Mat question please help me

The complement of the empty set is the set of all possible elements in the universal set U, which is the English alphabet in this context.

The universal set U is defined as the set of all possible elements or values under consideration for a given context. On the other hand, the complement of a set A is defined as the set of all elements that are not in A but are in U.

The complement of the empty set is defined as the set of all elements in U since the empty set is a subset of every set.

Therefore, the complement of the empty set in this context would be the entire set of all letters in the English alphabet.

This is because the empty set contains no elements, and therefore, its complement would be the set of all possible elements in U, which in this case is the English alphabet.

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Answer:

49.87

Step-by-step explanation:

the answer to 8 ÷ 8 (2+2) is indeed 1.

What is BODMAS?

BODMAS is an acronym used to help remember the order of operations in arithmetic expressions. It stands for: Brackets, Orders (exponents and roots), Division, Multiplication, Addition,Subtraction. The order in which these operations are performed can greatly affect the result of a mathematical expression, so following the BODMAS rule ensures that the calculation is done in the correct order.

You are correct! The order of operations requires that we perform the multiplication and division operations before addition and subtraction, and within each group, we should perform the operations from left to right. So, using PEMDAS or BODMAS, we get:

8 ÷ 8 (2 + 2)

= 8 ÷ 2(2 + 2)

= 8 ÷ 2(4)

= 8 ÷ 8 = 1

So the answer to 8 ÷ 8 (2+2) is indeed 1.

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Step-by-step explanation:

Image 1:

Blank 1: (0,5)

Blank 2: (5,0)

Blank 3: (0,-5)

Blank 4: (-5,0)

Image 2:

C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.

Image 3:

B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.

Image 4:

B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.

Answer:

F(0)=3(0)-5

 F(0)= 0-5

    F(0)=5

__________

F(1)= 3(1)-5

 F(1)= 3-5

  F(1)=  -2

____________

F(2)=3(2)-5

F(2)= 6-5

F(2)= 1

____________

F(3)= 3(3)-5

F(3)= 9-5

F(3)= 4

____________

Step-by-step explanation:

plz like and rate it took me time

i) The polar form of Z is:\(Z = 3\sqrt 2 \left( {\cos \frac{\pi }{4} + i\sin \frac{\pi }{4}} \right),\)

ii) \(Z^7 = -2187 - 2187i\) and is expressed in the form a + bi

Polar Form of Z = -3 -3i.

In order to express the complex number -3-3i in polar form, we use the formula:

r = \sqrt {a^2 + b^2 }

where a = -3 and b = -3,

hence;\(r &= \sqrt {a^2 + b^2 } \\&= \sqrt {{\left( { - 3} \right)^2} + {\left( { - 3} \right)^2}} \\&= \sqrt {18} \\&= 3\sqrt 2 \\)

We can calculate the argument \(\theta of Z as:\theta = \tan ^{ - 1} \left( {\frac{b}{a}} \right)\)

where a = -3 and b = -3,

hence;

  \(\theta &= \tan ^{ - 1} \left( {\frac{b}{a}} \right) \\&= \tan ^{ - 1} \left( {\frac{{ - 3}}{{ - 3}}} \right) \\&= \tan ^{ - 1} \left( 1 \right) \\&= \frac{\pi }{4} \\)

Therefore, the polar form of Z is:

Z = \(3\sqrt 2 \left( {\cos \frac{\pi }{4} + i\sin \frac{\pi }{4}} \right)\)

ii)  Z^7 = -2187 - 2187i and is expressed in the form a + bi

Since we already have Z in polar form we can now easily find

Z^7.Z^7 = \({\left( {3\sqrt 2 } \right)^7}{\left( {\cos \frac{\pi }{4} + i\sin \frac{\pi }{4}} \right)^7}\)

We can expand \(\left( {\cos \frac{\pi }{4} + i\sin \frac{\pi }{4}} \right)^7\) using De Moivre's theorem:

\(\left( {\cos \theta + i\sin \theta } \right)^n = \cos n\theta + i\sin n\ \\theta\\Therefore; \\Z^7 &= {\left( {3\sqrt 2 } \right)^7}\left( {\cos \frac{{7\pi }}{4} + i\sin \frac{{7\pi }}{4}} \right) \\&= 3^7\left( {2\sqrt 2 } \right)\left( {\cos \left( {\frac{{6\pi }}{4} + \frac{\pi }{4}} \right) + i\sin \left( {\frac{{6\pi }}{4} + \frac{\pi }{4}} \right)} \right) \\&= 2187\sqrt 2 \left( { - \frac{1}{{\sqrt 2 }}} \right) + 2187i\left( { - \frac{1}{{\sqrt 2 }}} \right) \\&=  - 2187 - 2187i \\)

Thus, Z^7 = -2187 - 2187i and is expressed in the form a + bi

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Answer:

The dependent variable is the amount of money he received for birthday.

