equal to 5

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ f (x) = - 3x² + 5

Now, We an draw the graph of function f (x) = - 3x² + 5.

In graph the range is the defined as cover by up and down.

Hence, The range of the function f (x) = - 3x² + 5 is,

⇒ (- ∞, 5]

⇒ All real numbers less than or equal to 5

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Answer:

the andswer there is D

Step-by-step explanation:

just think of it as a cylinder and a square

put both circular parts together and you have a cylinder with the diameter of 12 and a height of 7 and find the volume of that which is πr²h so π 6² 7

then the volume of your rectangular prism is the length times width times height so 12 by 12 by 7

Answer:

5750

Step-by-step explanation:

\(\frac{5}{100}\)×5000=250

250×3=750

5000+750=5750

Answer:

A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36.

Rachel is setting up for her birthday. Rachel wants to put the same number of chairs around each table. How many chairs will Rachel place around each table at her birthday party?

✔ 6

Step-by-step explanation:

got it right on edge

Answer:

-5c+3c= -2c || 4f+(-3f)+c= 2c

The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

\(hyp^2 = a^2 + b^2\)

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

\(14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet\)

The wall reaches 10.7 feet high.

Answer:

498.66577718478985990660440293529019346230820547031354236157438292 seconds

Step-by-step explanation:

The equation of the quadratic model is \(f(x) = -16x^2 + 99x+ 6\)

A quadratic regression equation is represented as:

\(f(x) =ax^2 + bx + c\)

Where:

\(a = \frac{ [ \sum x^2 y * \sum xx ] - [\sum xy * \sum xx^2 ] }{ [ \sum xx * \sum x^2x^2] - [\sum xx^2 ]^2 }\)

\(b = \frac{ [ \sum xy * \sum x^2x^2 ] - [\sum x^2y * \sum xx^2 ] }{ [ \sum xx * \sum x^2x^2] - [\sum xx^2 ]^2 }\)

\(c = [ \frac{\sum y }{ n} ] - { b \times [ \frac{\sum x }{ n} ] } - { a * [ \frac{\sum x^2}{ n} ] }\)

Using a graphing calculator, we have:

\(a = -15.714\)

\(b= 98.857\)

\(c = 5.571\)

Approximate to the nearest integers

\(a = -16\)

\(b = 99\)

\(c = 6\\\)

Substitute these values in \(f(x) =ax^2 + bx + c\)

\(f(x) = -16x^2 + 99x+ 6\)

Hence, the equation of the quadratic model is \(f(x) = -16x^2 + 99x+ 6\)

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Answer:

The equation of the quadratic model is

A quadratic regression equation is represented as:

Where:

Using a graphing calculator, we have:

Approximate to the nearest integers

Substitute these values in

Hence, the equation of the quadratic model is

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Step-by-step explanation:

Answer:

Step-by-step explanation:

p=200+25(n)

The probability of getting at least 2 defective chips out of 8 is 0.0061, or about 0.61%

To solve this problem, we need to use the binomial distribution formula, which is:

P(X = k) = nCk * p^k * (1-p)^(n-k)

Where:
- P(X = k) is the probability of getting k successes
- n is the total number of trials (in this case, n = 8)
- k is the number of successes we're interested in (at least 2, so we need to calculate P(X = 2) + P(X = 3) + ... + P(X = 8))
- p is the probability of getting success on one trial (in this case, p = 0.01)

So let's calculate each term:

P(X = 2) = 8C2 * 0.01^2 * (1-0.01)^(8-2) = 0.0059
P(X = 3) = 8C3 * 0.01^3 * (1-0.01)^(8-3) = 0.0002
P(X = 4) = 8C4 * 0.01^4 * (1-0.01)^(8-4) = 0.0000
P(X = 5) = 8C5 * 0.01^5 * (1-0.01)^(8-5) = 0.0000
P(X = 6) = 8C6 * 0.01^6 * (1-0.01)^(8-6) = 0.0000
P(X = 7) = 8C7 * 0.01^7 * (1-0.01)^(8-7) = 0.0000
P(X = 8) = 8C8 * 0.01^8 * (1-0.01)^(8-8) = 0.0000

Now we can add up all the probabilities:

P(at least 2 defective chips) = P(X = 2) + P(X = 3) + ... + P(X = 8) = 0.0061

So the probability of getting at least 2 defective chips out of 8 is 0.0061, or about 0.61%. This is a relatively small probability, but it's not impossible, so the manufacturer should still take measures to minimize the number of defective chips produced.

