Find the Laplace transform of the following time functions: (a) f(t)=1+7t (b) f(t)=4+7t+t2+δ(t), where δ(t) is the unit impulse function (c) f(t)=e−t+2e−2t+te−3t (d) f(t)=(t+1)2 (e) f(t)=sinht

9514 1404 393

Answer:

Step-by-step explanation:

When you have a wording that matches ...

  A depends on B

It means that A is the dependent variable, and B is the independent variable.

Here, the total monthly cost depends on the number of cups purchased.

That statement tells you that "total monthly cost" is the dependent variable, and "number of cups purchased" is the independent variable (x).

The first four (4) blanks you're to fill represent two different ways of saying this same thing.

__

The equation is a mathematical expression of the way the costs add up.

  total monthly cost = (program cost) + (per-cup cost) × (number of cups)

  M(x) = 15 + 2x

Then M(13) is ...

  M(13) = 15 + 2·13 = 15 +26 = 41

So the total monthly cost for the purchase of 13 cups of coffee is $41.

Answer:

answer: 12

Step-by-step explanation:

You get 12 by doing base × height. So our base in this problem is 2.5 and our height is 4.8 so

2.5 × 4.8 = 12 Hope this helps!

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

(y÷2) -15

Step-by-step explanation:

quotient of y and 2= y/2

15 less = -15

hope this helped

Answer:

30

Step-by-step explanation:

2^3=8

8x3=24

24+6=30

Answer:

C Not a mandatory instruction

Step-by-step explanation:

Answer:

78=c98

Step-by-step explanation:

this is easy

Answer:

Step-by-step explanation:

Given: He needs 8ft and 6 ft

The trim costs 2.95 per foot

so if we do 8 times 2.95 we get 23.60

Next we do the same with 6 and we get 17.7

Add then together and we get $41.30

If this isn't right, i think you wrote either the answer choices wrong or the question itself wrong because it kinda confused me.

Answer:c

Step-by-step explanation:

Answer:

El total de líquido utilizado es \(\frac{5}{6} de litro\). Se echa \(\frac{1}{6}\) de litro más de leche que de jugo

Step-by-step explanation:

Para saber la cantidad total de líquido, basta con sumar las cantidades de leche y de jugo de naranja. Vamos a asumir que usa 1/3 de litro de jugo de naranja.

En este caso el total de líquido es 1/2 litro + 1/3 litro. Dado que estas fracciones tienen distinta denominador, debemos sumarlas de la siguiente manera

\( \frac{1}{2}+\frac{1}{3} = \frac{1\cdot 3 + 2\cdot 1}{2\cdot 3} = \frac{5}{6}\)

Para calcular la cantidad extra de leche de más que la cantidad de jugo, restamos estos números. Es decir

\( \frac{1}{2}-\frac{1}{3} = \frac{1\cdot 3 - 2\cdot 1 }{2\cdot 3} = \frac{1}{6}\)

Es decir, que echamos \(\frac{1}{6}\) de litro más de leche que de jugo.

Answer:

72 degrees is it's supplement

The probability that all three wires will meet the specifications is approximately 0.173 .

Expected value (mean) of wire resistance = 0.13 ohms Standard deviation of wire resistance = 0.005 ohms

the probability for each wire, we need to standardize the range of resistance values using the expected value and standard deviation. We can use the Z-score formula:

Z = (X - μ) / σ

Z is the standard score (Z-score) X is the observed value (resistance) μ is the mean (expected value) σ is the standard deviation

For the lower specification of 0.10 ohms

Z1 = (0.10 - 0.13) / 0.005

For the upper specification of 0.17 ohms

Z2 = (0.17 - 0.13) / 0.005

Using a standard normal distribution table , we can find the probability associated with each Z-score.

Lower bound of standardized range = (0.10 - 0.13) / 0.005 = -0.06

Upper bound of standardized range = (0.17 - 0.13) / 0.005 = 0.80

Let's calculate the probabilities for each wire

P(z < -0.60) ≈ 0.2743

P(z < 0.80) ≈ 0.7881

Since we want the probability that all three wires meet the specifications, we need to multiply these probabilities together since the wires are selected independently.

