There are twenty marbles in a jar: some are red, some are
blue. You are blindfolded and choose two marbles. No matter how
you choose, at least one marble is guaranteed to be blue. Is it
possible to figure how many blue marbles are in the jar? If so,
how
many are there?

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

To find the area of a square, multiply the side length by itself, also known as sqaring the side length.

We must solve 3/5 x 3/5.

3/5 x 3/5 = 0.36

The units we'll use is u^{2}u2 because units are the unt we're given, and it is squared because it is the area of a shape.

Your final answer is 0.36 u^{2}u2 .

Hope this helps

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Step-by-step explanation and Answer:

1: 2x+6=96  => x = 45

2: 2x+3+x-6=180  => x = 39

3: x+4+3x+2=90  => x = 21

4: x+16=4x-5  => x = 7

5: 2x+20+x+40=180  => x = 40

6: 7x-9+4x=90  => x = 9

In the context of intergroup sources of power, dependencies are activities that other groups depend on to complete their tasks.

Dependencies refer to the specific tasks or activities that one group relies on another group to fulfill. These dependencies create interdependencies between groups, establishing power dynamics and influencing the relationships between them. When one group possesses certain dependencies that are crucial for the functioning or success of other groups, it can leverage these dependencies to gain power and influence within the intergroup dynamics. For example, if Group A is responsible for providing essential raw materials that Group B needs to manufacture their products, Group A holds a dependency advantage over Group B. Group B is reliant on Group A's timely and reliable provision of the raw materials to carry out their production processes. In this scenario, Group A can use their control over the supply of raw materials as a source of power to negotiate favorable terms, pricing, or other concessions from Group B. The dependency of Group B on Group A's resources strengthens the power position of Group A within the intergroup relationship.

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Answer:

333354

Step-by-step explanation:

Simplify the expression.

Answer:

333,354

Step-by-step explanation:

First, we add the 3's. And get 21.

333,333 + 21 = 333,354

Answer:

Step-by-step explanation:

1500

Answer:

13500

Step-by-step explanation:

Answer:

3.0pages

Step-by-step explanation:

If Tiffany type a page in an hour, then;;

1 page = 1 hour

To calculate the number of pages typed in 3 hours, we can express as;

x pages = 3 hours

Divide both expressions

1/x = 1/3

x* 1 = 1* 3

x = 3pages

She will type 3.0pages in 3 hours

The distance between the two cars  after three hours is 300 km

Cars a and b leave town at the same time.

The speed of the car that went to south = 80 km/hour

The total distance traveled in three hours = 80 × 3

= 240 km

The speed of the car that went to the west = 60 km/hour

The  total distance traveled in three hours = 60 × 3

= 180 km

The distance between the two car is the hypotenuse of the right triangle

The distance between the two cars after three hours = \(\sqrt{240^2+180^2}\)

= \(\sqrt{57600+32400}\)

= \(\sqrt{90000}\)

= 300 km

Hence, the distance between the two cars  after three hours is 300 km

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Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

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To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. miae is baking .the recipe uses 3/4 cup sugar.Miae needs 3/8 cup of sugar for 1/2 of a batch.

To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. A fraction is a part of a whole, it is represented by a numerator and denominator, the numerator represents the number of parts and the denominator represents the total number of parts. In this question, the recipe calls for 3/4 cup of sugar for the entire batch, so to get 1/2 of the batch, Miae needs to divide the fraction by 2. To do this, we can either divide the numerator and denominator by 2, or multiply the fraction by 1/2. In this case, 3/4 multiplied by 1/2 is 3/8, so Miae needs 3/8 cup of sugar for 1/2 of a batch.

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The ways that can be used to solve a quadratic equation include:

Factorization

Using the quadratic formula.

Completing the squares.

It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.

Here, the factorization, using the quadratic formula, and completing the squares method can be used.

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The standard size of the rectangle's area is x² + 12x + 35

Given:

a diagram that depicts the polynomial that denotes a rectangle's length and width.

The rectangle's area is equal to its length x width.

Given that length is equal to x + 7 and width is equal to x + 5, the area is equal to length plus width.

Add the numbers in brackets: Area = x2 + 5x + 7x + 35

Area = x2 + 12x + 35

A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. We are surrounded by numerous rectangular objects. The length and width of a rectangular shape are the two dimensions that define it. The rectangle's length and width are its longer and shorter sides, respectively. We will learn about the properties of the rectangle shape in this chapter.

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Full Question = Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

x+7 x+5

From Longman Dictionary of Contemporary English opens an account to start an account at a bank or other financial organization by putting money into it Mary was in the bank to ask about opening a current account.

Step 1: Visit the official website of the bank in which you wish to open an account. Step 2: Fill in the application form online along with a digital copy of address proof, identity proof, age proof, income/employment proof, and photographs.

You need to be at least 18 years old to open an account. However, you can open a joint account as a minor with a parent or legal guardian as an account co-owner. Some banks do offer accounts tailored for minors.

