Find the volume of a cylinder with a height of 9 cm and a radius of
3 cm.

Answer:

a = 13, b = 28, c = 6, d = 22, e = 31

Step-by-step explanation:

Answer:

1. y2-y1/x2-x2

2.y=mx+b

3.Ax+By=C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Discussion

Think of what it would be like in your own household. If your mom has been away and the food is starting to spoil, you can't be picky. If you are not picky, you will get by until someone goes shopping.

That's the way its going to work in the ecosystem. I would pick B and hope that it the bad times won't last too long.

Answer:

d

Step-by-step explanation:

The standard deviation of T is equivalent to 5.

       \($\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}\)

Given is that a factory process requires 3 steps to finish a product. The steps each have a mean completion time of A = 10 seconds and a standard deviation of O = 5 seconds. The time it takes to complete each step is independent from the other steps.

We can write that -

5 = √∑(x{i} - 10)²/√3

√∑(x{i} - 10)² = 5√3

(√∑(x{i} - 10)²)² = (5√3)²

∑(x{i} - 10)² = 25 x 3

∑(x{i} - 10)² = 75

Now, we can write that -

σ = √(75/3)

σ = √25

σ = 5

Therefore, the standard deviation of T is equivalent to 5.

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Answer:

44 cents

Step-by-step explanation:

First we need to find out how much per inch so do 84 divided by 21 which is 4 then get the closest to the number 47 which is 44 so 4x11=44 cents I'm not sure if it's right tho

The formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

We have Reabilwe who is conducting an experiment in which the temperature is measured carefully. The temperature was 106°C at the end of the first minute, and then it falls by 6°C every minute after that.

We have to tp determine a formula to calculate the temperature (T) after m minutes.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to question, we have -

Initial Temperature = 106 degrees Celsius

Temperature increase per minute = 6 degrees Celsius

Assume that the Temperature fall after m minutes is T. Then -

T = 106 - 6m

Hence, formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

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The standard matrix A of T is:

\(A = [ T(e1) | T(e2) ]= [ 3 | -5 ][ 1 | 6 ][ 3 | 0 ][ 1 | 0 ]\)

As per the question given,  

To find the standard matrix of the linear transformation T: R2 -> R4, we need to determine the images of the standard basis vectors e1 = (1, 0) and e2 = (0, 1) of R2 under T and use them as columns of the standard matrix.

We are given that T(e1) = (3, 1, 3, 1) and T(e2) = (-5, 6, 0, 0). Therefore, the standard matrix A of T is:

A = [ T(e1) | T(e2) ]

= [ 3 | -5 ]

[ 1 | 6 ]

[ 3 | 0 ]

[ 1 | 0 ]

Note that the vertical bar separates the columns of the matrix. Each entry in the matrix corresponds to the coefficient of the corresponding basis vector in the image of the transformation.

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Answer:

the standard form a linear equation is

y = mx + c

therefore m = -3

parallel lines have equal gradient therefore the gradient of the equation is m = -3

coordinates for the x intercept (1;0)

y = mx + c

for x intercept let y = 0

0 = -3(1) + c

c = 3

therefore the equation is

y = -3x + 3

Answer:

The answer is -285

Step-by-step explanation:

Answer:

Muercury 3

Venus 6

Mars 2

pluto 5

Jupiter 1

Nucleus4

Step-by-step explanation:

There is no vector u such that T(u) = b. (b = 11). Hence, the answer is (b) b = 11.

Given A is a 3 × 3 matrix defined as below.

2 -4 4 2 4 6 -3 6 -4

Transformation is defined as T(u) = Au for the transformation of a vector u.

Let's find the vector u such that I maps u to b, if possible.

For part (a), b = 10 0 4

To find u, we can solve the equation bu = b. (b is the given vector, and u is what we are looking for)

⇒ Au = b

Since b is a 3 × 1 matrix, and A is a 3 × 3 matrix, u must also be a 3 × 1 matrix.

⇒ 2u₁ - 4u₂ + 4u₃ = 10

⇒ 2u₁ + 4u₂ + 6u₃ = 0

⇒ -3u₁ + 6u₂ - 4u₃ = 4

The above system of linear equations can be represented in the form of an augmented matrix as shown below.

