What's the slope of this line

The standard form of  (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form

Take 10^199 from the equation

=10^199((3x1)+(2x10^2))

=10^199(3+(2x100))

=10^199(3+200)

=10^199(203)

=203x10^199

2.03 x 10^201

1. there are 201 zeros after 2 and 199 zeros after 3

2. difference  between  201 and 199 is 2

3. on adding both of them the 3 will come 2 spaces to the right of 2

The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

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The volume of the solid obtained by rotating the region bounded by the curves y = x^2, x = 0, and y = 1 about the y-axis is π/2 cubic units.

The solid obtained by rotating the region bounded by the curves y = x^2, x = 0, and y = 1 about the y-axis can be found using the method of disks or washers.

To use the method of disks, we can imagine dividing the region into thin vertical strips, each with width dx. The volume of each disk is then πy^2dx, where y is the distance from the strip to the axis of rotation (which is the y-axis in this case). We can find y in terms of x by solving y = x^2 for x, which gives x = sqrt(y).

Thus, the volume of each disk is π(sqrt(y))^2dx = \(\pi ydx\). Integrating from y = 0 to y = 1, we get the total volume of the solid as π∫(0 to 1) \(ydx\).

Using the power rule of integration, this simplifies to π[x^2/2] from 0 to 1, which equals π/2.

To use the method of washers, we can imagine dividing the region into thin horizontal strips, each with height \(dy\). The volume of each washer is then π(R^2 - r^2)\(dy\), where R is the outer radius (which is 1 in this case) and r is the inner radius. The inner radius is simply the distance from the strip to the y-axis, which is x.

Using the equation y = x^2, we can solve for x in terms of y to get x = sqrt(y).

Thus, the inner radius is sqrt(y) and the volume of each washer is π(1^2 - (sqrt(y))^2)\(dy\) = π(1 - y)\(dy\). Integrating from y = 0 to y = 1, we get the total volume of the solid as π∫(0 to 1) (1 - y)\(dy\).

Using the power rule of integration, this simplifies to π[y - y^2/2] from 0 to 1, which equals π/2.

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x^2, x = 0, and y = 1 about the y-axis is π/2 cubic units, regardless of which method we use.

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The 25th percentile is 35 and the 60th percentile is 46.

Given,

The following are the ages of 15 of the signers of the declaration of Independence 47, 46, 54, 31, 50, 46, 27, 62, 40, 39, 50, 44, 35, 30, and 41 Send data to Excel Find 25th and 60th percentiles for these ages.

(a) 25th percentile = (n + 1) * Pth value

                             = (15 + 1) * 0.25th value

                             = 4th value

                             =35

(b) 60th percentile = (n + 1) * Pth value

                               = (15 + 1) * 0.6th value  

                               = 9.6th value

                               =46

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Answer:

Both packages are 3.5 lb.

The equation is 7 / 2

Step-by-step explanation:

All you have to do is divide 7 by 2.

7 / 2 = 3.5

3.5 * 2 = 7

So, the answer is 3.5

Hope this helps! :)

Answer:

daddy

Step-by-step explanation: daddy for ever

We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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Answer:

9,2,8

Step-by-step explanation:

A whole number is a number with no fractions or Integers.

Moments and convex optimization are valuable tools for the analysis and control of nonlinear partial differential equations.

Moments are statistical measures used to characterize the properties of a probability distribution. In the context of nonlinear partial differential equations (PDEs), moments can provide insights into the behavior and dynamics of the underlying system.

Convex optimization, on the other hand, is a powerful mathematical framework that deals with minimizing convex objective functions subject to a set of constraints. It has proven to be effective in solving a wide range of optimization problems arising in the analysis and control of nonlinear PDEs.

By leveraging moments and convex optimization techniques, researchers and practitioners can analyze and understand the behavior of nonlinear PDEs, design control strategies to stabilize or manipulate the system, and make informed decisions based on the underlying dynamics.

Utilizing moments and convex optimization enables a deeper analysis and control of nonlinear partial differential equations, empowering researchers and practitioners to gain insights and develop effective strategies for these complex systems.

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The matrix transformation

rotates the plane counter-clockwise about the origin through 45°: True.
This matrix is an example of a rotation matrix which rotates a given vector in the plane by an angle of 45° counter-clockwise about the origin. The matrix is calculated using the formula:

Where θ is the angle of rotation. Therefore, this matrix transformation rotates the plane counter-clockwise through 45° about the origin.

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The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is

d.

Step 1: x² + 10x + 24 + 1 = 0 + 1

Step 2: x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

To transform x² + 10x + 24 = 0 into the form (x − p)² = q where [p and q are integers], we perform the following steps of transformation.

