find the general indefinite integral. (use c for the constant of integration.) (u 6)(2u 5) du

Answer:

  1

-------

mn³

Step-by-step explanation:

              ¹/₂

( m²n⁻⁶ )

-----------

( m⁴p⁰ )

( mn⁻³ )

-----------

( m² )

m - m² = m⁻¹

   1

--------

 mn³

I hope this helps!

The total revenue generated from the start of 2005 to the start of 2017 is $5119 billion, which is the answer.

Given, f(t) = -1.38t² + 44t - 1175 and the interval is 0 to 17, corresponding to the years 2005 to 2017. We need to calculate the total revenue generated between the start of 2005 and 2017. We will calculate the revenue generated for each year in the given interval using the given function f(t) and then add them up.

The revenue generated for each year will equal to the value of the function f(t) for that year. Since we have been given the function in terms of t, we will also convert the interval to t.

The start of 2005 corresponds to t = 0 and the start of 2017 corresponds to t = 12. So, we will convert the interval [0, 17] to [0, 12].

To calculate the total revenue generated between 2005 and 2017, we will find the definite integral of the given function f(t) from t = 0 to t = 12. The definite integral of a function between two values gives us the area under the function curve between those two values.

In this case, the area under the curve will represent the revenue generated between 2005 and 2017. Hence, the definite integral of f(t) from 0 to 12 will give us the total revenue generated between 2005 and 2017.

Using the definite integral to find the total revenue:

= ∫₀¹²(-1.38t² + 44t - 1175) dt

= [-0.46t³ + 22t² - 1175t] from 0 to 12

= [-0.46(12)³ + 22(12)² - 1175(12)] - [-0.46(0)³ + 22(0)² - 1175(0)]

= -6656 billion + 0 billion + 1175 billion

= 5119 billion.

The total revenue generated from the start of 2005 to the start of 2017 is $5119 billion. (Round to the nearest integer as needed). Hence, the total revenue generated from the start of 2005 to the start of 2017 is $5119 billion which is the answer.

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Answer:

3/8

Step-by-step explanation:

Let's use a sample number of 100 miles

If 3/8 was traveled the first day, then 37.5m were traveled on the first day.

Now on Sunday, there are 62.5m remaining in the trip. They travel 3/5 of that, meaning they went 62.5 * 3/5m. This turns out to be 37.5 miles that were traveled on Sunday.

37.5/100 = 3.8

Answer: Picture ?

Step-by-step explanation:

Answer:

14 gm

Step-by-step explanation:

34 minutes is TWO half lives   1/2 * 1/2 = 1/4   will be left

   1/4 * 56 = 14 gm

Answer:

The number is 4

Step-by-step explanation:

17 - 5 = 12

12 ÷ 3 = 4

Answer:

4

Step-by-step explanation:

17-5=12

4x3=12

To determine the percentage of women in a sample with a master's degree using Excel, you need to follow:

First, make sure your data is organized in columns, with one column for gender and another for education level.

Next, use the filter feature in Excel to display only the rows where the gender is "Female" or "Woman". This will help isolate the data for women in the sample.

Then, focus on the education level column and filter it to show only the rows where the education level is "Master's Degree". This will narrow down the data to women with a master's degree.

Count the number of women with a master's degree by using the COUNTIFS function in Excel. Set the criteria to match "Female" or "Woman" in the gender column and "Master's Degree" in the education level column. This will provide the count of women with a master's degree.

Now, calculate the total number of women in the sample by using the COUNTIF function. Set the criteria to match "Female" or "Woman" in the gender column. This will give you the count of all women in the sample.

Finally, divide the count of women with a master's degree by the count of all women in the sample and multiply by 100 to obtain the percentage. This will represent the percentage of women in the sample with a master's degree.

By following these steps and adapting them to your specific dataset in Excel, you can determine the percentage of women in the sample with a master's degree.

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Answer:

A

Step-by-step explanation:

x=

−b±√b2−4ac

2a

x=

−(2)±√(2)2−4(2)(15)

2(2)

x=

−2±√−116

4

and there is really no solution

Second-order partial derivatives are constant, and 2 > 0 and -2 < 0, the utility function does not have convex indifference curves.

a) The marginal rate of substitution (MRS) is a measure of the rate at which a consumer is willing to exchange one good for another while keeping the utility constant. To find the MRS, we need to calculate the partial derivatives of the utility function with respect to x and y, and then take the ratio:

U(x, y) = x^2 - y^2

Taking the partial derivative with respect to x:

∂U/∂x = 2x

Taking the partial derivative with respect to y:

∂U/∂y = -2y

The MRS is the ratio of these partial derivatives:

MRS = (∂U/∂x) / (∂U/∂y) = (2x) / (-2y) = -x/y

b) To determine whether the utility function has convex indifference curves, we need to examine the second-order partial derivatives of the utility function. If the second-order derivatives are positive, then the indifference curves are convex.