2 -4 4 10 2 4 6 0 -3 6 -4 4 [A|b]

Applying Gauss-Jordan elimination method, we get the following augmented matrix.

1 0 0 3/2 0 1 0 5/4 0 0 1 -1/2 [A|b]

Thus, we have obtained a solution, u = 3/2i + 5/4j - 1/2k so that T(u) = b.

Now, for part (b), b = 11

To find u, we can solve the equation bu = b. (b is the given vector, and u is what we are looking for)

⇒ Au = b

Since b is a 3 × 1 matrix, and A is a 3 × 3 matrix, u must also be a 3 × 1 matrix.

⇒ 2u₁ - 4u₂ + 4u₃ = 11

⇒ 2u₁ + 4u₂ + 6u₃ = 0

⇒ -3u₁ + 6u₂ - 4u₃ = none

The last equation in the system has no solution, as the left-hand side is odd, while the right-hand side is even. Therefore, there is no vector u such that T(u) = b. (b = 11)

Hence, the answer is (b) b = 11.

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When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

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

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

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Answer:

x = 8

y = 36

Step-by-step explanation:

The triangle shown in the image is an isosceles triangle.

We can find the value of x using the above mentioned information:

∠B = ∠A

5x = 40 divide both sides by 5

x = 8

The sum of interior angles in a triangle is equal to 180°.

Since ∠B and ∠C are both 40°:

40 + 40 + 3y - 8 = 180 add/subtract like terms

72 + 3y = 180 subtract 73 from both sides

3y = 108 divide both sides by 3

y = 36

Answer:

r = \(\sqrt{\frac{3V}{4\pi h} }\)

Step-by-step explanation:

V = \(\frac{4}{3}\) πr²h ( multiply both sides by 3 to clear the fraction )

3V = 4πr²h ( isolate r² by dividing both sides by 4πh )

\(\frac{3V}{4\pi h}\) = r² ( take square root of both sides )

\(\sqrt{\frac{3V}{4\pi h} }\) = r

He puts 100$ in the bank on the 25th week.

An example of a financial institution that lends money is a bank, which both collects deposits from the public and creates demand deposits. Through the capital markets, the bank may engage in lending activities directly or indirectly.

Banks are heavily regulated in most countries because they are essential to the financial stability and economic health of a nation. The fractional reserve banking system, in which banks maintain liquid assets that are only partially comparable to their current liabilities, has been institutionalized in the majority of countries. In addition to other constraints intended to assure liquidity, banks are often subject to minimum capital requirements based on an international set of capital norms known as the Basel Accords.

Explanation:

First term(\(a_{1}\))= 1

Common difference= 1.25-1=0.25

\(a_{25}\)=1+(25-1).25

        =1+(24)(.25)

        = 1+6

        =7

\(S_{25}\)=25/2 (1+7)

    =25/2 (8)

    =100

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Answer:

x ≤ -7

(-∞, -7]

Step-by-step explanation:

         3x + 5

2x - --------------- ≤ -10

             4

1. Multiply 4 on both sides. This eliminates the denominator 4

            3x + 5

(4)2x - --------------- ≤ -10(4)

             4 (4)

2. Combine like terms

8x - (3x + 5) ≤ -40

8x - 3x - 5x ≤ -40

= 5x - 5 ≤ - 40

3. Add 5 on both sides

5x - 5 ≤ -40

     +5      +5

5x ≤ -35

4. Divide

5x ≤ -35

÷5     ÷5

x ≤ -7 or (-∞, -7]

I hope this helps!

Answer:

Step-by-step explanation:

x=115/11

The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

By using Python, you will come up with your own challenging algorithm for other students to trace.

If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.

The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.

These conditional statements are available in Python:

If you want a block of code to run only if a certain condition is true, use the if statement.

If the same expression is false, use instead that to provide a set of instructions that should be run.

If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.

To choose which of the several program code should be performed, use the switch.

How to write the code?

num = 100

if num < 20:

print('Less than 20')

if num < 30:

print('Less than 30')

if num < 40:

print('Less than 40')

if num < 50:

print('Less than 50')

if num > 100 or num == 100:

print('More than or equal to 100')

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The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Answer:

It would be zero

Step-by-step explanation:

Answer: x=−8

Evaluate

2x−9=3x−1

Move the variable to the left side

2x−9−3x=−1

Subtract the terms

−x−9=−1

Move the constant to the right side

−x=−1+9

Add the terms

−x=8

Divide both sides

−1

−x

​

=

−1

8

​

Simplify

−1

−x =

−8

Solution

x=−8

Step-by-step explanation:

Hey!

