Q4. Find the particular solution for the following non-homogeneous system of first- order linear differential equation. Y = 54 -5x² +6x+25 5 Y(0)= 1 2 -x²+2x+4

a) It is not possible for everyone in a group of 5 friends to have exactly two friends.

b) It is possible for everyone in a group of 5 friends to have exactly three friends.

(a) It is not possible for everyone in a group of 5 friends to have exactly two friends. To see why, suppose that each person has exactly two friends. This means that each person is connected to two other people in the group. If we start at any person in the group, we can follow their connections to the other people in the group.

Since each person has only two friends, the connections will form a chain or loop. However, if we keep following the connections, we will eventually return to the original person, forming a loop. This means that the group must be connected in a loop or chain, but this is impossible with 5 people.

(b) It is possible for everyone in a group of 5 friends to have exactly three friends. One example is the complete graph on 5 vertices, denoted K5, where every vertex is connected to every other vertex. In this graph, every person has exactly 4 friends, since they are connected to all of the other people in the group.

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Answer:

A=4.5π

The formula for finding a circle is A=πr² so just plug in the value for the radius. Don't forget to divide the entire thing by 2 when you finish, cos it's a semi circle (which is a half circle)

Step-by-step explanation:

Cos Milky Said it.

Answer:

Answer=4.5π

Step-by-step explanation:

you square 3 and then divide it by 2 and then just add pi

If the standard length of one kind of nail is 5 cm, and we want to test whether the nails produced on a particular day fit the standard requirement, we would set up the following hypotheses:

Null hypothesis (H0): The mean length of nails produced on the particular day is equal to the standard length of 5 cm.
Alternative hypothesis (Ha): The mean length of nails produced on the particular day is not equal to the standard length of 5 cm.

To test these hypotheses, we would take a sample of nails produced on the particular day and measure their lengths. We would then calculate the sample mean and compare it to the standard length of 5 cm using a hypothesis test.

In conclusion, If the sample mean is significantly different from the standard length, we would reject the null hypothesis and conclude that the nails produced on the particular day do not meet the standard length requirement. If the sample mean is not significantly different from the standard length, we would fail to reject the null hypothesis and conclude that the nails produced on the particular day meet the standard length requirement.

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The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.

In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.

Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.

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We conclude that the conjecture that the quotient of a number and its reciprocal is always equal to 1 is not correct.

Conjecture: The quotient of a number and its reciprocal is always equal to 1.

To test this conjecture, let's consider a specific number, x, and its reciprocal, 1/x.

According to the conjecture, the quotient of x and its reciprocal should be 1.

Let's perform the calculation:

\(x / (1/x) = x * x/1 = x^2\)

Based on the calculation, we see that the quotient of x and its reciprocal simplifies to x^2, not necessarily equal to 1. Therefore, the conjecture is not true in general.

Hence, we conclude that the conjecture that the quotient of a number and its reciprocal is always equal to 1 is not correct.

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Answer: 9 x 3 ( 5 x + 8 )

Step-by-step explanation:

Factor  9 x 3  out of  45 x 4 + 72x 3 .

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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The value of x in miles is 18 miles.

The beach is x miles away from home.  

Distance is a numerical description of how far apart two objects are. Therefore,

The distance between beach and his home is x miles. He travelled to and fro at a distance of 36 miles. Therefore,

Travelling to and fro simply means he travelled back and forth. Therefore,

x = 36 / 2

x = 18 miles

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Answer:

length of shorter side = 6.5 cm

Step-by-step explanation:

the upper sides are congruent and the lower sides are congruent.

given perimeter = 33

then sum the sides and equate to 33

2(3x - 1) + 2(2x + 5) = 33 ← distribute parenthesis and simplify left side

6x - 2 + 4x + 10 = 33

10x + 8 = 33 ( subtract 8 from both sides )

10x = 25 ( divide both sides by 10 )

x = 2.5

then

shorter side = 3x - 1 = 3(2.5) - 1 = 7.5 - 1 = 6.5 cm

Answer:

3/4

Step-by-step explanation:

since they already have a common denominator you'd add the numerators and keep the denominator. you'd get 6/8. Then you'd divide both the numerator and denominator by 2. 3/4 is your final answer.

