Part 2
Use your answer above (and more differentiation/integration) to now express the following function as a power series (centered at x = 0).
g(x) = 1/(9+x)³

Answer:

1/2 (one over two)

Step-by-step explanation:

when you are finding an a slope, or inequality as you wrote here, you are using formula: y/x ( y over x )

the graph dotes show how they are moving 2 to the right(x) and 1 up(y), so it’s 1/2!

Answer:

Group the like terms together:

4x²y + 6x²y + 12z² - 2z

Simplify:

10x²y + 12z² - 2z

The simplified expression is 10x²y + 12z² - 2z.

Step-by-step explanation:

Answer:

The simplified expression is 10x²y + 12z² - 2z

Step-by-step explanation:

To simplify the expression, we combine like terms, which are terms that have the same variables raised to the same powers. In this case, we have two terms with the variable 4x²y and two terms with the variable -2z. We can combine these like terms by adding their coefficients:

4x²y + 6x²y = 10x²y

-2z + (-2z) = -4z

So the expression simplifies to:

10x²y + 12z² - 4z

We can further simplify this expression by combining the terms with the variable z:

12z² - 4z = 4z(3z - 1)

Therefore, the final simplified expression is:

10x²y + 4z(3z - 1)

We can also write this expression as:

10x²y + 12z² - 2z

which is the answer provided.

The first matrix.

A matrix is an array of numbers arranged in rows and columns.

Analysis:

1/2R2 +R3 to R3

means divide row 2 by 2 and add it to row 3 to form row 3 of the new matrix.

1/2R2 = -1 -3 3 -2

R3 = 0 3 -2 -9

1/2R2 + R3 = -1  0  1  -11

In conclusion, the matrix with the above operation is the first matrix.

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Answer:

$170

Step-by-step explanation:

Sally costs 30

Max costs 40

Goliath costs 80(1.25) = 100

add them up

$170

Answer:

1. area = 1/2bh = (1/2)(21)(18) = 189 yd²

2. 3x2x3x2 = 36 different ways

3. area of kite = (1/2)(18)(24) = 216 units²

4. 8:52  or reduced,   2:13

5. Sorry, this is not my strong point

Step-by-step explanation:

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

Step-by-step explanation:

Length of Fence

Cost

Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

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Answer:

\(16.5 \div 10 = 1.65 \\ 16.5 \div 100 = 0.165\)

The part of the expression which represents the discounted price before tax is x-35.

The given expression is 0.12x+(x-35).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

a) The part of the expression represents the discounted price before tax is x-35

b) The part of the expression represent the amount of sales tax in dollars is 0.12x

Hence, the part of the expression which represents the discounted price before tax is x-35.

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Answer:

(a) 1.645

(b) 2.5758

Step-by-step explanation:

The complete question is: Find Z(\(\alpha\)/2) for the confidence level 90% and for the confidence level 99%.

Firstly, as we know that \(\alpha\) represent the level of significance, i.e;

Level of significance = 1 - confidence level

(a) We are given the confidence level of 90%, so;

     Level of significance = 1 - 90%

                                         = 1 - 0.90 = 0.10 or 10%

Now, \(Z_(_\frac{\alpha}{2}_)\) = \(Z_(_\frac{0.10}{2}_)\) = \(Z_(_0_._0_5_)\)

This means that we have to look for a critical value in the z table at a 5% level of significance which gives us a value of 1.645.

(a) We are given the confidence level of 99%, so;

     Level of significance = 1 - 99%

                                         = 1 - 0.99 = 0.01 or 1%

Now, \(Z_(_\frac{\alpha}{2}_)\) = \(Z_(_\frac{0.01}{2}_)\) = \(Z_(_0_._0_0_5_)\)

This means that we have to look for a critical value in the z table at a 0.5% level of significance which gives us a value of 2.5758.

True statement for Protecting classified data is classified material must be appropriately marked.

Classified information being transmitted from one commission office to another shall be protected with a classified document cover sheet and hand delivered by an appropriately cleared person to another appropriately cleared person.

Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties.