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Answer:

4175.40384   Dutch guilders

Step-by-step explanation:

The main objective here is to convert the currency at hand (2,000 swiss francs) to Dutch guilders. In order to achieve that ; we need first require to convert the currency at hand into United states dollars

So ; if 1 swiss francs  =  1.0328 united states dollars  (as at Wednesday)

Then 2000 swiss francs  will be = 2000  ×  1.0328 united states dollars  = 2065.6 united states dollars

SO; if  1 united states dollars = 2.0214 Dutch guilders ( as at Wednesday)

Then 2065.6 united states dollars will be = 2065.6 × 2.0214

= 4175.40384   Dutch guilders

Answer:

closest would be 3,500

Step-by-step explanation:

Since at least one of the three series diverges, the original series ∑(N=1 to infinity) (3n + 14 - N) will also diverge. Therefore, the series is divergent, and we cannot find its sum.

To determine whether the series ∑(N=1 to infinity) (3n + 14 - N) is convergent or divergent, we can examine its behavior. Let's simplify the series and analyze it:

∑(N=1 to infinity) (3n + 14 - N)

Rearranging the terms:

∑(N=1 to infinity) (3n - N + 14)

We can split this series into three separate series:

Series 1: ∑(N=1 to infinity) 3n

Series 2: ∑(N=1 to infinity) -N

Series 3: ∑(N=1 to infinity) 14

Series 1 is a geometric series with a common ratio of 3, and it will be convergent if |r| < 1. In this case, |3| = 3, so it is divergent.

Series 2 is an arithmetic series with a common difference of -1, and it will be divergent since the terms do not approach a finite limit.

Series 3 is a constant series, and it will be divergent since the terms do not approach a finite limit.

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Answer:

52.948 m²

Step-by-step explanation:

→ State the formula for the area

length × width

→ Substitute in the numbers

8.68 × 6.1 = 52.948 m²

The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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The 95% confidence interval for the population proportion is approximately 0.3573 to 0.7141. None of the given options (A, B, C, D) match the calculated interval.

To construct a confidence interval for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± critical value * standard error

Where the sample proportion (p-hat) is calculated by dividing the number of successes (x) by the total sample size (n). In this case, n = 56 and x = 30, so the sample proportion is 30/56 = 0.5357.

The critical value is determined based on the desired degree of confidence. For a 95% confidence level, which is given in this case, the critical value can be obtained from a standard normal distribution. For a two-tailed test, the critical value is approximately 1.96.

The standard error is calculated by taking the square root of (p-hat * (1 - p-hat) / n). Plugging in the values, we get sqrt(0.5357 * (1 - 0.5357) / 56) = 0.0907.Now, we can construct the confidence interval:Confidence Interval = 0.5357 ± 1.96 * 0.0907Calculating the upper and lower bounds of the interval:

Lower bound = 0.5357 - (1.96 * 0.0907) ≈ 0.3573

Upper bound = 0.5357 + (1.96 * 0.0907) ≈ 0.7141\

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Answer:

Solve the equation below for unknown x (x is the money she had initially)

x - 8 - 5 - (x-8-5)/2 = 2

Step-by-step explanation:

Answer:

x > -3.4

Step-by-step explanation:

1 < (x + 5.5) / 2

first multiply each side by 2

2 < x + 5.5

Then subtract 5.5 from each side

-3.4 < x

x has to be on the left so you switch the hole equation around to get

x > -3.4

Answer:

assuming that the problem was actually

-1/12 x ^ 2 + 2x + 4

height = 16

(12,16)

forty feet (40) feet

vertex = -b/2a = -2/(-1/6) = 12

f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4   = 16

Step-by-step explanation:

The given expression:

The expression can be written as :

Take 9 common :

Since 3 x 3 = 9

Apply the property of factorization:

So, the expression can be written as :

So, the factorization is : 9(x + 3) (x - 3)

Answer :

The area of the region enclosed by one loop of the curve r = 3 cos(5θ) is (9/2) π square units

To find the area of the region enclosed by one loop of the curve given by the polar equation r = 3 cos(5θ), we can integrate over the corresponding range of θ values.

The curve r = 3 cos(5θ) represents a cardioid with five petals.

