Find the area and the circumference of a circle with radius 9km.
Write your answers in terms of π, and be sure to include the correct units in your answers.

Thus, the solution to the initial value problem is:[tex]y(t) = - y'(t) + \frac{5}{2} (-\frac{1}{5} (y''(0) - 20)) e^{2t} + 3 e^{2t}[/tex]

In this case, the student is asking about an initial value problem with a given differential equation. The differential equation is:[tex]y(t) = y'(t) - 2y(0) + 5[/tex]The initial condition is:y'(0) = 4To solve this initial value problem, we can use the method of integrating factors. First, we need to find the integrating factor. The integrating factor is given by:[tex]e^{∫ -2 dt} = e^{-2t}[/tex]

Now we can multiply both sides of the differential equation by the integrating factor to get:

[tex]e^{-2t} y(t) = e^{-2t} y'(t) + 5e^{-2t} y(0)[/tex]

We can now integrate both sides of this equation with respect to t to get:[tex]e^{-2t} y(t) = - e^{-2t} y'(t) + \frac{5}{-2} e^{-2t} y(0) + C[/tex]where C is the constant of integration.

To find C, we can use the initial condition:y'(0) = 4Substituting this into the equation above gives:C = 3Now we can solve for y(t) by multiplying both sides of the equation by[tex] e^{2t}:y(t) = - y'(t) + \frac{5}{2} y(0) e^{2t} + 3 e^{2t}[/tex]

Finally, we can use the initial condition y'(0) = 4 to solve for the value of[tex] y(0):y'(0) = - y''(0) + 5y(0) + 6y'(0) = - y''(0) + 5y(0) + 24[/tex]

Since y'(0) = 4, we have:[tex]4 = - y''(0) + 5y(0) + 24[/tex]Solving for y(0), we get:[tex]y(0) = -\frac{1}{5} (y''(0) - 20)[/tex]

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Answer:

In this diagram, "F" represents the set of students who study French, "G" represents the set of students who study German, "F∩G" represents the set of students who study both French and German, "G∩F" represents the same set but the order of the labels has been reversed to emphasize that this is the same set, and the numbers inside the diagram indicate how many students belong to each set.

Based on the given information, 13 students study French, 5 study only German (i.e., not French), and 6 study both French and German. Therefore, the number of students who study French only is 13 - 6 = 7.

Step-by-step explanation:

To arrive at the number of students who study French only, we subtract the number of students who study both French and German (6) from the total number of students who study French (13), which gives us 7. This means that there are 7 students who study French but do not study German.

Answer: 210

Step-by-step explanation: i learned that today in school

The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.

[tex]w-[0.15]=146.54[/tex]

so [tex]w-85p=146.54[/tex]

[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.

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Step-by-step explanation:

y=mx+b

let(-4,-1)

x. y

then lets fill it with the formula

-4=-45(-1)+b

-4=45+b

-b=45+4

-b=49

b=-49

The height of the cone is 13.38 units

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone = 1/3 πr²h

volume = 2016 units³

r = d/2 = 24/2 = 12 units

2016 = 1/3 × 3.14 × 12² h

6048 = 452.16h

h = 6048/452.16

h = 13.38units

therefore the height of the cone is 13.38 units

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Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:

n = 2f

We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:

7s = f + n

Since n = 2f, we can substitute 2f for n in the equation:

7s = f + 2f

Simplifying, we get:

7s = 3f

Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:

f + n = 7s + r

Substituting 2f for n, we get:

f + 2f = 7s + r

Simplifying, we get:

3f = 7s + r

Now we can solve for "f":

3f = 7s + r

f = (7s + r) / 3

We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:

f + n = 70

f + 2f = 70

3f = 70

f = 23.33

Since we can't have a fractional number of books, we would round down to the nearest whole number and get:

f = 23

We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:

23 = (7s + 0) / 3

69 = 7s

s = 9.86

Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:

s = 9

So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

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The perimeter of the rectangle is approximately 208.9 meters.

To find the perimeter of the rectangle, we need to know the length of the other side.

