Create Write a real-world problem that can be
solved using the equation 9 + 4x = 21 - 2x

I can explain some key terms related to integrals :Integral,Definite Integral,Indefinite Integral and Antiderivative

The integral that resembles the given question is not clear due to insufficient information. However
1. Integral: A mathematical operation used to find the area under a curve, represented by the symbol ∫. Integrals can be definite (with specific limits) or indefinite (without limits).

2. Definite Integral: A definite integral has specific limits (a and b) and is used to find the exact area under a curve between those limits. It is written as ∫[a, b] f(x) dx.

3. Indefinite Integral: An indefinite integral does not have specific limits and represents the family of antiderivatives of a function. It is written as ∫ f(x) dx, and its result includes a constant of integration (C).

4. Antiderivative: A function whose derivative is the given function. The process of finding an antiderivative is called integration.

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The integral of the function (cos 5x)/(sin 5x) dx is similar to the integral of cotⁿ u du. Therefore ∫cotⁿ udu = -1/(n-1) cotⁿ⁻¹ u - ∫cotⁿ⁻² u du.  Option A

Looking at the list of integral provided,

5∫((cos 5x)/sin 5 x) dx seems most similar to ∫cotⁿ u du = -1/(n-1) cotⁿ⁻¹ u - ∫cotⁿ⁻² u du. Why?

(cos 5x)/(sin 5x) dx is similar ⇒ cotⁿ u du.

(cos 5x)/(sin 5x) dx can be written as cot(5x) dx,

This falls under the general formula for the integral of cotⁿ u du.

For the integral provided, n = 1. The integral simplifies to

-ln |sin u| + C, where u = 5x.

Substitute u back in, we obtain -1/5

ln |sin(5x)| + C as the integral of the function.

The function cot(5x) is equivalent to 1/tan(5x), but cot(5x) is not equal to tan²(5x). ∫tan² udu = tan u - u + C, therefore it cannot be Option D.

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Answer:

15

Step-by-step explanation:

Given that:

Mean (μ) = 1500

Standard deviation (σ) = 150

Sample size = 100

Mean (m) = 1400

Margin of Error of sample :

Standard deviation / √sample size

σ / √n

150 / √100

150 / 10

= 15

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

As given in the question,

Rules to round of nearest thousand are:

Check the near by hundred digit :

Given is the actual ticket rates of the different events tickets sales ,round off to the nearest thousand is given by:

 Events                                         Nearest thousand

Therefore, For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

   Events                                         Nearest thousand

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

The correct answer is (j - k)(x) = 10 + x.

To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).

(j - k)(x) = (25 + 3x) - (15 + 2x)

            = 25 - 15 + 3x - 2x

            = 10 + x

This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.

Therefore, the correct function is (j - k)(x) = 10 + x.

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The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.

The last payment amount is the result of the mathematical operations of subtraction and multiplication.

The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.

Using multiplication, the monthly payments are determined to be $3,400 for 17 months.  This is subtracted from the remaining balance to obtain the last payment amount.

The cost of a custom video game/virtual sound system = $4,210

Down payment = $100

The remaining balance for monthly payment = $4,110 ($4,210 - $100)

Payment period = 18 months (1¹/₂ years)

Monthly payments = $200

Payment for the first 17 months = $3,400 (17 x 200)

Last payment = $710 ($4,110 - $3,400)

Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.

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He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?

The given expression is:

It is required to write the expression in factored form.

Next, factor out 3 in the last two terms of the expression:

Factor out the binomial 2x+5 in the expression:

Answer:

11cm

Step-by-step explanation:

Given data

Volume of cuboid =385 cm^3

Base area= 35cm^2

We know that

Volume = Area* Height

substitute and solve for Height

385=35*H

H= 385/35

H= 11cm

Hence, the height is 11cm

Answer: i think its D

Step-by-step explanation:

the answer is 4/5 this is know to be hard

Margin of error is the maximum difference between the point estimate of an unknown population parameter and the true value of that parameter.

Point estimate: A single number estimate of an unknown population parameter. This is the value that is calculated based on the data collected from a sample of the population.

Confidence level: The proportion of times a confidence interval will capture the true value of an unknown parameter assuming the estimation process is repeated many times.

Confidence interval: The plausible range of values for an unknown population parameter based on an observed sample and a confidence level. This is calculated based on the point estimate and the margin of error.

Critical value: A value that separates statistics that are likely to occur from those that are unlikely to occur. This value is determined by the level of significance and the degrees of freedom for the statistical test.

Margin of error: The maximum difference between the point estimate of an unknown population parameter and the true value of that parameter. This is calculated based on the level of confidence and the variability in the sample data.

To summarize:

Point estimate is a single number estimate of an unknown population parameter.

Confidence level is the proportion of times a confidence interval will capture the true value of an unknown parameter assuming the estimation process is repeated many times.