Data classification is broadly defined as the process of organizing data by relevant categories so that it may be used and protected more efficiently. Data classification involves tagging data to make it easily searchable and trackable.  

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Answer:

{a} {b} {c} {ab} {ac} {bc} {abc}

Answer:

option A

Step-by-step explanation:

∠WPS +∠OPW  = 180   {straight line}

∠WPS +110 = 180

∠WPS = 180 - 110

∠WPS = 70°

∠RWQ + ∠QWT +∠TWU = 180   {straight line}

∠RWQ + 60 + 50 = 180

∠RWQ + 110 = 180

∠RWQ = 180 - 110

∠RWQ= 70°

∠PWU +  ∠USP + ∠ WPS = 180  {angle sum property of triangle}

∠PWU + 40 + 70 = 180

∠PWU + 110 = 180

∠PWU = 180 - 110  

∠PWU = 70°

Answer:

A

Step-by-step explanation:

∠WPS +∠OPW  = 180 (adj angles on a str line)

       ∠WPS +110 = 180

                ∠WPS = 180 - 110

                            = 70°

∠RWQ + ∠QWT +∠TWU = 180 (adj angles on a str line)

            ∠RWQ + 60 + 50 = 180

                   ∠RWQ + 110 = 180

                             ∠RWQ = 180 - 110

                                         = 70°

∠PWU +  ∠USP + ∠ WPS = 180 (adj angles on a str line)  

            ∠PWU + 40 + 70 = 180

                     ∠PWU + 110 = 180

                              ∠PWU = 180 - 110  

                                          = 70°

Answer:

\(x=25^o\)

Step-by-step explanation:

Angle sum of a triangle: \(< A + < B+ < C=180^o\\\)

Types of Triangles: Isosceles, Equilateral, Scalene

Given AB = AC are two sides of the big triangle, then ΔABC is Isosceles.

Isosceles triangles are defined to have two equal sides and two equal angles (opposite the congruent(equal) sides).

Also, since ABC is defined as a triangle, BC is a straight line, a.k.a., it is a \(180^o\) angle. As the image shows, the line, AD creates a right angle on one side, therefore it creates a right angle(\(90^o\)) on the other side.

Back to Isosceles Triangles, AD = AE means ΔADE is isosceles and <ADE = <AED

Using the Angle sum formula of a triangle, you can fill in <A, <B, and <C with the following:

<A=\(50^o\)

<B=<C=y [This is because <ADE = <AED]

\(50^o+2y=180^o\\2y=130^o\\y=65^o\)

Now, this means that <ADE=\(65^o\) and <ADC =\(90^o\)

<x is better seen as <EDC

<EDC+<ADE=<ADC

Since we know <ADE is 65 and <ADC is 90, we can plug in these to the formula above.

\(x+65^o=90^o\\x=25^o\)

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Given Data:

Using the property of linear pair,

Thus, option (A) is the correct answer.

The area of the complex figure is 132 square units

From the information given, we have that the composite shape is a combination of a:

The formula for area of a square is given as:

Area = a ²

Where 'a' is the length of it side

Area = 6²

Area of square = 36 square units

The formula for area of a rectangle is given as:

Area = width × length

Area = 8 × 12

Area of rectangle = 96 square units

Area of the complex figure = Area of square + area of rectangle

= 36 + 96

= 132 square units

Thus, the area of the complex figure is 132 square units

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The probability of drawing two slips of paper containing numbers that are the lengths of two sides of a triangle in the (3,4,5) family is 1/50.

The (3,4,5) family of triangles is a set of triangles that are similar to the triangle with side lengths 3, 4, and 5. In particular, the sides of any triangle in the (3,4,5) family must satisfy the Pythagorean theorem, i.e., the sum of the squares of the two shorter sides must equal the square of the longest side.