Let's use the formula for the area of a rectangle:

area = length x width

We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:

length = area / width

length = 717.8 / 7.4

length ≈ 97.05 m

Now we have both the length and width of the rectangle, so we can find the perimeter:

perimeter = 2 x (length + width)

perimeter = 2 x (97.05 + 7.4)

perimeter = 2 x 104.45

perimeter = 208.9 m

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The length of the side EF is equal to 18 units since the triangle DEF and triangle ABC are similar and DEF is bigger than ABC in the margin of 3 times.

Given, two triangles ABC and DEF.

The length of AB = 8 units

The length of its concurrent side DE = 24 units

Also given that the length of BC = 6 units

Here we can see that:

As both triangles are similar, their corresponding sides are in proportion.

This means that:

[tex]\frac{BC}{EF} = \frac{AE}{DE} =\frac{AC}{DF}[/tex]

Length of AB * 3 = Length of DE

Now the length of the side EF will be 3 times more than the side BC.

Length of EF = Length of BC * 3

Length of EF = 6 * 3

Length of EF = 18 units.

Therefore, the length of the side EF is equal to 18 units.

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330 litres per hour = 5489.64 millimeter³ per minute.

Given that330 litres per hour needs to be converted into millimeters per minute.

Conversion factor: 1 litre =1000 cubic centimeter 1 cubic centimeter =1 millimeter³

∴ 1 litre=1000 millimeter³

∴ 1 litre per hour=1000 millimeter³ per hour
Also, 1 hour = 60 minutes

∴ 1 hour = 60 × 60 seconds = 3600 seconds

∴ 1 second = 1/3600 hours=0.0002778 hours

Thus, 1 litre per hour =1000/3600 millimeter³ per second =0.2778 millimeter³ per second

Therefore, 330 litres per hour = 330 × 0.2778 millimeter³ per second=91.494 millimeter³ per second

Also, 1 minute =60 seconds

∴ 1 minute = 60 × 60 seconds=3600 seconds

∴ 1 second = 1/60 minutes=0.01667 minutes

Thus, 91.494 millimeter³ per second = 91.494/0.01667 millimeter³ per minute = 5489.64 millimeter³ per minute

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Answer: Line PQ is parallel to line LM

Step-by-step explanation:

We can check if they are of equal distance apart by checking if the ratios of the given lines are equal...in other words we must check if LP/PN=MQ/QN

We know that triangle PNQ is inscribed inside triangle LNM

Using the information we have we see that side LP is 18 units, PN is 16 units, MQ is 27, and QN is 24. With this information we can write out LP/PN=MQ/QN and see if it's true.

LP= 18, PN= 16, 18/16= 1.125

MQ= 27, QN=24, 27/24= 1.125

therefore, LP/PN=MQ/QN is true. Making line PQ and line LM parallel.

Answer:The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.

Step-by-step explanation:

There are a total of 7 ways to seat eight people around a table if Alice and Bob won't sit next to each other. This is because the seating arrangement must be a permutation of the seven people not including Alice and Bob.

We can calculate this by taking the factorial of the number of people not including Alice and Bob, which is seven. Since a factorial is the product of an integer and all the integers below it, we can calculate the factorial of seven by multiplying all the integers from one to seven.

This gives us 7=5040, which is the total number of ways to seat eight people around a table if Alice and Bob won't sit next to each other.

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Answer: I am terrible at these kinds of "sit-uating" problems (haha). My idea is that the three people can be situated in (3−1)!

ways and that the rest can be situated in (5−1)!

ways. Then, the ordering of the five people depends on the partitions of 5 into 3 groups:

Step-by-step explanation:

The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.

To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.

Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.

We must use the following formula to calculate the surface area:

Surface area = πr2 + πrl

Where r is the radius and l is the slant height of the cone.

As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by

2.r = d/2 = 2/2 = 1 inch.

Substitute the values of r and l in the formula, and then calculate the surface area of the cone.

π = 3.14r = 1 inchl = 4.25 inches

Surface area = πr2 + πrl

                     = 3.14 × 1² + 3.14 × 1 × 4.25

                     = 3.14 + 13.435

                     = 16.575 square inches

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The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.