This is process of converting one expression to the other by performing some mathematical operations.

x² + 10x + 24 = 0

We add 1 to both sides.So,

Step 1: x² + 10x + 24 + 1 = 0 + 1

Thus, we have

Step 2: x² + 10x + 25 = 1

Since the left-hand-side x² + 10x + 25 = (x + 5)²

So, we have

x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

So, the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is

d.

Step 1: x² + 10x + 24 + 1 = 0 + 1

Step 2: x² + 10x + 25 = 1

Step 3: (x + 5)² = 1

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\(1.16 \times {10}^{ - 7} = \)

\(116 \times {10}^{ - 2} \times {10}^{ - 7} = \)

\(116 \times {10}^{ - 9} = \)

\(0.000000116\)

_________________________________

Done...

♥️♥️♥️♥️♥️

The expected value of the sample proportion is 0.82 and the standard error of the sampling distribution of the sample proportion is 0.0426.

To find the expected value (or mean) of the sampling distribution of the sample proportion,

We can use the formula p = P(success) = 0.82,

which is the proportion of all college graduates who believe their degree was a good investment.

We can then use the formula E(p) = p = 0.82 to find the expected value of the sample proportion.

So, E(p) = 0.82.

To find the standard error of the sampling distribution of the sample proportion,

We can use the formula SE(p) = sqrt[p(1-p)/n],

Where p is the population proportion, 1-p is the proportion of failures, and n is the sample size.

In this case,

p = 0.82,

1-p = 0.18,

And n = 100.

We can plug these values into the formula to get,

SE(p) = √[(0.82 x 0.18)/100] = 0.0426

So,

The expected value of the sample proportion is 0.82 and the standard error of the sampling distribution of the sample proportion is 0.0426. We can use these values to calculate confidence intervals, hypothesis tests, and other statistical analyses.

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Answer:

  (b)  There are infinitely many solutions

Step-by-step explanation:

You want to know the number of solutions to the system of equations ...

A set of equations is dependent, and has infinitely many solutions, if one of the equations can be obtained from some combination of the others.

Here, dividing the first equation by 2 gives you ...

  8/2x -2/2y =-4/2

  4x -y = -2

This equation is identical to the second equation, so every one of the infinitely many solutions to this will also be a solution to that.

The system has infinitely many solutions.

__

Additional comment

When the equations are written in standard form (or general form), the determinant of the variable coefficients can tell you a story. For equations ...

The determinant of the coefficients is ae -db.

For your equations, this is 8(-1) -(4(-2)) = -8 +8 = 0.

When the determinant is zero, there will not be a unique solution. There will be either none or infinitely many.

You can perform the same calculation on another two columns of the coefficients to see which:

  bg -ec = -2(-2) -(-1)(-4) = 4 -4 = 0

When this value is also zero, it means the system is dependent and has infinitely many solutions. (If it is non-zero, the system is inconsistent and has no solutions.)

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Answer:

10 miles

Step-by-step explanation:

Given

\(\displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed of Driving}}=\frac{\text{Distance}}{\text{25\,\text{mph}}}\)

\(\displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed of Cycling}}=\frac{\text{Distance}}{\text{10\,\text{mph}}}\)

\(36\,\text{minutes}=0.6\,\text{hours}\)

Create an equation and solve

\(\displaystyle \text{Driving Time}+\text{Extra Time}=\text{Cycling Time}\\\\\frac{\text{Distance}}{\text{Speed of Driving}}+0.6=\frac{\text{Distance}}{\text{Speed of Cycling}}\\\\\frac{\text{Distance}}{25}+0.6=\frac{\text{Distance}}{10}\\\\2*\text{Distance}+30=5*\text{Distance}\\\\30=3*\text{Distance}\\\\10=\text{Distance}\)

Therefore, George's home is 10 miles from his school.

27 tiles will be needed along the wall. To find the number of tiles needed along the wall, we divide the length of the wall by the length of each tile.

The length of the wall is given as 9 1/4 feet, which can be expressed as 9.25 feet. The length of each tile is given as 1/3 foot. To find the number of tiles needed, we divide the length of the wall by the length of each tile: Number of tiles = Length of wall / Length of each tile. Number of tiles = 9.25 feet / 1/3 feet. To divide by a fraction, we can multiply by the reciprocal: Number of tiles = 9.25 feet * 3/1 feet. Simplifying the expression, we have: Number of tiles = 27.75.

Therefore, approximately 27.75 tiles will be needed along the 9 1/4 foot wall. Since we cannot have a fraction of a tile, we round down to the nearest whole number. Hence, 27 tiles will be needed along the wall.

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Answer:

33

Step-by-step explanation:

The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.

An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.

Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30

Probability = 25

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The expression for the total online social group membership M(t) at time t is M(t) = -2.2t^3 + 7t^2 + 230t + 360 million members.

