Five children played a card game. At some point, each of them had to give a card to each of the other ones. Then, everybody had to discard the cards just received, and continue the game without them. How many cards in total were in the game before this exchange if after it only one half of the cards were played with?

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the non-homogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the no non-homogeneous part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

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Answer:

A , B and C

Step-by-step explanation:

182 is a rational number as it can be written in p/q form. (182/1)

182 is a positive integer.   {Integers:   ........ -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 .......}

182 is a whole number. {0, 1 , 2 , 3 ,...............}

Answer:

The value of [tex]x[/tex] is [tex]55\textdegree[/tex].

Step-by-step explanation:

A straight line is equal to 180 degrees.

So any angles that forms on the same side of a straight line always add to 180 degrees.

We are given an angle of [tex]130\textdegree[/tex] on the exterior of the triangle.

Lets call the angle next to that [tex]\angle B[/tex].

We can conclude that

[tex]\angle B+130=180[/tex]

[tex]\angle B=180-130[/tex]

[tex]\angle B=50[/tex]

The sum of the interior angles in a triangle is 180 degrees. This is because a triangle is a polygon with three sides and three angles, and the sum of the angles in any polygon can be found by using the formula:

sum of interior angles = (n - 2) x 180 degrees

Note: n is the number of sides.

A triangle has 3 sides. So substituting 3 in for n gives us

(3 - 2) x 180 degrees = 180 degrees

So the sum of the interior angles in a triangle is always 180 degrees.

[tex]x\textdegree=180\textdegree-75\textdegree-50\textdegree\\x\textdegree=55\textdegree[/tex]

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The solution for x in the circle is x = 12

Since the measure of angle EFG is m∠EFG = 9x-7 and the measure of arc GE is 17x-2

We can determine the value of x using the inscribed angle theorem.

Thus, we have:

m∠EFG = 1/2 (arc GE)

9x-7  = 1/2 * (17x-2)

2(9x-7) = 17x - 2

18x - 14 = 17x - 2

18x - 17x = -2 + 14

x = 12

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The slopes for the given pairs of points are:

To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using this formula for each pair of points, we get:

(19, 3), (20, 3)

slope = (3 - 3) / (20 - 19) = 0/1 = 0

(3,0), (-11, -15)

slope = (-15 - 0) / (-11 - 3) = -15 / -14 = 15/14

(19,-2), (-11, 10)

slope = (10 - (-2)) / (-11 - 19) = 12 / (-30) = -2/5

(6, -10), (-15, 15)

slope = (15 - (-10)) / (-15 - 6) = 25 / (-21) = -25/21

(12,-18), (-15, -18)

slope = (-18 - (-18)) / (-15 - 12) = 0 / (-27) = 0

(3,-20), (5, 8)

slope = (8 - (-20)) / (5 - 3) = 28 / 2 = 14

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If one object has twice as much mass as another object it also has twice as much Inertia.

Let the mass of object A= m₁

mass of object B = m₂

Given that m₁ = 2m₂

Speed, velocity and acceleration are subject to motion of the object. Given the insufficiency of information in the question, nothing can be said about these.

This is basically Newton's first law of motion, this law states that, every object continues in a state of rest of uniform motion in a straight line, unless acted upon by an external force

On the other hand, inertia is directly dependent on the mass. Hence, inertia of object A would be twice the inertia of object B.

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Answer:

He will need 6/5 cans of paint.

The answer could also be written as 1 1/5 cans of paint or 1.2 cans of paint.

Step-by-step explanation:

Since 2/5 filled 1/3 of the room, he will need 3 times that amount.

2/5 * 3/1 = 6/5

Answer:

= 16.

Step-by-step explanation:

x= 2

y = -1

[tex] {(2xy)}^{2} \\ = {(2(2)( - 1)) \\ }^{2} \\ = {(2( - 2)) \\ }^{2} \\ = {( - 4)}^{2} \\ = - 4 \times - 4 \\ = 16[/tex]

10 mL is equal to 2 teaspoons or 0.67 tablespoons. One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, divide 10 by 5. One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, divide 10 by 15.

10 mL is equal to 2 teaspoons (tsp) or 0.67 tablespoons (tbsp).

One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, you can divide 10 by 5, which gives:

10 mL / 5 mL/tsp = 2 tsp

Therefore, 10 mL is equal to 2 teaspoons.