What exactly are binomials?

In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:

ax + b

where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.

Now,

The correct answer is (A) r² - 2rs +s².

This is a perfect square trinomial, which can be written as (r - s)².

Option (B) c² + d² is not a binomial, it is the sum of two squares.

Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).

Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.

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The initial number of newts and toads in the pond were in the ratio 3:4, making the total number of organisms in the pond 7x. Solving for x, we get the initial number of toads and newts in the pond as 108 and 81.

Let's assume that the initial number of newts and toads in the pond were 3x and 4x, respectively. Therefore, the total number of organisms in the pond would be 7x.

When 9 more toads entered the pond, the number of toads became 4x + 9, and the ratio of newts to toads changed to 3:5. This means that the number of newts and toads in the pond increased by a factor of 3/2 and 5/4, respectively. We can set up the following equation to solve for x:

3/2n = 4x + 9

5/4n = 4x + 9

Simplifying these equations, we get:

6x + 18 = 5x + 45

x = 27

So, the initial number of toads in the pond was 4x = 108, and the initial number of newts was 3x = 81.

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Answer:

x ≈ 3.24

Step-by-step explanation:

using the cosine ratio in the right triangle

cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )

3.7 × cos29° = x , then

x ≈ 3.24 ( to the nearest hundredth )

The solution to the system of equations are (-4, 5), (2, 7), (3, -1), no solution, (-5, 8) and (7, -3)

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Question 1 and 2

See attachment for the graphs, where we have the solutions to be

System 1: (-4, 5)

System 2: (2, 7)

Question 3 and 4

Here, we solve the system of equation by substitution method.

So, we have

2x - 7y = 13

3x + y = 8

Make y the subject in (2)

y = -3x + 8

Let's substitute the value of y in equation (i)

2x - 7(-3x + 8) = 13

2x + 21x - 56 = 13

23x = 13 + 56

23x = 69

Divide both sides by 23

x = 69 / 23

x = 3

Let's find y

y = -3(3) + 8

y = -9 + 8

y = -1

For system (4), we have

x - 3y = 2

2x - 6y = 6

So, we have

x = 2 + 3y

By substitution, we have

2(2 + 3y) - 6y = 6

4 + 6y - 6y = 6

4 = 6

The system has no solution

Question 5 and 6

Here, we have

x + y = 3

x - 3y = -29

By eliminating x, we have

4y = 32

So, we have

y = 8

This means that

x + 8 = 3

x = -5

So, the solution is (-5, 8)

For system 6, we have

3y = 26 - 5x

6x + 7y = 21

So, we have

5x + 3y = 26

6x + 7y = 21

This gives

30x + 18y = 156

30x + 35y = 105

By elimination, we have

17y = -51

y = -3

This means that

6x + 7(-3) = 21

6x = 42

So, we have

x = 7

So, the solution is (7, -3)

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If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.

Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.

The formula to calculate the future value of an annuity due is:

[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]

Where,

FV = Future Value

PMT = Payment (amount) each period

r = Interest Rate per period

n = Number of periods

To find the future value of an annuity due for 20 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]

To find the future value of an annuity due for 40 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]

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Answer:

-0.2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

^This here is how I calculated the slope^

Y2=4

Y1= 2

4-2= 2

X2=-7

x1=3

-7-3=-10

2/-10

or -2/10

According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.

This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.

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Answer: To find the mean of this data set, we need to add up all the heights of lilies and divide by the total number of lilies. We can estimate the heights from the line plot:

There is 1 lily at a height of 18 inches.

There is 1 lily at a height of 19 inches.

There are 2 lilies at a height of 20 inches.

There are 2 lilies at a height of 21 inches.

There are 3 lilies at a height of 22 inches.

There are 0 lilies at a height of 23 inches.

There is 1 lily at a height of 24 inches.

To calculate the mean, we need to multiply each height by the number of lilies at that height, then add up these products, and divide by the total number of lilies:

(1 x 18) + (1 x 19) + (2 x 20) + (2 x 21) + (3 x 22) + (0 x 23) + (1 x 24)

markdown

Copy code

                    10

= (18 + 19 + 40 + 42 + 66 + 0 + 24) / 10

= 209 / 10

= 20.9

Therefore, the mean height of lilies in this data set is 20.9 inches. The answer is (B) 20.9.

