In 10 and 11 complete each sentence then use the laws of exponents to write an equivalent expression for the given expression.

To prove the opposite, we need to show that if G is not a pseudorandom generator (PRG), then Construction 3.17 cannot be EAV-secure.

Assume that G is not a PRG, which means it fails to expand the seed sufficiently. Let's suppose that G is computationally indistinguishable from a truly random function on its domain, but it does not meet the requirements of a PRG.

Now, consider the private-key encryption scheme Π described in Construction 3.17 using G as the pseudorandom generator. If G is not a PRG, it means that its output is not sufficiently pseudorandom and can potentially be distinguished from a random string.

Given this scenario, an adversary A could exploit the distinguishability of G's output and devise an attack to break the security of the encryption scheme Π. The adversary could potentially gain information about the plaintext by analyzing the ciphertext and the output of G.

Therefore, if G is not a PRG, it implies that Construction 3.17 cannot provide EAV-security, as it would be vulnerable to attacks by distinguishing the output of G from random strings. This contradicts Theorem 3.18, which states that if G is a PRG, then Construction 3.17 achieves indistinguishable encryptions.

Hence, by proving the opposite, we conclude that if G is not a PRG, then Construction 3.17 cannot be EAV-secure.

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Answer:

8 units

Step-by-step explanation:

If the area of the squares are 32 units^2, we have that:

Area = Side * Side

Side^2 = 32

Side = sqrt(32) = 5.657 units

So as the squares are adjacent to two sides of the triangle, we have that the triangle has two sides of 5.657 units

As it is a right triangle, we can use the Pythagoras' theorem:

c^2 = a^2 + b^2

c^2 = 5.657^2 + 5.657^2

c^2 = 64

c = 8 units

Answer:

its 8

Step-by-step explanation:

By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

A mathematical statement known as an equation is made up of two expressions joined by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the number of the variable x is 7.

So, calculate as follows:

Let g represent giraffes and o represent ostriches.

g + o = 70 ...(1)

4*g + 2*o = 200  ...(2)

g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:

4*g + 2*o = 200

4*(70-o) + 2*o = 200

280 - 4o + 2o = 200

-2o = 200 - 280

2o = 80

o = 80/2

o = 40

Ostriches are 40 then giraffes will be:

70 - 40 = 30

Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The answer is 0.68 and 2/3

Hoped that helped

The probability of rolling a number greater than 3 is equal to

   --> # of numbers greater than 3 / total # of numbers on the dice

   --> \(\frac{3}{6} =\frac{1}{2}\)

There the probability of rolling a number greater than 3 is 1/2

Hope that helps!

The integral of $f(x,y,z) = y^2$ over the given region is $\boxed{\frac{31 \pi}{10}}$.

We can solve this problem using cylindrical coordinates.

First, we note that the region of integration is within the cylinder $x^2 + y^2 = 4$. This means that $r^2 = x^2 + y^2$ must be less than or equal to 4. We also know that $0 \leq z \leq 1$.

Using cylindrical coordinates, we have $x = r \cos \theta$, $y = r \sin \theta$, and $z = z$. We also have the Jacobian for cylindrical coordinates:

$$J = r$$

Thus, the integral becomes:

$$\int_0^1 \int_0^{2\pi} \int_0^2 r^3 \sin^2(\theta) \, dr \, d\theta \, dz$$

We integrate with respect to $r$ first:

$$\int_0^1 \int_0^{2\pi} \frac{1}{4} (2^4 - r^4) \sin^2(\theta) \, d\theta \, dz$$

Simplifying, we get:

$$\frac{\pi}{2} \int_0^1 (8 - r^4) \, dz$$

Integrating with respect to $z$, we get:

$$\frac{\pi}{2} (8z - \frac{1}{5}z^5)\bigg\rvert_0^1 = \frac{31 \pi}{10}$$

Therefore, the integral of $f(x,y,z) = y^2$ over the given region is $\boxed{\frac{31 \pi}{10}}$.

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Answer:

option b (4,-4)

Step-by-step explanation:

this is because this is a less than or greater than inequality and there is no equal so we can’t have anything touching the line and that eliminates d. But all the others are outside the shaded blue so, option b is the only one in there

The fractions in the options are equivalent to the fraction 18/8, except the option

D; 6/4

A fraction is a representation of a part of an item, by the expressing the proportion consisting of a numerator, divided by a numerator, between which is the divisor bar.