Taking the second-order partial derivatives of U(x, y):

∂²U/∂x² = 2

∂²U/∂y² = -2

Since both second-order partial derivatives are constant, and 2 > 0 and -2 < 0, the utility function does not have convex indifference curves.

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a) The MRS is the ratio of these partial derivatives is  -x/y.

b)Second-order partial derivatives are constant, and 2 > 0 and -2 < 0, the utility function does not have convex indifference curves.

Exp:

a) The marginal rate of substitution (MRS) is a measure of the rate at which a consumer is willing to exchange one good for another while keeping the utility constant.

To find the MRS, we need to calculate the partial derivatives of the utility function with respect to x and y, and then take the ratio:

U(x, y) = x^2 - y^2

Taking the partial derivative with respect to x:

∂U/∂x = 2x

Taking the partial derivative with respect to y:

∂U/∂y = -2y

The MRS is the ratio of these partial derivatives:

MRS = (∂U/∂x) / (∂U/∂y) = (2x) / (-2y) = -x/y

b) To determine whether the utility function has convex indifference curves, we need to examine the second-order partial derivatives of the utility function. If the second-order derivatives are positive, then the indifference curves are convex.

Taking the second-order partial derivatives of U(x, y):

∂²U/∂x² = 2

∂²U/∂y² = -2

Since both second-order partial derivatives are constant, and 2 > 0 and -2 < 0, the utility function does not have convex indifference curves.

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Answer: 15

Step-by-step explanation:

Let the length of the width = w.

Then, the length of the length is w + 2.

The perimeter of a rectangle is 2*length + 2*width.

Therefore, 2*(w+2) + 2*w = 64

2w + 4 + 2w = 64

4w + 4 = 64

4w = 60

w = 15

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

the point is (-2 , -13)

Point slope form is: y - y1 = m(x - x1)

y1= -13

x1= -2

y - -13 = 5 (x - -2)

y +13 = 5(x+2)

The derivative of ℎ(x) at x=16 is -64. To find the derivative of ℎ(x) using the product rule, we need to differentiate the two functions being multiplied together and then add them.

Let's first rewrite ℎ(x) using the exponent rule:

ℎ(x) = (-1/2)4(x^(3-1)) = -2x^2

Now we can use the product rule to find the derivative:

(ℎ(x))' = (d/dx)(-2x^2) = (-2)*(d/dx)(x^2)

To differentiate x^2, we can use the power rule: (d/dx)(x^2) = 2x

Putting it all together, we get:

(ℎ(x))' = (-2)*(d/dx)(x^2) = (-2)*2x = -4x

Now we can evaluate the derivative at x=16:

(ℎ(16))' = -4(16) = -64

Therefore, the derivative of ℎ(x) at x=16 is -64.

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No, the average troposphere is not harmful to humans. It is the layer of the atmosphere closest to the Earth's surface and provides us with the air we breathe.

No, the troposphere is not harmful to humans. It is the layer of the atmosphere closest to the Earth's surface and provides us with the air we breathe. The troposphere contains about 80% of the atmosphere's mass and is responsible for weather and climate patterns. It also contains water vapor which contributes to precipitation, as well as ozone and other gases which are essential for life. The troposphere has an important role in the Earth's climate system and helps regulate the planet's temperature. The troposphere can be affected by human activities, including the burning of fossil fuels which can cause an increase in greenhouse gases and lead to global warming. However, the troposphere itself is not harmful to humans and is essential for our survival.

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Answer:

y = -1/2 x + 2

Step-by-step explanation:

A (0,2)

B (4,0)

(y-2)/(0-2) = (x-0)/(4-0)

(y-2)/-2 = x/4

(-y+2)/2 = x/4

4 * (-y+2)/2 = x/4 * 4

-2y+4 = x

-2y = x -4

2y = -x + 4

y = - 1/2 x + 4/2

y = -1/2 x + 2

Answer:

\(c=5b\)

Step-by-step explanation:

Since we're solving for c, it should be by itself (normally on the left). If you look at the table, c is just 5 times what it's corresponding b value is, so that's what you write as the equation.

Answer:

Step-by-step explanation:

B

Answer:

So the answer is 20/64=5/16

The probability of getting at least 3 heads when a fair coin is tossed 6 times is 3/64.