Step-by-step explanation:

As per the given average, the solution of the breakeven w/ hidden costs is 62% higher.

Let's assume that the costs associated with running a 315-ticket run are $7,592. This means that on average, each ticket needs to sell for $24.10 (($7,592/315) = $24.10) to break even.

Similarly, if we consider the other two runs, we can calculate the average number of tickets needed to break even per show as follows:

For the 323-ticket run, the average number of tickets needed to break even per show is 65. (($7,784/323) = $24.10)

For the 331-ticket run, the average number of tickets needed to break even per show is 56. (($7,977/331) = $24.10)

Furthermore, we can calculate the break-even occupancy percentage for each run, which is the percentage of tickets that need to be sold to break even. The break-even occupancy for each run is as follows:

For the 331-ticket run,

=> 56/331 = 0.17 or 17%,

=> 1-0.17 = 0.83 or 83%,

=> 0.83/0.17 = 4.88,

=> 4.88 x 100% = 488%,

=> 488% x 0.62 = 303%,

=> 303%/4.88 = 62%

Hence the break-even occupancy is 62%.

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a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.

b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.

c) The drug's concentration is decreasing at 115 minutes.

a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.

f'(x) = (f(x+h) - f(x-h))/2 × h    ....(1)

As per the question, we have h = 10 and x = 50

Substitute the values of h = 10 and x = 50 in (1),

f'(40) = (f(50+10) - f(50-10))/2 × 10

f'(40) = (89-55)/20

f'(40) = 1.7 mg/min

b) For the rate of change of concentration at 85 minutes:

Here, f(80) = 111 mg and f(90) = 113.

The concentration at 90 minutes is 113 mg.

Rate of change = (f(90) - f(80)) / h

= (113 - 111) /10

= 2 / 10

= 0.2 mg/min

c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.

Therefore, the drug's concentration is decreasing at 115 minutes.

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In the following question, among the conditions given, the option- a,b and c stand the same ie- The level of measurement is a ratio. The statistic used for the central tendency is the mean or median, whereas d. birth, "is ordinal."

1. Body weight in pounds: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.

2. Number of cigarettes smoked in a day: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.

3. Ethnicity: The level of measurement is nominal. The statistic used for the central tendency is the mode, while for variability, there is no appropriate statistic.

4. Birth order: The level of measurement is ordinal. The statistic used for the central tendency is median or mode, while for variability, range or interquartile range can be used.

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Answer:  ^4√11^5 = 11^(5/4)

Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.

So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:

^4√11^5 = (11^5)^(1/4) = 11^(5/4)

Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.

Hope this helps, and have a great day!

Answer: 196 Joules (J)

Step-by-step explanation:

To calculate the potential energy of the apple, we can use the formula:

Potential Energy = Mass x Gravity x Height

First, let's convert the height from kilometers to meters:

100 km = 100,000 meters

Now, let's convert the mass of the apple from grams to kilograms:

0.2 gram = 0.0002 kilograms

Using these values, we can calculate the potential energy:

Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m

Potential Energy = 196 Joules (J)

Therefore, the potential energy of the apple is 196 Joules (J).

We use the formula I = Prt where I is the interest earned, P is the principal, r is the interest rate per year, and t is the time in years. Substituting the values, we find that it will take 4 years for a $5000 balance to reach $6500 with a 7.5% simple interest rate.

To solve this problem, we can use the formula for simple interest:

I = Prt

Where I is the interest earned, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.

In this case, we know that the principal is $5000, the interest rate is 7.5% or 0.075, and we want to find the time required for the balance to reach $6500.

Substituting these values into the formula, we get:

I = $6500 - $5000 = $1500

P = $5000

r = 0.075

t = ?

Solving for t, we get:

$1500 = $5000 * 0.075 * t

t = $1500 / ($5000 * 0.075)

t = 4

Therefore, it will take 4 years for the balance of the account to be $6500 with a 7.5% simple interest rate.

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