2x-9=3x-1

Lets put the x on 1 side

2x 2x

- 2x -9= 3x-1

-9= x -1

-1 -1

-8 = x

X = -8 is your answer

Hope this helps!

Answer:

256

Step-by-step explanation:

65% is 208

15% is 48

15% + 65% is 80%

So, just add 48 and 208 together:

48 + 208 = 256

Therefore, 80% of that number is 256.

Answer:

256

Step-by-step explanation:

We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.

We have three linearly independent eigenvectors, the matrix A is diagonalizable for all values of λ.  .If there are no such values, the answer would be "none."

To determine if a matrix is diagonalizable, we need to find the eigenvectors and eigenvalues of the matrix. If there are enough linearly independent eigenvectors, then the matrix is diagonalizable.

If we let A be the given matrix, then we can find the eigenvalues by solving the characteristic equation det(A-λI) = 0, where I is the identity matrix. This gives us:

det(A-λI) = (4-λ)(3-λ)(2-λ) = 0

So the eigenvalues are λ = 4, λ = 3, and λ = 2.

To find the eigenvectors, we need to solve the equation (A-λI)x = 0 for each eigenvalue. This gives us the following:

For λ = 4, we have:

(A-4I)x = \begin{pmatrix} 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}

Solving this system of equations gives us the eigenvector x = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}

For λ = 3, we have:

(A-3I)x = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}

Solving this system of equations gives us the eigenvectors x = \begin{pmatrix} -1 \\ 0 \\ 1 \end{pmatrix} and x = \begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}

For λ = 2, we have:

(A-2I)x = \begin{pmatrix} 2 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}

Solving this system of equations gives us the eigenvector x = \begin{pmatrix} -1 \\ 0 \\ 1/2 \end{pmatrix}

Since we have three linearly independent eigenvectors, the matrix A is diagonalizable for all values of λ. Therefore, the answer is none.

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Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.

Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.

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The volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis is 160π/3 cubic units.

To use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis, we need to integrate the volume of a cylindrical shell.

The formula for the volume of a cylindrical shell is:

V = 2πrhΔx

where:

r is the distance from the axis of rotation (the x-axis) to the edge of the shell

h is the height of the shell (which is equal to the difference between the y-coordinates of the two curves)

Δx is the thickness of the shell (which becomes an infinitesimal dx in the limit)

We can see from the given equations that the two curves intersect at x=0, so we will integrate from x=0 to x=a, where a is the point where the curve y=2 intersects the x-axis. To find a, we set y=2 and solve for x:

y = |x|/4 = 2

|x| = 8

x = ±8

Since we are only interested in the region bounded by the curves in the first quadrant, we take a=8.

Now we can set up the integral for the volume using the shell method:

V = ∫(0 to 8) 2πr * h * dx

= ∫(0 to 8) 2πx * [2 - (|x|/4)] * dx

Note that we multiply by 2 because we are integrating only over the first quadrant, and we obtain the full volume by doubling that result.

Since the function inside the integral is not continuous at x=0, we split the integral into two parts:

V = 2 ∫(0 to 8) 2πx * [2 - (x/4)] * dx + 2 ∫(0 to 8) 2πx * [2 - (-x/4)] * dx

Simplifying, we get:

V = 2π ∫(0 to 8) (15/2)x - (1/4)x^2 dx

= 2π [(15/4)x^2 - (1/12)x^3] | from 0 to 8

= 160π/3

Therefore, the volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis is 160π/3 cubic units.

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Answer:

6

Step-by-step explanation:

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer:

See below (and attached file)

Step-by-step explanation:

The value of \(a\) in the equation \(y=a(x-h)^2+k\) represents how much a vertical parabola will stretch or compress, as well as whether it opens upward or downward:

If \(0<|a|<1\), it is a horizontal stretch

If \(|a|>1\), it is a horizontal compression

If \(a<0\), the parabola opens downward

If \(a>0\), the parabola opens upward

The file attached shows a graph with different examples of what happens to a parabola when the value of \(a\) changes.