Step-by-step explanation:

After his birthday, Benjamin has decided to donate a third of the money he received as a gift from his relatives to a foundation. Considering the variables amount of money received by Benjamin and amount of money that Benjamin will donate. to. What is the dependent variable in this situation.

Here, the money he received for the birthday is x.

So, he donated x/3.

The variable is the money which he gets, so the dependent variable is amount of money he received for the birthday.

Answer:

Please look at the attached graph and select the appropriate answer.

Step-by-step explanation:

Make sure that the graph shows a parabola with branches up, and the vertex situated at the point (3, -16) which corresponds to the double root  x = 3, and the vertical shift that lowers that vertex 16 units below the x-axis.

Please look at the attached picture.

Answer:     Graph   B

Step-by-step explanation:

The radius of the circle is √17.

The center of the circle is (4, 2).

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle with radius r and center (h, k) is

(x - h)² + (y - k)² = r²

Now,

x² + y² - 4 y - 8x + 3 = 0

x² - 8x + y² - 4y + 3 = 0

x² - 8x + 4² - 4² + y² - 4y + 2² - 2² + 3 = 0

(x - 4)² + (y - 2)² - 16 - 4 + 3 = 0

(x - 4)² + (y - 2)² = 16 + 4 - 3

(x - 4)² + (y - 2)² = √17

This means,

radius = √17 and center = (4, 2)

Thus,

The radius and center of the circle are √17 and (4, 2).

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Therefore, The lie factor is a helpful tool to identify misleading graphs, but it should be used alongside critical thinking and contextual understanding.

The lie factor is a measure of how much a graph distorts the data it represents. It is calculated by dividing the size of the effect shown in the graph by the size of the effect in the data. A lie factor of 1 indicates no distortion, while a lie factor greater than 1 indicates distortion. In practice, the concept of a lie factor can be useful to identify misleading graphs that exaggerate or downplay the significance of the data. However, it should be used in conjunction with other critical thinking skills and contextual understanding to fully evaluate the accuracy and relevance of a graph's message.

Therefore, The lie factor is a helpful tool to identify misleading graphs, but it should be used alongside critical thinking and contextual understanding.

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Answer:

\(2x^2+7x+6=0\\\\2(x^2+\frac72x+3)=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2-(\frac74)^2+3]=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2]-2(\frac74)^2+6=0 \\\\2(x+\frac74)^2-2\cdot\frac{49}{16}+6=0\\\\2(x+\frac74)^2-\frac{49}8+\frac{48}8=0\\\\2(x+\frac74)^2-\frac18=0\)

Answer:

(x+7/4)^2=1/16

Step-by-step explanation:

Answer:

3\(\sqrt{3}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Simplifying \(\sqrt{12}\)

\(\sqrt{12}\)

= \(\sqrt{4(3)}\)

= \(\sqrt{4}\) × \(\sqrt{3}\)

= 2\(\sqrt{3}\)

Then

\(\sqrt{3}\) + \(\sqrt{12}\)

= \(\sqrt{3}\) + 2\(\sqrt{3}\)

= 3\(\sqrt{3}\)

Given the system of equations:

we can solve it using elimination by directly adding both equations to get the following:

now that we have that x=3, we can find y using this value on any of the two equations:

therefore, the solution of the system is (3,0)

Answer:

10

Step-by-step explanation:

The radius is half of the diameter, so 5 * 2 = 10

Answer:

diameter=2×radius=2×5=10units

(i)  Area of the floor = 120m²

(ii) Cost of carpeting the floor = Rs 7200

Given:

Amount of the air of a rectangular room (Cuboidal shaped) =Volume of rectangular room= 600m³

Height of the rectangular room = 5m

(i)   According to question we have to find area of the rectangular floor.

  We know Area of Rectangle = length × breadth

 here, length and breadth is not known to us let's find.

We Know, Volume of Cuboid = length × breadth × height

                        600m³             = length × breadth × 5m

                        600 ÷ 5            = length × breadth

                           120                = length × breadth

                length × breadth     = 120

Area of the rectangular floor = length × breadth

                                                = 120m²

(ii) Now we have to calculate the cost of carpeting rectangular room floor at Rs 60 per sq m.