To determine the range of θ values that corresponds to one loop, we can set the equation inside the cosine function equal to zero:

5θ = 0

This gives us θ = 0.

So, for one complete loop, we need to integrate from θ = 0 to θ = 2π.

The area formula for a polar curve is given by:

A = (1/2) ∫[θ₁,θ₂] r(θ)² dθ

In this case, the area can be calculated as:

A = (1/2) ∫[0, 2π] (3 cos(5θ))² dθ

Simplifying the integral, we have:

A = (9/2) ∫[0, 2π] cos²(5θ) dθ

Using the trigonometric identity cos²(θ) = (1 + cos(2θ))/2, we can rewrite the integral:

A = (9/2) ∫[0, 2π] (1 + cos(10θ))/2 dθ

Expanding the integral, we get:

A = (9/4) ∫[0, 2π] dθ + (9/4) ∫[0, 2π] (cos(10θ))/2 dθ

The first integral ∫ dθ over the interval [0, 2π] gives us 2π:

A = (9/4) (2π) + (9/8) ∫[0, 2π] cos(10θ) dθ

The second integral ∫ cos(10θ) dθ can be evaluated as:

(1/10) sin(10θ)

Evaluating the integral over the interval [0, 2π], we get:

A = (9/4) (2π) + (9/8) [(1/10) sin(10(2π)) - (1/10) sin(10(0))]

Since sin(0) = 0 and sin(20π) = 0, the second term becomes zero:

A = (9/4) (2π) + (9/8) (0)

Simplifying, we have:

A = (9/4) (2π)
A = (9/2) π

Therefore, the area of the region enclosed by one loop of the curve r = 3 cos(5θ) is (9/2) π square units.

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Answer:

17 w  +  35

Step-by-step explanation:

You get this answer by using PEMDAS.

Answer:

bottom: 12 x 12 = 144

1st triangle: (12 x 8)/2 = 48

2nd triangle: 48

3rd triangle: 48

4th triangle: 48

144 + 48 + 48 + 48 + 48 = 336 cm squared

The equation describes a linear relationship between two variables, where the output of the equation, y, is equal to two fifths of the input, x.

To calculate the value of y in the equation y=2/5x, we need to start by identifying the value of x. Once that is known, the value of y can be calculated by substituting x into the equation. For example, if x=10, then we can substitute 10 into the equation to get y=2/5 x 10. To solve this, we can multiply 2/5 by 10 to get 2x10/5, which simplifies to 20/5. Since dividing by 5 is the same as multiplying by 1/5, we can simplify this to 20/5 = 4. Therefore, when x=10, y=4.

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the complete question is

What is the verbal description of y=2/5x  and identify the value of x

Answer:a

Step-by-step explanation:

I am expecting a if not, change the sighns.

Answer:

3

Step-by-step explanation:

Answer:

AB =√( (13 - 5)² + (13-12)²) = √(8² + 1²) = √65

BC = √( (13 - 11)² + (13-5)²) = √(2² + 8²) = √68

AC =√( (11 - 5)² + (5-12)²) = √(6² + 7²) = √85

AB ≠ BC ≠ AC ∴ ABC is Scalene

Step-by-step explanation:

A scalene triangle is a triangle in which all the sides are different lengths.

In order to prove that ABC is scalene, we need to calculate the sidelengths and show them to be different.

The line between points A(x₁, y₁) and B(x₂, y₂) can be denoted AB.

the difference in x-coordinate is x₂ - x₁, and the difference in y-coordinates is y₂ - y₁.

this forms a triangle of length x₂ - x₁ and height y₂ - y₁ and the hypotenuse AB can be calculated using pythagoras' theorem:

AB = √((x₂ - x₁)² +(y₂ - y₁)²)

The triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given three vertices of triangle ABC are A(5, 12) B(13, 13) and C (11,5).

We know that in a scalene triangle all the three sides lengths are different.

Let us find distance of AB,BC, CA

Distance=√(x₂-x₁)²+(y₂-y₁)²

A(5,12), B(13, 13)

AB=√(13-5)²+(13-12)²

=√8²+1²=√64+1=√65

B(13, 13) C (11,5).

BC=√(11-13)²+(5-13)²

=√4+64=√68

C (11,5).A(5,12),

CA=√(5-11)²+(12-5)²

=√(-6)²+(7)²

=√36+49=√85

The lengths of triangle ABC are different so the triangle is Scalene.

Hence the triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.

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