Find a, b, and n of the factored form of the binomial expansion.
16x^4 + 480x^3y + 5,400x2y^2 + 27,000xy^3 + 50,625y^4

Answer:

56 degrees

Step-by-step explanation:

The angles are all supplementary, so they add up to 180 degrees. Subtract 90 and 34 from 180 to get your answer.

The surface obtained by rotating the curve y = 1/(2x^2) for 0 ≤ x ≤ 1 about the y-axis can be calculated by integrating the formula for the surface area of a curve rotated about the y-axis. The final answer is [pi/4 + ln(2)] square units.

To find the surface area, we use the formula for the surface area of a curve rotated about the y-axis: A = 2π ∫[a,b] x(y) √(1 + [dy/dx]^2) dy. In this case, the curve is y = 1/(2x^2) and we need to find the surface area for 0 ≤ x ≤ 1. To apply the formula, we first solve for x in terms of y, giving us x = sqrt(1/(2y)).

Next, we find dy/dx = -1/(2x^3), which simplifies to dy/dx = -sqrt(2y^3). Substituting these values into the formula and integrating, we get the surface area as [pi/4 + ln(2)] square units.


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Selected values of a function g and it's first four derivatives are given in the table below. What is the approximation for the value of g(-2) obtained by using the third degree Taylor polynomial for g about x= -3is (B) -7/3.


To use the third degree Taylor polynomial for g about x = -3, we need to find the function's values at -3, its first derivative at -3, its second derivative at -3, and its third derivative at -3. Then we can use the formula for the third degree Taylor polynomial:

P3(x) = g(-3) + g'(-3)(x+3) + g''(-3)(x+3)^2/2 + g'''(-3)(x+3)^3/6

From the table, we can see that g(-3) = -4, g'(-3) = 2, g''(-3) = -1, and g'''(-3) = 2. Substituting these values into the formula for P3(x), we get:

P3(x) = -4 + 2(x+3) - (x+3)^2/2 + 2(x+3)^3/6

Now we need to approximate the value of g(-2) using P3(x). To do this, we plug in x = -2 into P3(x):

P3(-2) = -4 + 2(-2+3) - (-2+3)^2/2 + 2(-2+3)^3/6 = -7/3

Therefore, the approximation for the value of g(-2) obtained by using the third degree Taylor polynomial for g about x = -3 is -7/3.

The answer is (B) -7/3.

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Answer:

20c+14

Step-by-step explanation:

To find the perimeter we have to add up all the sides

4c+6c+7+4c+6c+7

Combine light terms

20c+14

Answer:

Well your not given C so we just leave that be and we can just add up all 4 sides since perimeter means outside length total. Now when added up,

6c+7+6c+7+4c+4c= 20c+14

20c+14 is the perimeter

Answer:

Rr = 51 : 68

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Oranges: 3.46 $

Grapes: 1.36 $

Apple: They didn't leave you with the cost of the apple so I don't know

Add 3.46 plus 1.36 and you get 4.82. Then round that to 5.00.

Brainlist maybe? :)

Answer:

25%

Step-by-step explanation:

To exclude the value \($x=0$\) since division by zero is not allowed.

The expression is well-defined for \($x \in (0,1]$\).

Expression is well-defined for \($0\leq x\leq 1$\).

In interval notation, we can write this as \($[0,1]$\).

Therefore, the expression \($\frac{\sqrt{x\cdot 1} \sqrt{1 - x}}{\sqrt{x}}$\) is well-defined for \($ x\in [0,1]$\).

Expression to be well-defined, we need to ensure that we do not perform any illegal operations.

This means that we cannot take the square root of a negative number, and we cannot divide by zero.

Let's consider each of the factors in the expression separately.

The first factor is.

\($\sqrt{x\cdot 1}=\sqrt{x}$\).

To ensure that this is well-defined, we need.

\($x\geq 0$\) since we cannot take the square root of a negative number.

The second factor is

.\($\sqrt{1-x}$\).

To ensure that this is well-defined, we need.

\($1-x\geq 0$\), or equivalently, \($x\leq 1$\), since we cannot take the square root of a negative number.

The denominator is.

\($\sqrt{x}$\).

To ensure that this is well-defined, we need.

\($x\geq 0$\), since we cannot divide by zero.

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Answer:

The answer will be ( x = 10)

Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

If a random variable X is distributed normally with zero mean and unit standard deviation (X ~ N(0, 1)), the probability that 0 < X < 1 can be calculated using the standard normal distribution table or a statistical software.