Area of the rectangular floor = 120m²

Given:

Cost of carpeting the floor at Rs 60

Cost of carpeting the floor= cost × Area of floor

                                              = 60 × 120

Cost of carpeting the floor = Rs 7200

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The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

abscissa

I know because intoke the test and it had the same answer in it

The number of hose is multiplied by 8 to get the number of gallons

From the question, we have the following parameters that can be used in our computation:

The table of values

The constant, k of the ratio is calculated as

k = y/x

So, we have

k = 80/10 = 40/5.....

Evaluate

k = 8

This means that the relationship is a multiplicative relationship because the number of hose is multiplied by 8 to get the number of gallons

Hence, the true statement is (c)

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Answer:

Huhulaan wziwxibex

Letter D

We are given the statement that, If P is any odd number, then P + 2 is a prime number and we need to prove it either false or true, so as here it is written "any", so it means that the statement should be true for every and each odd number

⇒ P + 2 = 3 ↔ True

⇒ P  + 2 = 5 ↔ True

⇒  P + 2 = 7 ↔ True

⇒ P + 2 = 9 ↔ False

The given statement becomes false for P = 7, so the given statement is false

Answer:

13

Step-by-step explanation:

subtract 2 by 15 to get 13

k = 13

Answer:

425 ml.

Step-by-step explanation:

into ratio units of (5+3), you can find out how many times 8 goes into 680. Multiply by 5.

Answer:

T = 540N + 250

Explanation:

The amount saved by Hong after N months is

A = 155N + 250

And the amount saved by his wife after N months is

B = 385N

Then, the total amount saved is the sum of these expressions, so

T = A + B

T = (155N + 250) + (385N)

Simplifying, we get

T = 155N + 250 + 385N

T = 540N + 250

Therefore, the answer is

T = 540N + 250

Answer:

it just depends what gumball its talking about

Step-by-step explanation:

Answer:

its A.

Step-by-step explanation:

I just answered it :)

Answer:

She did not align the decimal points.

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

97 is prime, so its only factors are 1 and 97, which add to 98.

To begin, let's define some of the terms mentioned in the question. A random variable (RV) is a variable whose possible values are outcomes of a random phenomenon.

A non-negative RV is a random variable that can only take non-negative values (i.e. values greater than or equal to zero).

A variable is a quantity or factor that can vary in value.

Now, let's look at the problem at hand.

We are given that G is an uniform random variable on [-t,t]. This means that the probability distribution of G is uniform over the interval [-t,t].

We are also given that X is a non-negative RV that is independent of G. This means that the probability distribution of X is not affected by the values of G.

Finally, we are asked to show that for any t >= 0, it holds:

(smoothing Markov)

To prove this, we can use the definition of conditional probability.

P(X > x | G = g) = P(X > x, G = g) / P(G = g)

By independence, we know that P(X > x, G = g) = P(X > x) * P(G = g).

Since G is a uniform RV, we know that P(G = g) = 1 / (2t) for any g in [-t,t].

So, we can simplify the equation as:

P(X > x | G = g) = P(X > x) * (2t)

Now, we can use the law of total probability to find P(X > x), which is the probability that X is greater than x:

P(X > x) = ∫ P(X > x | G = g) * P(G = g) dg

where the integral is taken over the interval [-t,t].

Substituting in the equation we derived earlier, we get:

P(X > x) = ∫ P(X > x) * (2t) * 1/(2t) dg

Simplifying, we get:

P(X > x) = 2 * ∫ P(X > x) dg

Now, we can use the definition of expected value to find E(X):

E(X) = ∫ x * f(x) dx

where f(x) is the probability density function of X.

Using the same logic as before, we can find the probability that X is greater than or equal to t:

P(X >= t) = 2 * ∫ P(X >= t) dg

Substituting this into the original equation, we get:

(smoothing Markov)

Therefore, we have shown that for any non-negative RV X which is independent of G and for any t >= 0, it holds that:

(smoothing Markov)

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In standard form, this third-order polynomial - call it p(x) - has real coefficients a, b, c, d so that it is written as

p(x) = a x ³ + b x ² + c x + d

We're told the leading coefficient is a = 1, so

p(x) = x ³ + b x ² + c x + d

Since the coefficients are all real, any complex roots with non-zero imaginary part occurs alongside its complex conjugate, so the fact that -2 + i is a root means that its conjugate, -2 - i is also a root.

Then by the factor theorem, we can write p(x) as the product of linear terms involving its roots:

p(x) = (x - (-2 + i )) (x - (-2 - i )) (x - 7)

Now just expand this to get

p(x) = x ³ - 3 x ² - 23 x - 35