(a) To find the expression for the total online social group membership M(t), we integrate the given rate function m(t) with respect to t.

Integrating m(t) = -6.6t^2 + 14t + 230, we get M(t) = -2.2t^3 + 7t^2 + 230t + C, where C is the constant of integration.

Since the initial membership at the start of 2010 is given as 360 million, we can substitute the value of M(0) = 360 into the equation to solve for the constant C.

360 = -2.2(0)^3 + 7(0)^2 + 230(0) + C

360 = C

Substituting C = 360 into the expression, we get the final equation for M(t): M(t) = -2.2t^3 + 7t^2 + 230t + 360.

(b) To estimate the online social group membership midway through 2014, we substitute t = 4.5 into the expression M(t):

M(4.5) = -2.2(4.5)^3 + 7(4.5)^2 + 230(4.5) + 360

M(4.5) ≈ 435 million members (rounded to the nearest 1 million members).

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Answer: $45

Step-by-step explanation: 10 for the hour she scrubbed the floor half of that which is 5 for the half hour she scrubbed so that would be $15, then 7.50 times 4 for the hours she dusted which would be 30, and 30 plus 15 is 45

Answer:

subtract and then subtract again until you get to one answer

Percent decrease from 100 to 82 is 18% decrease.

Calculating the % decrease from 100 to 82,

\(\frac{82-100}{100}\)×100%

\(\frac{-18}{100}\)×100%

on simplifying we get,

-18%

here, negative sign indicates that there is a decrease of percentage.

Hence, we get 18% decrease from 100 to 82.

How to calculate Percent decrease?

Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.

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Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

The area of the region bounded by the graphs of the given equations is 0.

To find the area of the region bounded by the graphs of the given equations y = -2x - x^2 and y = -8, we need to determine the points of intersection between the two curves.

Setting the equations equal to each other:

-2x - x^2 = -8

Rearranging and simplifying the equation:

x^2 - 2x + 8 = 0

This quadratic equation does not have real solutions. Therefore, the two curves do not intersect, and there is no region bounded by them.

As a result, the area of the region bounded by the graphs of the given equations is 0.

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Answer:

Yes.

Step-by-step explanation:

As long as there is exactly one y value for each x value, it is a function.

Answer:

C D

Step-by-step explanation:

a point is a point. an infinitely small item indicating an exact real (R) number (or even a group of such numbers, when it stands for a point in a coordinate grid : a location - no matter how many dimensions).

so, and now it depends on your teacher, if C is true or not.

the general definition is that a point has no size and no dimension.

but when you look at it in detail, then a point is the dimension 0, and it's size is 0.

and as 0 is not "nothing", you could make a case for a point having a dimension and a size.

D is definitely true, as explained.

and I would also mark C as correct answer.

Answer:

48in²

Step-by-step explanation:

to find the area of a triangle you first divide the base by 2 then multiply it by the height

Solving for all value of x (x - 1)/(x - 4) = -6/x has two solutions which are: x = -8 and x = 3.

Solve for all values of x.

x-1/x-4 = -6/x

In order to solve the given   equation we can start by simplifying the equation by cross-multiplying:

x(x - 1) = -6(x - 4)

Expand

x^2 - x = -6x + 24

x^2 + 5x - 24 = 0

Solve this quadratic equation by factoring or using the quadratic formula:

(x + 8)(x - 3) = 0

For x = -8

(x-1)/(x-4) = (-8-1)/(-8-4) = -9/-12 = 3/4

-6/x = -6/-8 = 3/4

x = -8

For x = 3

(x-1)/(x-4) = (3-1)/(3-4) = -2

-6/x = -6/3 = -2

x =3

So,

x = -8 or x = 3

Therefore the value of x = -8 and x = 3.

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Answer:

-3.5

Step-by-step explanation:First you need to order the numbers so the numbers ordered would be -20,-16,-10-,10-,7,0,1,2,5,8 the median is finding the middle number in a list so you would cross of the end numbers until you are left -7 and 0 you then find the mid point of these two numbers which is -3.5 so that would be the answer.

Answer:

The median is -3.5

Step-by-step explanation:

hope this helps

-16, -20, -10, 1, -10, 5, 0 ,8 ,2 ,-7

Arrange the number in numerical order.

-20,-16,-10,-10,-7,0,1,2,5,8

There's two number is the middle which is -7 and 0 all you have to do is add them together and divide by 2.

-7+0= -7÷2=-3.5

Answer:

B. -$0.75

Step-by-step explanation:

that is really very simple.

the value on day 1 (the begin) is $2.50.

the value on day 5 (the end of the week I assume) is $1.75.

so, the value changed by -$0.75 from $2.50 to $1.75.

yes, this is the sum of all little individual changes day by day. but there is no need to do these detailed calculations. at the end it is just

value end - value begin