In this case, we need to find the area under the normal curve between 0 and 1 standard deviations from the mean. Since the standard deviation is 1, we are interested in finding the probability that the value of X falls between 0 and 1.

Using the standard normal distribution table, we can look up the cumulative probability associated with 1 standard deviation from the mean, which is approximately 0.8413. Similarly, we can look up the cumulative probability associated with 0 standard deviations from the mean, which is 0.5.

To find the probability that 0 < X < 1, we subtract the probability associated with 0 from the probability associated with 1:

P(0 < X < 1) = P(X < 1) - P(X < 0) = 0.8413 - 0.5 = 0.3413

Therefore, the probability that 0 < X < 1 is approximately 0.3413, or 34.13%.

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Answer:

The total area of the field is 343 square feet

Step-by-step explanation:

Let us solve the question

∵ There are 7 workers hired to seed a field by hand

∵ Each is given a plot 7 x 7  feet in size

→ The plot has shaped a square because its two dimensions equal

∴ The side of the plot = 7 feet

∵ The area of the square = side × side

∴ The area of each plot = 7 × 7

∴ The area of each plot = 49 square feet

→ To find the total area multiply the area of 1 plot by the number

   of the workers

∵ The total area = 49 × 7

∴ The total area = 343 square feet

∴ The total area of the field is 343 square feet

To find the value of y'' at the point where x=0, we need to take the second derivative of y with respect to x. First, let's find the first derivative of y: xy = e^y .

Differentiating both sides with respect to x: y + xy' = e^y * y', Simplifying: y' (1 - e^y) = -y, y' = -y / (1 - e^y)
Now, let's find the second derivative of y:
Using the quotient rule,
y'' = [(1 - e^y) (-y') - (-y)(e^y * y')] / (1 - e^y)^2

Substituting y' = -y / (1 - e^y)
y'' = [(1 - e^y) (-(-y / (1 - e^y))) - (-y)(e^y * (-y / (1 - e^y)))] / (1 - e^y)^2
y'' = [(y / (1 - e^y)) + (y * e^y) / (1 - e^y))] / (1 - e^y)^2
y'' = [y + y * e^y] / (1 - e^y)^3

Now we can find the value of y'' at x=0:
Since xy = e^y, when x=0,
0y = e^y, This is only true when y=-infinity, so the point where x=0 is not defined, Therefore, we cannot find the value of y'' at the point where x=0.

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Answer:

X=2

Step-by-step explanation:

\(\frac{x}{40} =\frac{5}{100} \\\)

Cross multiply

100 x X = 5 x 40

100X=200

Divide both sides by 100

\(\frac{100x}{100} =\frac{200}{100}\)

X=2

The mean of the data set is approximately 210.94. The median of the data set is 101. The mode of the data set is 343.

To determine the mean, median, and mode of the data set:

Data set: 343, 45, 340, SN, 105, 343, 29, 340, 101, 343, alelse, 1, 340, 343, 101, 312, 142, 340, 36

To calculate the mean, we need to find the average of all the values in the data set. However, it seems that there are some non-numeric entries like "SN" and "alelse." We need to remove these non-numeric entries before calculating the mean.

After removing the non-numeric entries, the data set becomes: 343, 45, 340, 105, 343, 29, 340, 101, 343, 1, 340, 343, 101, 312, 142, 340, 36.

Mean: Sum all the values and divide by the number of values.

Mean = (343 + 45 + 340 + 105 + 343 + 29 + 340 + 101 + 343 + 1 + 340 + 343 + 101 + 312 + 142 + 340 + 36) / 17

Mean ≈ 210.94 (rounded to two decimal places)

To calculate the median, we need to find the middle value of the data set when it is arranged in ascending order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

Arranging the data set in ascending order: 1, 29, 36, 45, 101, 101, 105, 142, 312, 340, 340, 340, 343, 343, 343, 343, 340.

Median: Since the number of values is odd (17), the median is the middle value.

Median = 101

To calculate the mode, we need to find the value(s) that appear(s) most frequently in the data set.

Mode: In this data set, the value 343 appears most frequently, so the mode is 343.

In summary:

Mean ≈ 210.94

Median = 101

Mode = 343

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Answer:

1 Answer. The chance of anding on A for one spin is 90+45360=38. So the probability of that happening twice in a row is 38×38=964.