Please check the attached file for a complete answer.

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There are 45,697,600 possible license plates that can be made using 2 digits and 4 letters if repeated digits and letters are allowed.

There are 10 digits (0-9) and 26 letters in the English alphabet. Therefore, to make a license plate using 2 digits and 4 letters, there are 10^2 = 100 ways to choose the digits and 26^4 = 456976 ways to choose the letters.

To find the total number of possible license plates, we multiply the number of ways to choose the digits by the number of ways to choose the letters:

100 * 456976 = 45697600

So, 45,697,600 reprents possible numbers of license plates that can be made using 2 digits and 4 letters with allowed repeatations of digits and letters.

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Answer:

Step-by-step explanation:

11 is B and 12 is B. 11 is B because perimeter means to add all the outside values of the shape. 2.5+5+4+1 and then there are two missing side values which are 1.5 and 1, add them all together and the perimeter is 15. For the area, separate the small square with the big rectangle to have two full shapes. The area of the rectangle is 4x2.5=10. Area of the small square is 1x1=1. 10+1=11. Hope this helps, ask questions if you need to

cos 36= x/8√5+1/4 = x/8

4.7 is the approximate answer

The answer is D. 2a²+ab+a.

What is perimeter of a triangle?

The perimeter of a triangle is the sum of the lengths of its sides.

The perimeter of the triangle with sides a²-ab, a-2a², and a²+2ab is:

Perimeter = (a² - ab) + (a - 2a²) + (a + 2ab)

Simplifying and combining like terms, we get:

Perimeter = 2a² - ab + a + 2ab

Perimeter = 2a² + a + ab

Perimeter = a(2a + 1 + b)

Therefore, the perimeter of the triangle is a(2a + 1 + b). The answer is D. 2a²+ab+a.

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Answer:

The number is 3

Step-by-step explanation:

Ok, first thing's first: we need to make the words into an actual equation.

since it just says a number I'll use x

3 times x + 4 = 13

3x +4 =13

Now that we have our equation, we can solve for x

3x + 4 = 13

     -4      -4

3x = 9

I subtracted 4 on both sides to get rid of the 4 and move it to the other side of the equation, so we can try to get x by itself.

3x =9

/3     /3

x = 3

I divided both sides by 3 to get rid of the 3 that's being multiplied by x

Now we have our number : x = 3

I hope this helps :)

Answer:

14  28   28 22  23 19 12

Step-by-step explanation:

Answer:

7. B

8. C

9. E

10. A

11. D

Step-by-step explanation:

Answer:

f(x)=10(-1/2)-3=-8

Step-by-step explanation:

Answer:

f(x)=10x-3 = x=1/10y+3/10

x=-1/2 = x=−1/2 is going to be the same thing I just did it

Step-by-step explanation: hope this help

Answer: 77°

Step-by-step explanation:

103° - 90°= 13°,  13° = 10 min

13°+13°= 26°

103°-26°= 77°

Since the given equation is 0x² + 10x - 27, which is a linear equation, it does not have any real solutions. Therefore, there are no negative or positive solutions between any specific intervals.

Consider the quadratic equation 0x² + 10x - 27.

To determine the solutions to the equation, we can use the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 0, b = 10, and c = -27. Plugging these values into the quadratic formula, we get:

x = (-10 ± √(10² - 4(0)(-27))) / (2(0))

x = (-10 ± √(100)) / 0

x = (-10 ± 10) / 0

We can see that the denominator is 0, which means the equation does not have real solutions. The quadratic equation 0x² + 10x - 27 represents a straight line and not a quadratic curve.

Therefore, there are no negative or positive solutions between any specific intervals since the equation does not have any real solutions.

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Answer: $ 45,444.44

Step-by-step explanation:

Given: Jill budgets 18% of her yearly salary for clothing.

His total clothing bill for the year is $8,180.

Let x=  her yearly salary

Then according to the question , we have

18% of x = 8180

Convert 18% into decimal by dividing it by 100 , we get

0.18 x= 8180

Multiply both sides by 100

⇒ 18x = 818000

Divide both sides by 18 , we get

x= 45444.44

Hence, her yearly salary = $ 45,444.44

Answer:

When travelling downstream, the speed of the boat and the current add up.

Let the speed of the boat is b and the speed of the current is c.

Use distance formula:

a)

Then we have equation:

b)

If c = 2, then the equation is:

Answer: \(8(4x^3-y^2)\)

Step-by-step explanation:

\(32x^3-8y^2\)

\(8(4x^3-y^2)\)

Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

The area of a sector of a circle can be found using the formula:
Area = (θ/2π) * πr²
where θ is the central angle and r is the radius of the circle.
In this case, the radius is given as 3.2 m and the central angle is 2π/3.
Substituting these values into the formula, we get:
Area = (2π/3 * 1/2π) * π(3.2)²
Simplifying further, we have:
Area = (1/3) * 3.2²
Calculating the value, we get:
Area ≈ 3.4133 square meters
Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

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