P(all three wires meet specifications) = P(z < -0.60) × P(z < 0.80) × P(z < 0.80)

P(all three wires meet specifications) ≈ 0.2743 × 0.7881 × 0.7881 ≈ 0.1703

Therefore, the probability that all three wires will meet the specifications is approximately 0.173, or 17.3% .

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21.The probability that a class of 10 students will have more than 4 males is 0.3222

22.The probability that a number drawn from this distribution will have a value between -1 and 2 is 0.8185.

The probability that a class of 10 students will have more than 4 males is given by:

P(X > 4) = 1 - P(X ≤ 4)

The probability that a student is male is

P(male) = 1 - P(female)

            = 1 - 0.80

            = 0.20

The number of male students in a class of 10 students follows a binomial distribution with n = 10 and p = 0.20.

The probability that a class of 10 students will have exactly 4 males is:

P(X = 4) = nCₓpˣ(1 - p)ⁿ⁻ˣ

where n = 10,

p = 0.20, and

x = 4

nCₓ = n! / x!(n - x)!

      = 10! / 4!(10 - 4)!

      = 210P(X = 4)

      = 210 × (0.20)⁴ × (0.80)⁶

      = 0.0880

The probability that a class of 10 students will have 4 or fewer males is:

P(X ≤ 4) = Σ P(X = x) where

x = 0, 1, 2, 3, 4

P(X ≤ 4) = P(X: 0) + P(X: 1) + P(X :2) + P(X: 3) + P(X:4)

P(X ≤ 4) = (0.80)¹⁰ + 10 × (0.20)¹ × (0.80)⁹ + 45 × (0.20)² × (0.80)⁸ + 120 × (0.20)³ × (0.80)⁷ + 210 × (0.20)⁴ × (0.80)⁶

             = 0.6778P(X > 4)

             = 1 - P(X ≤ 4)

             = 1 - 0.6778

             = 0.3222

Therefore, the probability that a class of 10 students will have more than 4 males is 0.3222

22.Let X be the random variable of the normal probability distribution having a mean of 0 and a standard deviation of 1.

The probability that a number drawn from this distribution will have a value between -1 and 2 is given by:

P(-1 ≤ X ≤ 2) = Φ(2) - Φ(-1) where

Φ(z) is the standard normal cumulative distribution function, which gives the probability that a number drawn from a standard normal distribution is less than or equal to z.

Using a standard normal distribution table or calculator, we can find that:

Φ(2) ≈ 0.9772Φ(-1)

       ≈ 0.1587

Therefore,P(-1 ≤ X ≤ 2) = Φ(2) - Φ(-1)

                                     = 0.9772 - 0.1587

                                     = 0.8185

The probability that a number drawn from this distribution will have a value between -1 and 2 is 0.8185.

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False. It is necessary to have a base case in all recursive algorithms.

A base case is a condition that stops the recursion process and returns a result. Every recursive algorithm must have a base case. The base case is the point at which the recursion will stop, and the function will begin to return the values from the call stack. The base case is necessary to stop the recursive algorithm from entering an infinite loop that will cause it to consume all available resources, resulting in a stack overflow error. If there is no base case, the algorithm will continue to call itself until the stack overflows, which will result in a runtime error.

In conclusion, a base case is essential in all recursive algorithms, and the lack of one can result in a stack overflow error.

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Answer:

since Bus A runs every 10 minutes while Bus B runs every 14 minutes

first add the minutes to get equivalent value

=10+14

=24

the value gotten will be added to the time

=24mins+11hrs

=11:24mins

PLEASE RATE AS BRAINLIEST

The minimum number of boxes a participant needs to eliminate is 12. The half chance of holding at least $100,000 as his/her chosen box is 7/14 from the whole chances of 7/26.

There are 26 boxes.

The required money is at the 7 the stage box.

So, the chance of holding at least $100,000 is 7/26.

Since the required value is available at a 7/26 chance of holding, the boxes that are less than $100,000 are removed.

So, 12 boxes holding less than $100,000. So, the probability of half chance of holding at least $100,000 is 7/14.

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Disclaimer: The given question on the portal is incomplete. Here is the complete question.