Step-by-step explanation:

1. (4s)³ = 64s³

2. (-s²t)³ = −s⁶t³

3. 4^-3 = 1/64

4. a^-⁷ b^-⁸ = 1/a⁷b⁸

5.(-3x)² (-xy)² = 9x⁴y²

Answer:

the answer is 17

Step-by-step explanation:

40-6=34. 34/2 = 17

Answer:

Step-by-step explanation:

Compact cars:

24 divided by 4 = 6

6 cars for 24 people

SUV's:

24 divided by 6 = 4

4 SUV's for 24 people

Answer:

\(4x+6y=24\)

See below for graph.

Step-by-step explanation:

A total of 24 people need to be transported.

Let x represent the number of Uber compact cars.

And let y represent the number of SUVs.

So, the number of people that can be picked up by x compact cars is 4x.

And the number of people that can be picked up by y SUVs is 6y.

And the total is 24 people. So, the two terms must total 24. So, we can write:

\(4x+6y=24\)

We can convert this to slope-intercept form. First, we can divide everything by  2:

\(2x+3y=12\)

Subtracting 2x from both sides yields:

\(3x=-2x+12\)

Finally, dividing both sides by 3 yields our linear equation:

\(\displaystyle y=-\frac{2}{3}x+4\)

Please refer to the below attachment for the graph.

*Note that we should restrain our graph to only QI. This is because we cannot use negative compact cars of SUVs. Also, only integer points on the line will work, as we cannot have, say, 2.5 compact cars.

**Also, the x- and y-intercepts tell us the maximum of each type needed. Either we need 6 compact cars and 0 SUVs, (6, 0); 4 SUVs and 0 compact cars (0, 4); or a combination of them.

Answer: 38.79 cu. mm.

Step-by-step explanation:

Volume = 4/3π x r^3

= 4/3π x 2.1^3

= 4/3 x 22/7 x 9.261

= 38.79

Answer:

38.792 or 38.808

Step-by-step explanation:

Formula for Volume of Sphere = 4 x pi x 1/3 x r cubed

So,

if diameter = 4.2, then radius = 4.2 divided by 2 = 2.1

Now, volume =

4 x 22/7 x 1/3 x 2.1^3 = 38.808

But is you used 3.14 as pi,

then the volume = 38.792

the probability that the sample standard deviation of service times is less than 2.24 minutes is 0.10. we need to know the distribution of the sample standard deviation of service times.

If service times are normally distributed, then the sample standard deviation will follow a chi-square distribution with n-1 degrees of freedom, where n is the sample size.

Using this distribution, we can use a chi-square table or calculator to find the value of the sample standard deviation that corresponds to a probability of 0.10. For example, if the sample size is n=30, then the critical chi-square value is 16.047.

We can then use the formula for the sample standard deviation:

s = sqrt((n-1)*s^2 / chi-square)

where s is the sample standard deviation, s^2 is the sample variance, and chi-square is the critical chi-square value.

If we assume that the sample mean service time is 10 minutes and the sample variance is 4, then the sample standard deviation is 2. Using the formula above with n=30 and chi-square=16.047, we get:

s = sqrt((30-1)*4 / 16.047) = 2.24 minutes

Therefore, the probability that the sample standard deviation of service times is less than 2.24 minutes is 0.10.

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The given information states that software architecture has been standardized to include five architectural segments, namely the operating system (OS), I/O services (IOS), and three additional segments not specified.

Software architecture has been standardized to have five architectural segments and two application program interfaces (APIs). The architectural segments consist of the operating system (OS), I/O services (IOS), and three additional segments that are not specified in the given information. These segments are typically designed to handle specific functionalities or components of the software system.

The operating system (OS) segment is responsible for managing the hardware resources and providing essential services to the software applications. It handles tasks such as memory management, process scheduling, file system management, and device drivers. The I/O services (IOS) segment is responsible for handling input and output operations, such as user interaction, data transfer between external devices and the software system, and file I/O operations.

The two application program interfaces (APIs) provide a means for different software components or modules to communicate and interact with each other. APIs define a set of functions, protocols, and data structures that enable the exchange of information and services between different software entities. They serve as an abstraction layer, allowing developers to build upon existing functionality without needing to understand the underlying implementation details.

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Answer:

Step-by-step explanation:

There is one negative number in the expression so the solution will be negative there isn’t a -1 in the denominator to cancel out the -1 in the numerator

Answer: -60  ft/4 increments

Step-by-step explanation:

Answer:

96%

Step-by-step explanation:

too easy for me

Here are the vectors **t**, **n**, and **b** at the given point:

* **t** = (-3 sin t, 3 cos t, 0)

* **n** = (-3 cos t, -3 sin t, 3 / cos^2 t)

* **b** = (3 cos^2 t, -3 sin^2 t, -3)

The vector **t** is the unit tangent vector, which points in the direction of the curve at the given point. The vector **n** is the unit normal vector, which points in the direction perpendicular to the curve at the given point. The vector **b** is the binormal vector, which points in the direction that is perpendicular to both **t** and **n**.