The fraction is; 18/8

Therefore, we get; 18/8 = (2 × 9)/(2 × 4)

The like terms indicates that we get;

(2 × 9)/(2 × 4) = 9/4

Therefore; 18/8 = 9/4

The above fraction is an improper fraction, therefore, we get;

9/4 = (2 × 4 + 1)/4 = 2 1/4

However; 18/8 = (2 × 18)/(2 × 8) = 36/16

Therefore, the numbers in the options A, B, and C are equivalent to the fraction 18/8

The fraction 6/4 is not equivalent to the fraction 18/8

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You would need to make a 94 on the next quiz to have a mean quiz score of 90.

If 90 is the desired mean, then you have to multiply it by the number of quizzes

5 x 90 = 450 is the total in the 5 quizzes.

Now, add the scores of the first four quizzes.

88 + 95 + 93 + 80 = 356

Then, take the amount of the 5 quizzes and subtract it from the amount of the total 4 quizzes.

450 - 356 = 94

Answer:

720 ways

Step-by-step explanation:

Hope this helps :)

The length of segment GF in the triangle is 8 inches

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

The triangle

On the triangle, we have the following ratio

3 : 6 = 4 : GF

So, we have

GF = 6/3 * 4

Evaluate

GF = 8 inches

Hence, the length is 8 inches

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Answer:

C

Step-by-step explanation:

We want the equation of the line that passes through (3, 6) and is perpendicular to:

\(3x-4y=-2\)

First, convert the second equation into slope-intercept form:

\(-4y=-3x-2\Rightarrow \displaystyle y=\frac{3}{4}x+\frac{1}{2}\)

So, we can see that the slope of the line is 3/4.

The slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of the new line is -4/3.

It passes through the point (3, 6).

We can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Substitute:

\(\displaystyle y-(6)=-\frac{4}{3}(x-3)\)

Distribute:

\(\displaystyle y-6=-\frac{4}{3}x+4\)

Therefore:

\(\displaystyle y=-\frac{4}{3}x+10\)

The answer is C.

Answer: \(57^{\circ}\)

Step-by-step explanation:

\(\triangle ACB \cong \triangle DBC\), so by CPCTC, \(x=57^{\circ}\)

True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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The price of the Motorcycle, not including the tax, is $11,500

The price of the motorcycle before the tax, we need to subtract the tax amount from the total price, including the tax. Let's denote the price of the motorcycle before tax as P.

Given:

Tax rate = 12.5%

Tax amount = $1437.50

We know that the tax amount is equal to 12.5% of the price of the motorcycle:

Tax amount = 0.125 * P

We can set up the equation and solve for P:

0.125 * P = $1437.50

To isolate P, divide both sides of the equation by 0.125:

P = $1437.50 / 0.125

Performing the calculation:

P = $11,500

Therefore, the price of the motorcycle, not including the tax, is $11,500.

Tax amount = 0.125 * $11,500 = $1437.50

The tax amount matches the given information, confirming that the price of the motorcycle before tax is indeed $11,500.

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Answer:

2,920

Step-by-step explanation:

did the math, so im 100% sure im correct

The simplest form of the expression 365 x 8 will be 2920.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that there are two numbers 365 and 8 multiplied by each other.

The solution of the expression 365 x 8 will be:-

E = 365 x 8

E =2920

Therefore, the simplest form of the expression 365 x 8 will be 2920.

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Answer:

The answer is he will need 6/10 strips.

Convert 3/5 so that it has a denominator of 10. You know that 5 x 2 is 10, so you must multiply the numerator by 2 as well, giving you 6/10.

It's honestly very simple to work out and understand! Ps. Please pay attention in class it will help you so much in future references.

Hope that helps. x

Answer:

The answer is he will need 6/10 strips.

Convert 3/5 so that it has a denominator of 10. You know that 5 x 2 is 10, so you must multiply the numerator by 2 as well, giving you 6/10.

It's honestly very simple to work out and understand! Ps. Please pay attention in class it will help you so much in future references.

Step-by-step explanation:

The answer is he will need 6/10 strips.

Convert 3/5 so that it has a denominator of 10. You know that 5 x 2 is 10, so you must multiply the numerator by 2 as well, giving you 6/10.

It's honestly very simple to work out and understand! Ps. Please pay attention in class it will help you so much in future references.