One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, you can divide 10 by 15, which gives:

10 mL / 15 mL/tbsp = 0.67 tbsp

Therefore, 10 mL is equal to approximately 0.67 tablespoons.

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Answer: 89 mm^2; Option 1

Step-by-step explanation: Solve the area of the largest rectangle by multiplying 7 and 8. That equals 56. Then do 4 times six to get the area of the medium rectangle and thats 24. Do the same thing with the small square and you get nine. Add them up to get 89.

If FG is parallel to KL , then the ratio of FJ to KJ must be equal to GJ to JL. Therefore FG is not parallel to KL

Two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling, possibly with additional translation, rotation and reflection.

The ratio of corresponding sides of Similar triangles are equal.

This means that 32/72 must be equal to 48/64

32/72 = 8/18 = 4/9

48/64 = 12/16 = 3/4

Since the ratio of the corresponding sides are not

equal ∆FGJ is not similar to JKL and thus FG is not parallel to KL

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Answer: 36

Step-by-step explanation:

g divided by 18 equals 2; g = 36 gifts.

The correct option is (3).

The fundamental ideas in number theory, measurement, and calculation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number"). (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

A community toy drive for holidays was organized my Max.

Each family has to donate a total of 2 gifts.

Total number of families were equal to 18.

Let's assume the total number of gifts from all the families is g.

For finding the equation to find the total number of gifts given by all the families:

g = Gifts given by each family × Number of families

g = 18 × 2

∴ g divided by 18 equals 2; g = 36 gifts.

Hence, g divided by 18 equals 2; g = 36 gifts.

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To calculate marginal utility, you need to determine the additional utility that a consumer derives from consuming an additional unit of a good or service. This involves finding the difference in total utility before and after consuming the additional unit.

Marginal utility is the additional utility (or satisfaction) that a consumer derives from consuming an additional unit of a good or service. To calculate marginal utility, you can follow these steps:

1. Determine the total utility that a consumer derives from consuming a certain amount of a good or service.

2. Increase the amount consumed by one unit.

3. Determine the new total utility that the consumer derives from consuming the additional unit.

4. Subtract the initial total utility from the new total utility to obtain the marginal utility of the additional unit.

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The size of the cube that can be used to fill the [tex]1\frac{2}{3}[/tex] inches, [tex]\frac{2}{3}[/tex] inch, [tex]2\frac{1}{3}[/tex] inches is the cube with edge length of 1/3 inches

A cube is a three dimensional solid with six congruent square faces.

The expression the height and length dimensions of the rectangular prism as improper fractions, indicates that we get;

Height = (1 2/3) cm = (3 × 1 + 2)/3 cm = 5/3 cm

Length = (2 1/3) cm = (3 × 2 + 1)/3 cm = 7/3 cm

The denominators of the dimensions of the height, length and width of the rectangular prism are equivalent to 3. The edge length of the cube that can be used to fill the container should have a denominator that is a factor of 3.

The size of the cube that can be used to fill the container is therefore the cube with side length of 1/3 inches

The volume of the container = (5/3) in × (2/3) in × (7/3) in = 70/27 in³

The volume of the (1/3) inch cube = (1/3) in ×(1/3) in ×(1/3) in = 1/27 in³

The number of 1/3 inch cubes that fills the container = (70/27)/(1/27) = 70

The possible dimensions of the rectangular prism container in the question obtained from a similar question posted online are;

Height = (1 2/3) centimeters

Width = (2/3) centimeters

Length = (2 1/3) centimeters

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Answer:

I got 7 as the answer

Step-by-step explanation:

I hope this helps!!

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Overall, building a theory is a complex process that requires careful planning, attention to detail, and a willingness to remain open to alternative explanations and interpretations.

An important first step when building a theory is to formulate a clear and testable research question or hypothesis. A research question or hypothesis is a statement that suggests a relationship between two or more variables, and it guides the development of the theory. The research question or hypothesis should be specific, measurable, and falsifiable, meaning that it can be tested and potentially proven false through empirical research. Once a clear research question or hypothesis has been formulated, the researcher can then begin to gather and analyze data to support or refute the theory.