To find the vectors **t**, **n**, and **b**, we can use the following formulas:

```

t(t) = r'(t) / |r'(t)|

n(t) = (t(t) x r(t)) / |t(t) x r(t)|

b(t) = t(t) x n(t)

```

In this case, we have:

```

r(t) = (3 cos t, 3 sin t, 3 ln cos t)

r'(t) = (-3 sin t, 3 cos t, 3 / cos^2 t)

```

Substituting these into the formulas above, we can find the vectors **t**, **n**, and **b** as shown.

The vectors **t**, **n**, and **b** are all orthogonal to each other at the given point. This is because the curve is a smooth curve, and the vectors are defined in such a way that they are always orthogonal to each other.

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The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.

To find the vectors t, n, and b at the given point, we need to calculate the first derivative, second derivative, and third derivative of the position vector r(t).
Given r(t) = (3 cos t, 3 sin t, 3 ln cos t), we can calculate the derivatives as follows:
First derivative:
r'(t) = (-3 sin t, 3 cos t, -3 sin t / cos t)
Second derivative:
r''(t) = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 sin^2 t / cos t)
       = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 tan^2 t)
Third derivative:
r'''(t) = (3 sin t, -3 cos t, 6 cos t / cos^3 t - 6 sin t / cos t)
        = (3 sin t, -3 cos t, 6 sec^3 t - 6 tan t sec t)
At the given point (3, 0, 0), substitute t = 0 into the derivatives to find the vectors:
r'(0) = (0, 3, 0)
r''(0) = (-3, 0, 3)
r'''(0) = (0, -3, 6)
Therefore, at the given point, the vectors t, n, and b are:
t = r'(0) = (0, 3, 0)
n = r''(0) = (-3, 0, 3)
b = r'''(0) = (0, -3, 6)
These vectors represent the tangent, normal, and binormal vectors, respectively, at the given point.
The tangent vector (t) represents the direction of motion of the curve at that point. The normal vector (n) is perpendicular to the tangent vector and points towards the center of curvature.

The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.
Remember to check your calculations and units when applying this method to different functions.

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Answer:

Step-by-step explanation:

-2 (x -4) - 1/2 (3-4x) = -12

                ×(-2)           ×(-2)

4(x - 4) + (3 - 4x) = 24

4x - 16 + 3 - 4x = 24

     -13 = 24            <-- it's not true so it's no solution

Answer:

x = 11

Step-by-step explanation:

Given

4(x - 7) = 2x - 6 ← distribute parenthesis on left side

4x - 28 = 2x - 6 ( subtract 2x from both sides )

2x - 28 = - 6 ( add 28 to both sides )

2x = 22 ( divide both sides by 2 )

x = 11

To solve this problem, we'll use the concept of the sampling distribution of the sample mean. Given that the average time to run a 5k is 30 minutes with a standard deviation of 3 minutes, we can assume that the distribution of the sample mean of 15 finishers will be approximately normally distributed.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is 30 minutes.

The standard deviation of the sampling distribution of the sample mean, also known as the standard error, is given by the formula: standard deviation / sqrt(sample size).

In this case, the standard error is 3 minutes / sqrt(15) ≈ 0.775 minutes.

To find the probability that the average finishing time is faster than 29 minutes, we need to find the z-score corresponding to 29 minutes and then look up the corresponding probability in the standard normal distribution table (Z-table).

The z-score is calculated using the formula: (x - μ) / σ, where x is the value we want to find the probability for, μ is the population mean, and σ is the standard deviation.

For 29 minutes:

z = (29 - 30) / 0.775 ≈ -1.29

Now, we look up the probability corresponding to the z-score of -1.29 in the Z-table.

The probability that the average finishing time is faster than 29 minutes is approximately 0.099.

Therefore, the probability is approximately 0.099 or 9.9% (rounded to three decimal places).

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Answer:

The one guy is right k equals 43.6

Hope This Helps!!!

The value of k using Vertical angles is 43.6 degree.

Vertical angles are a pair of non-adjacent angles that are formed by the intersection of two lines. When two lines intersect, they create four angles at the intersection point.

Vertical angles are the angles that are opposite to each other and share the same vertex but are not adjacent. They are Congruent.

As, k and 43.6 are Vertical angles.

So, k = 43.6

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