Confidence interval is the plausible range of values for an unknown population parameter based on an observed sample and a confidence level.

Critical value is a value that separates statistics that are likely to occur from those that are unlikely to occur.

Margin of error is the maximum difference between the point estimate of an unknown population parameter and the true value of that parameter.

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Answer:

x=7

Step-by-step explanation:

(x+16)=(4x-5)

Subtract x from both sides

16=3x-5

Add 5 to both sides

21=3x

Divide both sides to get x=7

Both angles are congruent due to the vertical angles theorem which states that if angles are vertical then they are congruent.

Hope this helps!

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

Answer:

3.01

Step-by-step explanation:

To Find :-

SOLUTION :-

=> Monthly salary = $ 37.165/12= $ 3.01

the annual expenditure of the US federal government is 4 trillion dollars and dollar bill is 0.001m then, the length of four trillion dollars would be 4×\(10^{9}\) m

Government spending or expenditure includes all government

consumption, investment, and transfer payments. In national income accounting, the acquisition by governments of goods and services for current use, to directly satisfy the individual or collective needs of the community, is classed as government final consumption expenditure.

Since we have given that annual expenditure = 4 trillion dollars,

1 dollar bill = 0.0001m

so, the thickness would be.

\(4*10^{12} *0.001\\\\=4*10^{12}*10^{-3}\\\\=4*10^{9}\)

the length of 4 trillion dollars would be. 4×\(10^{9}\)

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Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Answer:

2(x + 21y)

Step-by-step explanation:

Factorising is the reverse of expanding brackets, so you need to turn the equation into something that can be expanded.

In order to do this, you must find a common factor of your two values, which in this case is 2.

You put this common factor on the outside of your brackets, and then put on the inside your equation divided by that common factor - in this case 2.

This leaves us with our answer, 2(x + 21y)

You can check that this is right by multiplying everything on the inside of the brackets by 2. That will leave us with our original equation, 2x + 42y

Answer:

2(x + 21y)

Step-by-step explanation:

2x + 42y

~Rewrite

2x + 21 * 2y

~Factor out 2

2(x + 21y)

Best of Luck!

Answer:

It is A (5, -7)

Step-by-step explanation:

Answer:

A 5,-7

Step-by-step explanation:

Answer:

sept one

Step-by-step explanation:

The equation to solve the value of x is

12x - 29 + 4x + 1 = 180

Option D is the correct answer.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Line a and line b are parallel.

(12x - 29) and (4x + 1) are corresponding interior angles

(12x - 29) and (4x + 1) add upto 180°.

Now,

12x - 29 + 4x + 1 = 180

16x - 28 = 180

16x = 180 + 28

16x = 208

x = 13

Thus,

The value of x is 13.

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W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. If W is a vector space because it can be expressed as W = span {v1,. . . .,vn}. So the option A is correct.

Let W be the set of all vectors

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\)

where b and d are real.

We can write the matrix as;

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]=b\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right]+d\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

Remember that if aα + bβ ∈ W, ∀ α, β ∈ W and a, b are scalers, then W is a vector space. Let,

\(\alpha=\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right],\beta=\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

These are independent vectors.

bα + dβ ∈ W. where α, β are independent vectors.

That is WE is a span of {α, β}.

Hence, W is a vector space.

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The complete question is:

Let W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. Determine if W is a vector space and check the correct answer below.

A. W is a vector space because it can be expressed as W = span {v1,. . . .,vn}.

B. W is a vector space because it contains the zero element.

C. W is not a vector space because it does not have additive closure

D. W is not a vector space because it does not have a zero element.

Answer: 92x+6

Step-by-step explanation:

1. (42−2x)+52+8

2. 42−2x+52+8

3. 92−2x+8

4. 92+6x

 I hope this is the answer :P

If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.

They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt

Note that you need another r because you are integrating in cylindrical

coordinates.

conversion equations:

x = rcost

y = rsint

x² + y² = r²

(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt

W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.

Around the z-axis, cylinders take the forms of circles: x² + y² = r²

This cylinder will have the equation: x² + y² = 16

Its height is 3 so from z = -1 to z = 2

z bounds: -1 <= z <= 2

r bounds (based on the circle): 0 <= r <= 4

t bounds (based on the circle): 0 <= t <= 2pi

\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)

(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)

= 2r^3 + (8/3)r + r^3 + (1/3)r

= 3r^3 + 3r

dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216

dt integral gives: 216t --> 432pi

Hence we get the integral value as 432π

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Answer:

63

Step-by-step explanation:

180 -  143 = 37

80 + 37 + x = 180

117 + x = 180

x = 63

Answer:

jo wcdbiojcwijbcdwc. hi ihdhbhbhijbbhjbjkhbjihijbvhivvhiguccghvhi

Step-by-step explanation:

Answer:

3 2/6

hope this helped you out !!!!!