Answer:

P=x when Q=3, so x=k/3.  When Q=x, P=k/x. Next, simplify the two equations for the same variable. Technically, this is one of many techniques for solving a system of two equations with two unknowns.

x=k/3 and P=k/x become

k=3x and k=Px

Px = 3x. Divide both sides by x to produce

P=3

Step-by-step explanation:

Answer:

(5x + 2y)(5x - 2y)

Step-by-step explanation:

This is the difference of two squares whose factorisation is

a² - b² = (a + b)(a -  b)

25x² - 4y² =

= (5x)² - (2y)²

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

Volume of the solid obtained by rotating the region is 67π/6 .

Given,

Curves:

y=x², y=0, x=1, and x=2 .

The arc of the parabola runs from (1,1) to (2,4) with vertical lines from those points to the x-axis. Rotated around x=4 gives a solid with a missing circular center.

The height of the rectangle is determined by the function, which is x² . The base of the rectangle is the circumference of the circular object that it was wrapped around.

Circumference = 2πr

At first, the distance is from x=1 to x=4, so r=3.

It will diminish until x=2, when r=2.

For any given value of x from 1 to 2, the radius will be 4-x

The circumference at any given value of x,

= 2 * π * (4-x)

The area of the rectangular region is base x height,

= \(\int _1^22\pi \left(4-x\right)x^2dx\)

= \(2\pi \cdot \int _1^2\left(4-x\right)x^2dx\)

= \(2\pi \left(\int _1^24x^2dx-\int _1^2x^3dx\right)\)

= \(2\pi \left(\frac{28}{3}-\frac{15}{4}\right)\)

Therefore volume of the solid is,

= 67π/6

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Answer:i think its 115 degres

Step-by-step explanation:

Answer:

If you mean 0 + (-1) then it's -1

Answer:

Slope of the line is -1.2

Option B is correct option.

Step-by-step explanation:

We need to find slope of the line with given points (4, 10.5) and (8,5.7)

The formula used to calculate slope is: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

The points given are: (4, 10.5) and (8,5.7)

We have \(x_1=4,y_1= 10.5x_2=8,y_2=5.7\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{5.7-10.5}{8-4}\\Slope=\frac{-4.8}{4}\\Slope=-1.2\)

So, Slope of the line is -1.2

Option B is correct option.

Answer: Infinitely many

The answer is infinitely many

This is because if the sides are parallel, the other measurements must be the same. They can be any measurement

Answer:

Price: $178.57

30% off: -$53.57

Sale Price: $125.00

Step-by-step explanation:

She buys each shirt for $100.

She wants to make a profit of 25%.

25% of $100 = 0.25 × $100 = $125

She must sell the shirt at $125.

She wants to mark the shirt at a higher price than $125, so that after the 30% discount, she will still sell it for $125.

Call the higher price x.

x - 30% of x = 125

x - 0.3x = 125

0.7x = 125

x = 125/0.7

x = 178.57

The sale tag can read:

Price: $178.57

30% off: -$53.57

Sale Price: $125.00

Answer:

0 to 5

Step-by-step explanation:

i took it on edg

Answer:

I know it was 0 to 5 but I didn't get to this question fast enough so it look's like I copied it.

According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

According to the statement

We have to find that the value of the combination.

So, For this purpose, we know that the

A combination could be a mathematical technique that determines the quantity of possible arrangements in an exceedingly collection of things where the order of the choice doesn't matter.