We can start by listing all the possible pairs of numbers that can be drawn from the hat

(3,4), (3,5), (3,6), (3,7), (3,8), (3,10)

(4,5), (4,6), (4,7), (4,8), (4,10)

(5,6), (5,7), (5,8), (5,10)

(6,7), (6,8), (6,10)

(7,8), (7,10)

(8,10)

Out of these 20 possible pairs, we need to count the pairs that satisfy the conditions for being lengths of two sides of a triangle in the (3,4,5) family. For any such triangle, the longest side must be either 5 or 10. Therefore, we can split the pairs into two groups

Pairs that include 5: (3,4), (5,6), (5,8), (5,10)

Pairs that include 10: (6,8), (7,10), (8,10)

For a pair to be the lengths of two sides of a triangle in the (3,4,5) family, the sum of the squares of the two shorter sides must equal the square of the longest side. We can check this condition for each of the pairs in the two groups

Pairs that include 5

(3,4): not a valid triangle

(5,6): not a valid triangle

(5,8): the sum of the squares of the two shorter sides is 5^2 + 8^2 = 89, which is not equal to 10^2

(5,10): the sum of the squares of the two shorter sides is 3^2 + 4^2 = 25, which is equal to 5^2

Pairs that include 10

(6,8): the sum of the squares of the two shorter sides is 6^2 + 8^2 = 100, which is equal to 10^2

(7,10): not a valid triangle

(8,10): the sum of the squares of the two shorter sides is 4^2 + 8^2 = 80, which is not equal to 10^2

Therefore, out of the 20 possible pairs, only 2 pairs satisfy the conditions for being lengths of two sides of a triangle in the (3,4,5) family. The probability of drawing one of these pairs is 2/20 = 1/10.

Once the first number is drawn, there are only 5 slips of paper left in the hat, and only one of them is the other side of the triangle, so the probability of drawing the second number is 1/5. Therefore, the probability of drawing two numbers that are the lengths of two sides of a triangle in the (3,4,5) family is (1/10) × (1/5) = 1/50.

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Answer:

(2, 6), (4, 8), (6, 10), (8, 12), (10, 14)

Answer:

1)   3.401244 ft^3

2)  708.75

Step-by-step explanation:

1) take the cube root of the volume (gets you one side of the cube), divide it by 100, then cube that.

2) square the scale factor (3/4), and multiply the area by that number.

Answer:

d.) sinθ=0.763; tanθ=1.181

c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.

Step-by-step explanation:

Given that:

θ is in the IV quadrant (All is positive) that is sin, cos and tan are all positive.

Cosθ = 0.646

Θ = Cos^-1(0.646)

θ = 49.75930

Hence,

Tanθ = tan(49.75930) = 1.1816365 = 1.182

Sinθ = sin(49.75930) = 0.7633373 = 0.763

2.)

Let

Walking rate = x mph

Running rate = x + 4 mph

21 miles run time = 9 miles walk time

Recall :

Time = distance / speed or rate

21 / (x + 4) = 9 / x

Cross multiply :

21 * x = 9(x + 4)

21x = 9x + 36

21x - 9x = 36

12x = 36

x = 36 /12

x = 4 mph = walking rate

Running rate = x + 4 = 4 + 4 = 8 mph

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{18}}}}}\)

Step-by-step explanation:

Given, y = 3 , z = 3

\( \sf{z(y + y)}\)

Plug the value of y and z

⇒\( \sf{3(3 + 3)}\)

Add the numbers : 3 and 3

⇒\( \sf{3 \times 6}\)

Multiply the numbers : 3 and 6

⇒\( \sf{18}\)

Hope I helped!

Best regards! :D

Answer:

65*

Step-by-step explanation:

All angles in a triangle = 180 degrees.

Answer:

The first picture (x≤-3)

Step-by-step explanation:

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The length of the square in centimetres in algebraic expression is 25m

The perimeter of a square is m meters.

The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:

Therefore,

perimeter of a square = 4l

where

Therefore,

m = 4l

where

l = m / 4 meters.

Therefore, the side length of the square in centimetres is as follows:

1 meters = 100 cm

m / 4 meters  = ?

cross multiply

length of the square in meters = m / 4 × 100

length of the square in meters = 100m / 4

length of the square in meters = 25m

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