Here, correct answer will be 3/64

This means that there is a 3 in 64 chance that 3 or more heads will be obtained when the coin is flipped 6 times. This can be calculated by finding the total number of possible outcomes of flipping the coin 6 times and then subtracting the number of outcomes that contain fewer than 3 heads.

The total number of possible outcomes is 2^6, which is 64. The number of outcomes that contain fewer than 3 heads is 7, which is the total of 1 head, 2 heads, and 0 heads. Therefore, the probability of getting at least 3 heads when a fair coin is tossed 6 times is 3/64.

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The value of a is less than -1.

A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.

The function form of a parabola:

y = ±a (x - h)² + k,

where,

(h, k) is the vertex and, -a is the value of the parabola that is narrower.

Now, we have two functions,

g(x) = ax²

f(x) = x².

Given:

The graph of g(x) = ax² opens downward and is narrower than the graph of f(x) = x².

So, the value of a is less than -1.

Therefore, a < -1.

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Answer:

The total is 97/100

Step-by-step explanation:

47/100+3/100=50/100 (aka 1/2)

50/100+47/100=97/100

Answer:

47/100+3/10+47/10=97/100

¹

47

47

+3

__

97

The statement p is: Saturn is a planet.

The statement q is: Hong Kong is a city.

Now the first part of our composite proposition is:

This means that we have to negate the statement q, this would be: Hong Kong is not a city.

Now we make the disjunction between the statement p and the negation of q, then we have:

The second part of our composite porposition is:

This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:

Finally we make the disjunction between the statements discussed so far, hence the statament

means:

Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.

Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.

The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.

The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.

Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.

Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Given:

Step by step solution:

We need to comment on the number of solutions of the equation:

From here we can say that y will have only one solution, which is equal to y = 15.

Answer:

(6)⁷/(6)⁵ = 6²

Step-by-step explanation:

Given problem,

→ (6)⁷/(6)⁵

Let's solve the problem,

→ (6)⁷/(6)⁵

→ 279936/7776

→ 36 = 6²

Thus, the answer is 6².

Answer:

8 minutes = 3 songs

Step-by-step explanation:

Time taken for 1 song is,

→ 72/27

→ 2.6667

→ ≈ 2.7 minutes

Then songs played in 8 minutes,

→ Total time ÷ Time for 1 song

→ 8 ÷ 2.7

→ 2.96296

→ ≈ 3 songs

Hence, the answer is 3 songs.

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Option D is correct-  1/25 should be added to complete the square of the expression.

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

Expression

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

we have to add the 1/25 to the square of the equation, x^2 - 2/5x

by adding 1/25 in the equation, we get

x ^2 -2/5x +1/25

= (x)^2 - 2* x* 1/5 + (1/5)^2

= (x - 1/5)^2

so, 1/25 must be added.

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The rank of the standard matrix for T is 2, which is determined by the number of linearly independent columns in the matrix.

To find the rank of the standard matrix for the linear transformation T: R^5 → R^3, we need to determine the number of linearly independent columns in the matrix.

The standard matrix for T can be obtained by applying the transformation T to the standard basis vectors of R^5.

The standard basis vectors for R^5 are:

e1 = (1, 0, 0, 0, 0),

e2 = (0, 1, 0, 0, 0),

e3 = (0, 0, 1, 0, 0),

e4 = (0, 0, 0, 1, 0),

e5 = (0, 0, 0, 0, 1).

Applying the transformation T to these vectors, we get:

T(e1) = (1 + 0, 0 + 0 + 0, 0 + 0) = (1, 0, 0),

T(e2) = (0 + 1, 1 + 0 + 0, 0 + 0) = (1, 1, 0),

T(e3) = (0 + 0, 0 + 1 + 0, 0 + 0) = (0, 1, 0),

T(e4) = (0 + 0, 0 + 0 + 1, 1 + 0) = (0, 1, 1),

T(e5) = (0 + 0, 0 + 0 + 0, 0 + 1) = (0, 0, 1).

The standard matrix for T is then:

[1 0 0 0 0]

[1 1 0 1 0]

[0 1 0 1 1]

To find the rank of this matrix, we can perform row reduction or use the concept of linearly independent columns. By observing the columns, we see that the second column is a linear combination of the first and fourth columns. Hence, the rank of the matrix is 2.

Therefore, the rank of the standard matrix for T is 2.

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COMPLETE QUESTION - Let T: R5-+ R3 be the linear transformation defined by the formula T(x1, x2, x3, x4, x5) = (x1 + x2, x2 + x3 + x4, x4 + x5). (a) Find the rank of the standard matrix for T.