From the given information:

A red pebble is capable 3 yellow pebbles. A blue pebble is adequate a red pebble and a couple of yellow pebbles. Therefore, the blue pebbles will be:

= 3 yellow pebble + 2 yellow pebbles

= 5 yellow pebbles or 15 red pebbles

And

Two blue pebbles will be:

= 10 yellow pebbles

= 3 red pebbles and 1 yellow pebbles.

So, According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

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Question:

A red pebble is equal to 3 yellow pebbles A blue pebble is equal to a red pebble and 2 yellow pebbles. A green pebble is equal to 3 red pebbles

Using the smallest number of pebbles possible and without using blue pebbles, what is the value in pebbles of 2 blue pebbles?

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The star system is pictured is  open cluster

A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.

The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.

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I understand that the question you are looking for is :

| Will mark brainliest | Which type of star system is pictured? |

A. globular cluster

B. open cluster

C. binary

Answer:

B

Step-by-step explanation:

open cluster

Yes , the density of pure water at standard temperature and pressure (STP) is  very close to 1 g/mL .

The density of water is defined as the measure of  mass per unit volume of water, which is the mass of water per unit volume of water, the density is  expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).

The density of pure water at standard temperature and pressure (STP) is =  1 g/mL, which is also equivalent to "1000 kg/m³" .

The density of water  vary slightly with the temperature and pressure.

For Example , at room temperature (about 20°C), the density of water is about 0.998 g/mL, which is slightly less than 1 g/mL .

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Answer:

D 130 degrees

Step-by-step explanation:

got it right on the test

Answer:

130

Step-by-step explanation:

Answer:

$1060

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 5.3%/100 = 0.053 per year,

then, solving our equation

I = 2000 × 0.053 × 10 = 1060

I = $ 1,060.00

The simple interest accumulated

on a principal of $ 2,000.00

at a rate of 5.3% per year

for 10 years is $ 1,060.00.

In summary, there are 6 ways to distribute 9 identical balls into 3 identical boxes. This can be determined by finding the number of ways to write 9 as a sum of 3 integers.

To explain further, let's consider the problem of writing 9 as a sum of 3 integers. We can think of this as distributing 9 identical balls into 3 identical boxes, where each box represents one of the integers. Since the boxes are identical, we only need to consider the number of balls in each box.

To find the number of ways to distribute the balls, we can use a concept called "stars and bars." Imagine 9 stars representing the 9 balls, and we need to place 2 bars to separate them into 3 boxes. The positions of the bars determine the number of balls in each box.

For example, if we place the first bar after the 3rd star and the second bar after the 6th star, we have 3 balls in the first box, 3 balls in the second box, and 3 balls in the third box. This corresponds to one way of writing 9 as a sum of 3 integers (3+3+3).

By using stars and bars, we can determine that there are 6 different arrangements of bars among the 9 stars, resulting in 6 ways to distribute the 9 identical balls into the 3 identical boxes.

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Answer:

Simple random sampling

Step-by-step explanation:

Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.

He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.

So, primary data collection, simple random sampling - has been used as a type of data collection.

The intensive group had a sample size of 10, a sample average of 76, and a sample standard deviation of 6. The paced group had a sample size of 12, a sample average of 70, and a sample standard deviation of 8. In order to test the hypothesis, a two-sample t-test can be performed.

Null and alternative hypotheses:

The null hypothesis (H₀): There is no significant difference in proficiency between the intensive and paced tutoring groups.

The alternative hypothesis (H₁): The intensive tutoring group performs better than the paced tutoring group.

Calculator input and output values:

To perform the hypothesis test, we can use a calculator or statistical software. The input values are:

Intensive group: n₁ = 10, x₁ = 76, s₁ = 6

Paced group: n₂ = 12, x₂ = 70, s₂ = 8

The calculator output will provide the p-value, which is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

Using the provided sample data and conducting a two-sample t-test, the p-value can be calculated. If the p-value is less than the chosen significance level (commonly 0.05), we reject the null hypothesis in favor of the alternative hypothesis.

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