Answer:

the ansmwer is * grabs a notebook and doodle the equation* hmm.. it is 7m

happy to help!!!

Step-by-step explanation:

There are three big '1' blocks shaded in dark blue. They have a total sum of 3.

There are 9 small '1/3' blocks shaded in light blue. They also have a total sum of 3.

We can divide the total sum, 3, by the '1/3' blocks to get 9 blocks.

The division problem being shown is 3 / (1/3) = 9.

The division 3 ÷ (1/3) model shows 3 fraction bars. The bars are labeled 1 and each has 3 boxes underneath labeled one-third option first is correct.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

As we can see in the picture:

There is a dark blue box in which there are 3 times 1 so the total sum of the ones:

= 1

There are three sky blue boxes each box contains 1/3 of the sum of the all 1/3 is:

=9(1/3)

= 3

So the fraction becomes:

\(= \frac{3}{\frac{1}{3} }\)  or

= 3 ÷ (1/3)

= 9

Thus, the division 3 ÷ (1/3) model shows 3 fraction bars. The bars are labeled 1 and each has 3 boxes underneath labeled one-third option first is correct.

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Answer:

The last one is the answer

Answer:

25 / 2

Step-by-step explanation:

12.5% = 125 / 10 ( simplify the fraction with 5 )

= 25 / 2

while the derivative of a differentiable function is important in the computation of the convex conjugate, it is not accurate to say that the derivative is the maximizing argument.

The statement you provided is not entirely accurate. While it is true that the derivative of a differentiable function can play a role in computing the convex conjugate, it is not accurate to say that the derivative is the maximizing argument in the computation of the convex conjugate.

Let's clarify the concepts involved:

Convex conjugate: Given a function f, its convex conjugate (also known as the Legendre-Fenchel transform) is denoted as f∗ and is defined as:

f∗(y) = sup(x)(⟨x, y⟩ - f(x))

Here, sup denotes the supremum (least upper bound), ⟨x, y⟩ represents the inner product of x and y, and f(x) is the original function.

Derivative: The derivative of a function f(x) with respect to x, denoted as f'(x) or df/dx, gives you the rate of change of the function at a particular point.

The relationship between the derivative and the convex conjugate can be seen through the Moreau-Rockafellar duality theorem, which states that if f is a proper, convex, and lower-semicontinuous function, then its convex conjugate f∗ is also proper, convex, and lower-semicontinuous.

In this duality relationship, the gradient (or derivative) of f plays a crucial role, but it is not the maximizing argument itself.

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Answer:

D. the exponent can be odd

Step-by-step explanation:

A. (-4)² = 16 ⇒ -4 is even and the product is positive.

B. (-5)² = 25 ⇒ -5 is odd and the product is positive.

C. (-5)⁴ = 625 ⇒ The exponent 4 is even and the product is positive.

D. (-5)⁵ = -3125 ⇒ The exponent 5 is odd and the product is negative.

So, the answer is D.

Hope this helps.

Answer:

The time Jacob spent on the test represented by J = (m + 10) minutes

where m is the number of minutes spent by Mark on the test

Step-by-step explanation:

Here, we want to give an equation which represents the time taken for Jacob to finish his test compared to the time m which Mark spent on the test.

Since Jacob finished 10 minutes before Mark, it means Mark actually took longer on the test.

Now, we are told that Mark spent m minutes on the test, the time spent by Jacob on the test is thus (m + 10) minutes

Let the amount of time spent by Jacob be J minutes. This in relation to the amount of time spent by Mark will be ;

J = (m + 10) minutes

So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.

The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:

4(3x + 5y) = 4(17)

12x + 20y = 68

-3(4x + 4y) = -3(-13)

-12x - 12y = 39

then we can add these two equations:

12x + 20y = 68

-12x - 12y = 39

0 = 29

This is an impossible equation, which means that the system has no solution.

Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

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The radius of the cylindrical shaped soup can is r = 3.3 cm

Given data ,

A company is designing a soup can that is in the shape of a right circular cylinder. The height of the can will be 3 times the radius of the can. The volume of the can will be 350 cubic centimeters

Now , Volume of Cylinder = πr²h

where h = 3r

On simplifying , we get

350 = πr²3r

350 = 3πr³

Divide by 3π on both sides , we get

r³ = 37.13615

Taking cube root on both sides , we get

r = 3.3 cm

Hence , the radius of soup can is r = 3.3 cm

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