Another important first step when building a theory is to conduct a comprehensive review of existing literature and research in the field. This review helps the researcher to identify gaps or inconsistencies in current knowledge and to develop a clear understanding of the state of the field. This step can also help the researcher to refine their research question or hypothesis, as well as to identify potential variables and relationships that may be relevant to the theory.

Another important step when building a theory is to select an appropriate research design and methodology that will allow for the systematic collection and analysis of data. The research design should be aligned with the research question or hypothesis, and should enable the researcher to collect high-quality data that can be analyzed using appropriate statistical or qualitative methods.

In addition, it is important to be mindful of potential biases that can impact the development of a theory, such as confirmation bias or researcher bias. It is important for the researcher to be objective and to consider all possible explanations for their data, rather than solely seeking out evidence that supports their hypothesis or preconceived ideas.

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Using trigonometric identity, the value of the expressions are (Cosx + Cos5x)/2 + Sin3x.Cosx, √3/2, √3/2 and -√3/2

To solve this problem, we need to apply trigonometric identity;

1.

Cos2x · Cos3x - Sinax. Sin3x:

Using the identity Cos(A - B) = CosA.CosB + SinA.SinB, we can write:

Cos2x · Cos3x = (Cos(2x - 3x) + Cos(2x + 3x))/2 = (Cos(-x) + Cos(5x))/2 = (Cosx + Cos5x)/2

So the expression becomes:

(Cosx + Cos5x)/2 - Sinax. Sin3x

Using the identity Sin(A - B) = SinA.CosB - CosA.SinB, we can write:

Sinax. Sin3x = (Sin(ax - 3x) - Sin(ax + 3x))/2 = (Sin(-2x) - Sin(4x))/2 = (-Sin2x - Sin4x)/2

So the expression becomes:

(Cosx + Cos5x)/2 + (Sin2x + Sin4x)/2

Using the identity SinA + SinB = 2.Sin((A+B)/2).Cos((A-B)/2), we get:

(Sin2x + Sin4x)/2 = Sin3x.Cosx

Therefore, the expression simplifies to:

(Cosx + Cos5x)/2 + Sin3x.Cosx

2.

Sinzx Cosx+Cosex Sinx:

Using the identity Sin(A + B) = SinA.CosB + CosA.SinB, we can write:

Sinzx Cosx+Cosex Sinx = Sin(x + z)

So the expression is equivalent to Sin(x + z).

3.

Sın 85° Cos25°- Cos 85°. Sin 25°:

We can use the identity Sin(A - B) = SinA.CosB - CosA.SinB:

Sin 85° Cos25°- Cos 85°. Sin 25° = Sin(85° - 25°) = Sin60° = √3/2

4.

Cos 160°. Cos10° + Sin160°. Sin10°:

We can use the identity Cos(A - B) = CosA.CosB + SinA.SinB:

Cos 160°. Cos10° + Sin160°. Sin10° = Cos(160° - 10°) = Cos150° = -√3/2

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Answer: DON'T COPY AND PASTE!! a-lot of people say they get a plagiarism charge so try to switch or add more words to this but i hope it helps!!!

Step-by-step explanation:

Claim - The volume of the bowl is 715.17

evidence - The hemisphere has a radius of 8

- so its volume is 2/3πr³        r = radius

= 2/3 × π × (8)³

she can fill = 2/3 × 2/3 × 22/7 × (8)³   cm³

= 715.17cm³

reasoning - Therefore according to my calculations The volume will be 715.17 cm³

basically draw 1 linear line with domain constraints for the first two

y = 1/2x + 6 {7<x < 13}

y = 1/2x + 3 {x<7}

the values might have to be tweaked a little as the stars are not exactly on point

The radius of the circle is 7 centimeter.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the radius r of the circle when area is 153.9 square centimeter.

A=πr²

153.9=3.14r²

Divide both sides by 3.14

153.9/3.14=r²

49.01=r²

Take square root on both sides

r=7

Hence, the radius of the circle is 7 centimeter.

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The missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.

Given that, ∠ C ≅ ∠ E, and we need to find a reason to prove Δ ABC ~ Δ  DBE,

As we know that, to prove two triangles similar we can show two corresponding angles congruent in them, then they will be similar by AA rule,

Here, we already have, ∠ C ≅ ∠ E, we need one more,

If we see the figure, we get ∠ ABC and ∠ DBE are vertically opposite angles

We know that, Vertically opposite angles are equal to each other.