Question: In the game Deal or No Deal, participants choose a box at random from a set of one containing each of the following values:

$0.01, $1,000

$1, $5,000

$5, $10,000

$10, $25,000

$25, $50,000

$50, $75,000

$75, $100,000

$100, $200,000

$200, $300,000

$300, $400,000

$400, $500,000

$500, $750,000

$750, $1,000,000

After choosing a box, participants eliminate other boxes by opening them, showing the amount of money in the box to the crowd, and then removing that box (and its money!) from the game. What is the minimum number of boxes a participant needs to eliminate to have a half chance of holding at least $100,000 as his or her chosen box?

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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The area bounded by the intersection of the curves are as follows to find the area bounded by the intersection of the curves y = 1 and y = x², we need to find the points of intersection and calculate the area between them.

Setting the equations equal to each other, we have:

1 = x²

Solving for x, we find:

x = ±1

So the curves intersect at the points (-1, 1) and (1, 1).

2. To find the area between the curves, we integrate the difference between the curves over the interval between the x-values of intersection points:

Area = ∫[from -1 to 1] (x² - 1) dx

Integrating the expression, we get:

Area = [x³/3 - x] [from -1 to 1]

= [(1/3 - 1) - (-1/3 + 1)]

= [(1/3 - 3/3) - (-1/3 + 3/3)]

= [(-2/3) - (2/3)]

= -4/3

Therefore, the area bounded by the intersection of the curves y = 1 and y = x² is -4/3 square units.

To determine the arc length of the curve y = 2√(3) + 1 for 0 ≤ x ≤ 1, we need to evaluate the integral of the square root of the sum of the squares of the derivatives of x and y with respect to x over the given interval.

The derivative of y = 2√(3) + 1 with respect to x is 0 since y is a constant.

The arc length integral can be written as:

Arc Length = ∫[from 0 to 1] sqrt(1 + (dy/dx)²) dx

Since (dy/dx)² = 0, the integral simplifies to:

Arc Length = ∫[from 0 to 1] sqrt(1 + 0) dx

= ∫[from 0 to 1] sqrt(1) dx

= ∫[from 0 to 1] dx

= [x] [from 0 to 1]

= 1 - 0

= 1

Therefore, the arc length of the curve y = 2√(3) + 1 for 0 ≤ x ≤ 1 is 1 unit.

3. To find the volume of the solid of revolution that results from revolving the region under the curve y = √(x + 4) for 0 ≤ x ≤ 2 about the x-axis, we can use the method of cylindrical shells.

The volume can be calculated using the formula:

Volume = ∫[from 0 to 2] 2πx √(x + 4) dx

Integrating the expression, we get:

Volume = 2π ∫[from 0 to 2] x √(x + 4) dx

This integral can be evaluated using techniques such as substitution or integration by parts. Once the integration is performed, the result will give us the volume of the solid of revolution.

Please note that the calculation of this integral is more involved, and the exact value will depend on the specific method used for integration.

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Answer:

Step-by-step explanation:

the other angle is 38 as well

Answer:

T₁₀

Step-by-step explanation:

We know the first term is 21, which is a

We work out the difference by taking 21 away from 42 which equals 21.

We then use the general formula:

Tₓ = a + (x-1)(d)

We need to find the term which equals 210

210 = 21 + (x - 1)(21)

210 = 21 - 21 + 21x

210 = 21x

x = 10

Hence it is the 10 term when the thing equals 210.

Answer:

width = 14 feet

Step-by-step explanation:

the 7 part of the ratio relates to the length of the garden , then

24.5 feet ÷ 7 = 3.5 feet ← value of one part of the ratio , so

width = 4 × 3.5 feet = 14 feet

The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.

The trigonometric equation for this problem is defined as follows:

7cos(9x) - 1 = 17

Isolating the cosine, we have that:

7cos(9x) = 18

cos(9x) = 18/7

Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:

9x = arccos(18/7)

9x = undefined.

The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Based on the ratio of two colors used to produce the mixture, Tim’s grey would be darker.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. In mathematics, a ratio shows how many times one number contains another. In order to make a gray color mixture, black and white paints are mixed together in different ratios of the two given color paints. More black creates a darker gray, and more white creates a lighter gray. As the different parts of black and white colors are mixed, we can determine the darker shade by comparing the ratios.

Grey’s grey = 3/8 = 0.375

Tim’s grey = 4/9 = 0.444

As Tim’s grey ratio is higher than Grey’s grey i.e., 0.444 > 0.375, Tim’s grey would be darker.

