Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set U.)

Statement: For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.

Answer:

3/4

Step-by-step explanation:

Answer:

The Taylor series of f(x) around the point a, can be written as:

\(f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....\)

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

\(fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}\)

In this exercise we must calculate the Taylor series for the given function in this way;

\(f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}\)

The Taylor series of f(x) around the point a, can be written as:

\(f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....\)

Here we have:

\(f(x) = 4cos(x)\\a = 7\pi\)

Then, let's calculate each part:

\(f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4\)

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in \(x=7\pi\).

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

\(f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....\)

So we can write it as:

\(f(x)=\sum f_n\)

Such that the n-th term can written as:

\(f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}\)

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Answer:

I'm assuming this is a greatest to least, but in case it was not, I put least to greatest, too.

Step-by-step explanation:

Greatest to least:

6/5, 8/9, 0.5, 40%

Least to greatest:

40%, 0.5, 8/9, 6/5

Hope this helps!

Answer:

c

Step-by-step explanation:

4/3

3/5

keep change fli[

20/9=2 2/9

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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Answer and Step-by-step explanation:

Solution:

The equation is given by:

z – z0 = a(x – x0) + b(y – y0).

The point (1, 2, 3) is given , substitute them for x0, y0 and z0:

Z – 3 = a (x – 1) + b(y-2)

Both a and b should be negative, because normal vector to point in the negative x and y direction so that plane will enclose a tetrahedron with finite area in the first octant.

This will only happen if z becomes smaller as we move towards the positive x and y directions.

To find expressions for V, firstly find expression for x, y and z intercepts.

X – Intercepts (y and z = 0) : 2b +a -3 / a

y- Intercepts (x, z = 0): 2b + a- 3 / b

z – Intercepts( x, y = 0): 3 – a – 2b

The base is = (2b+a-3)2/ 2ab

Volume is 1/3 base x height, so

V (a, b) = - (2b+a-3)3 / 6ab

The gradient vector:

ΔV (a, b) = |- (3(2b+a-3)2 ab-b (2b+a-3)3)/6a2b2, (6(2b+a-3)2 ab-a(2b+a-3)3)/6a2b2| = 0

b (2b+a-3)2 [ (2b+a-3) -3a] = 0

a (ab + a-3)2 [(2b +a -3) – 6b] = 0

Where a, b not equal to 0.

We cannot solve for 2b +a-3 = 0 because, that will lead to V = 0, which is impossible.

Therefore, we only solve for second halves equations, which are system of linear equations:

-2a + 2b = 3 and a – 4b = 3

Which gives a = -3 and b = -3/2

Put in equation:

Z – 3 = -3 (x-1) – 3/2 (y-2)

3x +3/2 y +z = 9

Multiplying by 2:

6x + 3y + 2z = 18.

Step-by-step explanation: First, we need to solve this inequality.

When you're asked to solve an inequality like -3x > 18, your goal should be the same as it was when solving equations, to get x by itself on one side.

In this problem since x is being multiplied by -3 on the left side of the inequality, to get x by itself, we divide both sides by -3 but here is the rule you have to watch out for when solving inequalities.

When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign. So this greater than in our original problem becomes less than in our second step.

On the left side, the -3's cancel and we're left with

x and on the right side, 18 divided by -3 is -6.

So we have x < -6.

Now, we are asked to state some solutions to the inequality.

The inequality x < -6 means that any number

less than -6 is a solution to the inequality.

For example, -7 is a solution because -7 is less than -6.

-8 is also a solution because -8 is less than -6.

Other possible solutions include -23, -98, -982, and so on.

Any number less than -6 will be a solution.

Answer:

Step-by-step explanation:

Converting all fractions to decimal (for easier comparison) :

Hence,

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

Step-by-step explanation:

Remark

The surface area is the area of all six sides when the object is a box.

Formula

SA = 2*L*w + 2*L*h + 2*w*h

Givens

L = 6 ft

w= 3 ft

h = 2.5 feet

Substitute and Solution

SA = 2*6*3 + 2*6*2.5 + 2*3*2.5

SA = 36 + 30 + 15

SA = 81

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer:

d) 1/12

Step-by-step explanation:

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

Step-by-step explanation:

center=(-1,1)

radius=√16=4

distance between (-1,1) and (3,1)=√[(3+1)²+(1-1)²]=√[16+0]=√16=4=radius

Hence point lies on the circle.

Answer:

If the walls are the standard 8 feet tall and the room is square, then:

the wall length and width is both 7 feet.

The area of the walls would be 4x7x8 = 224 ft² (also providing there are no doors or windows)

Answer:

I think it's simple sentence

Answer:

B=10

Step-by-step explanation:

worked it out on a graph on the internet

The triangle is a not right triangle because it does not follow the Pythagoras theorem

From the question, we have the figure that represents the parameter that can be used in our computation:

The sides of the triangles are

6, 8 and 9

For a triangle to be a right triangle, the side lengths must follow the Pythagoras theorem

The Pythagoras theorem states that

Longest side² = Sum of the squares of the other sides

So, we have

9² = 6² + 8²

Evaluate

81 = 100

The above equation is false

Hence, the triangle is not a right triangle

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∑ Hey, claudiavg2000 ⊃

Answer:

No solutions.

Step-by-step explanation:

Given:

-2(x-2)-4x=3(x-1)-9x​

Solve:

-2 ( x - 2 ) - 4x : -6x + 4

3(x - 1) - 9x : -6x - 3

Now we have;

-6x + 4 = -6x - 3

Subtract 4 from both sides:

-6x + 4 - 4 = -6x - 3 - 4

-6x = -6x -7

Add 6x to both sides:

-6x + 6x = -6x - 7 + 6x

Simplifying:

0 = -7

As you can see the sides are not equal.

Hence, This problem has no solution.

xcookiex12

8/18/2022

Answer: the first one is 735.75

the second one is 69

Step-by-step explanation:

THEY ARE BOTH CORRECT!

Answer: They are both correct. Good job! :)

Step-by-step explanation:

Answer:

18 kg of 15% copper alloy

62 kg of 70% copper alloy

Step-by-step explanation:

Step 1: Calculate the total amount of copper present in 80 kg of 48% copper alloy

Total Copper = 80 x 0.48 = 38.4 kg

Step 2: Calculate the amount of 15% copper alloy required

15% Copper Alloy = 38.4 / 0.15 = 256 kg

Step 3: Calculate the amount of 70% copper alloy required

70% Copper Alloy = (80 - 256) = -176 kg

Step 4: Since the amount of 70% copper alloy required is negative, the metalworker should use 256 kg of the 15% copper alloy and 0 kg of the 70% copper alloy to create 80 kg of 48% copper alloy.

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

18n + 9

Step-by-step explanation:

Distribute 9 into the expression.

9*2n = 18n

9*1 = 9

18n + 9

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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Answer:

76

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

\( \sf \longmapsto \: \frac{{x}^{3} - {y}^{3} }{4} \\ \sf \longmapsto \: \frac{ {4}^{3} - {2}^{3} }{4} \\ \sf \longmapsto \: \frac{64 - 8}{4} \\ \sf \longmapsto \: \frac{56}{4} \: \: \: \: \: \: \: \: \\ \sf \longmapsto \: 14\)

Answer:b

Step-by-step explanation:

Answer:

c number is correct

Step-by-step explanation:

there is h-6= 10

the minus in six after going to other side makes the sign change into +