Therefore, ∠ ABC ≅ ∠ DBE

Hence, the missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ  DBE by AA rule.

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The fraction is given as follows:

8.3/10.3.

The fraction is modeled as follows:

x/y.

In which:

From the features of the problem, a system of equations is built to identify the variables.

If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4, hence the first equation is of:

4x/(y - 2) = 4.

Hence:

4x = 4(y - 2)

4x = 4y - 8

x = y - 2.

If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4, hence the second equation is of:

(x + 15)/(2y - 2) = 5/4.

We know that x = y - 2, hence the value of y is obtained as follows:

(y + 13)/(2y - 2) = 5/4.

5(2y - 2) = 4(y + 13)

10y - 10 = 4y + 52

6y = 62

y = 62/6

y = 10.3.

Then the value of x is of:

x = y - 2

x = 10.3 - 2

x = 8.3.

Hence the fraction is:

8.3/10.3.

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The population in 2020 is 2,240,700

A population is the set of people concentrated in a particular area.

Given that, in 2010, the population of a city was 88,000, from 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. We need to determine the population in 2020,

For population growing we will multiply the population is 104 and for population reducing we will multiply by 97,

Therefore, the population in 2020 =

88000 × 5(104/100) × 5(97/100)

= 88000 × 5.25 × 4.85

= 2,240,700

Hence, the population in 2020 is 2,240,700

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The solution to the system of equations:

y = -6x - 2

12x + 2y = -6

This is an inconsistent system of equations

What is an Equation ?

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

we can substitute the value of y from the first equation into the second equation:

12x + 2(-6x - 2) = -6

12x + -12x - 4 = -6

0x - 4 = -6

-4 = -6

This is an inconsistent system of equations, which means that there are no real solutions that satisfy both equations.

This means that there is no point at which both lines intersect and that the two lines are parallel, never meeting.

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Answer:

30 degrees.

Step-by-step explanation:

Angles must add up to 180 so,

180 - 150 = 30.

1 can only be divided by one other integer except1, hence it is not a prime number.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.

Given this definition, 1 is not a prime number because it can only be divided by one other integer, which is 1 itself.

Based on the explanation above, we can then conclude that 1 is not a prime number.

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Answer:

The Prime Factors and Pair Factors of 2023 are 7 × 17 and (1, 2023), (7, 289), (17, 119) respectively.

Answer:

To determine how many times 7 is a factor in 2023:

1. Divide 2023 by 7 to obtain the quotient: 2023/7 = 288.571.

2. If the result of the division is a whole number, 7 is a factor in 2023.

3. Round down 288.571 to obtain the integer 288.

4. Since the result of the division is a whole number, 7 is a factor in 2023 and occurs 1 time.

The slope is 1/19.5 and it is positive slope.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Given that, the cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets.

Here, the coordinates are (19.50, 1) and (78, 4)

Now, the slope = (4-1)/(78-19.50)

= 3/58.5

= 1/19.5

Therefore, the slope is 1/19.5 and it is positive slope.

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The ages of Gregory and Janet are 10 and 16 years respectively.

Gregory is six years younger than Janet. 7 years ago, Janet was thrice as old as Gregory. Therefore, the ages of Gregory and Janet are as follows:

Let

x = age of Janet

Gregory age = x - 6

x - 7 = 3(x - 6 - 7)

Hence,

x - 7 = 3(x - 13)

x - 7 = 3x - 39

x - 3x = -39 + 7

-2x = -32

divide both sides by -2

x = -32 / -2

x = 16 years

Therefore,

Janet age = 16 years

Gregory's age = 16 - 6 = 10 years

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Janet's current age is 16 and Gregory's current age is 10

Let's start by using algebra to represent the information in the problem.

Let's assume that Janet's current age is "J" and Gregory's current age is "G".

From the first sentence, we know that:

G = J - 6

From the second sentence, we know that 7 years ago, Janet was thrice as old as Gregory.

J - 7 = 3(G - 7)

So, we have

J - 7 = 3(J - 6 - 7)

This gives

J - 7 = 3J - 39

So, we have

2J = 32

This gives

J = 16

This also means that

G = 16 - 6

G = 10

Hence, Gregory's age is 10

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