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The equation for the plane tangent to each surface - -10x + 6y + z - 5 = 0

What is Plane Tangent?

a tangent is a line that touches a curve at exactly one point without intersecting it. Similarly, a plane tangent is a plane that touches a surface at only one point without intersecting it further. This concept is commonly used in calculus and differential geometry to study the behavior of curves and surfaces.

We usually use partial derivatives of the equation of the surface to find the equation of the plane tangent to the surface at a point. The normal vector to the surface at that point is obtained by taking the cross product of the partial derivatives evaluated at that point. Then, using the coordinates of the point and the normal vector, we can determine the equation of the plane using the point-normal form or the general form of the plane equation.

It is important to note that the tangent plane equation depends on the specific point on the surface where the tangent plane is desired. Different points on the surface will have different tangent planes associated with them.

To find the equation for the plane tangent to the surface z = f(x, y) at a point (a, b, c), we need to use the partial derivatives of f with respect to x and y at the point (a, b) to find the normal vector to the plane.

Then we can use the point-normal form of the equation of a plane to write the equation.

First, we need to find the partial derivatives of f(x, y) = x^2 + y^3 - 6xy with respect to x and y:

fx = 2x - 6y

fy = 3y^2 - 6x

Then we can evaluate these partial derivatives at the point (1, 2) to get the normal vector:

n = <fx(1, 2), fy(1, 2)> = <2(1) - 6(2), 3(2)^2 - 6(1)> = <-10, 6>

So the equation of the plane tangent to the surface z = f(x, y) = x^2 + y^3 - 6xy at the point (1, 2, 3) is:

-10(x - 1) + 6(y - 2) + (z - 3) = 0

Simplifying, we get:

-10x + 6y + z - 5 = 0

So the equation of the plane tangent to the surface z = x^2 + y^3 - 6xy at the point (1, 2, 3) is -10x + 6y + z - 5 = 0

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Answer:

on writing in expanded form we get

9167.364 = 9000 + 100 + 60 + 7 + 0.3 + 0.06 + 0.004

brainliest :)

Step-by-step explanation:

2(x-2)⅓=x+2

so we first cube each side,such that...

(2(x-2))⅓•³=(x+2)³

we get...

2(x-2)=(x+2)³

expanding...

2x-4=x³+6x²+12x+8

grouping....

x³+6x²+12x+8-2x+4=0

solving...

x³+6x²+10x+12=0

now you can use you calculator to solve for the possible values of x

I hope this will help

The correct answer is all of the above options affect the company's financial statements in different ways, but the establishment of the allowance directly affects the reported net income.

For a company using the allowance method of accounting for uncollectible accounts, the establishment of the allowance, writing off of a specific account, and recovery of an account previously written off as uncollectible all affect its financial statements, but in different ways:

The establishment of the allowance: This directly affects the amount of bad debt expense recognized in the income statement, which in turn affects the reported net income. When the company establishes an allowance for uncollectible accounts, it recognizes an expense for the estimated amount of uncollectible accounts, which reduces the reported net income.

The writing off of a specific account: This does not affect the net income directly because the expense for bad debt has already been recognized when the allowance was established. However, it does affect the balance sheet because the amount of accounts receivable and the allowance for uncollectible accounts are both reduced.

The recovery of an account previously written off as uncollectible: This affects both the income statement and the balance sheet. The amount of the recovery is recognized as revenue, which increases the reported net income. Additionally, the accounts receivable and allowance for uncollectible accounts are both increased by the amount of the recovery.

Therefore, the correct answer is all of the above options affect the company's financial statements in different ways, but the establishment of the allowance directly affects the reported net income.

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The inventory depreciation expense is determined as $9,000.

The inventory depreciation expense is calculated by applying the following formula as follows;

inventory depreciation expense = cost of the inventory x depreciation rate

The given parameters include;

cost of the inventory in month of June = $60,000

depreciation rate = 15%

The inventory depreciation expense is calculated as follows;

inventory depreciation expense = $60,000 x 15/100

inventory depreciation expense = $60,000 x 0.15

inventory depreciation expense = $9,000

Thus, the inventory depreciation expense is determined as $9,000.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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