Mike bought a lunch that cost $9.00. He also paid 5% for sales tax.
How much change did he receive from $20.00?

a) Alice cannot prove that the message was sent by Bob. b) 530 mod 29 = 8. c) Factoring an RSA modulus n = pq, where p and q are prime numbers, is a computationally intensive task that is considered difficult in practice. It is not feasible to factorize large prime numbers without using advanced factorization algorithms. d) The feedback polynomial is \(f(x) = x^2 + x + 1,\) and the minimum size LFSR that produces the output sequence (1001) has 4 stages. e) The total keyspace size is given by the product of the number of possible values for a and b, which is 12 * 26 = 312.

(a) In the given protocol, Alice is receiving a message y from Bob, which is encrypted using Alice's public key XA. To proceed on her side of the protocol, Alice would follow these steps:

Alice receives the encrypted message y from Bob.

Alice uses her private key xa to decrypt the message y. She applies the decryption algorithm D, which corresponds to the encryption algorithm E used by Bob.

After decrypting the message, Alice obtains M = D(y) = D(E(h(M))).

Alice can then compute the hash of the decrypted message, h(M), using the same hash function that was agreed upon, such as SHA-1.

Alice compares the computed hash value with the hash value received in the encrypted message. If they match, it indicates that the message has not been tampered with during transmission, ensuring data integrity.

Additionally, since Alice is the only one with access to her private key, she is the only party capable of decrypting the message correctly. This provides confidentiality, as only Alice can access the original content of the message.

Non-repudiation is not provided in this protocol because it does not involve the use of digital signatures or other mechanisms to guarantee the identity of the sender. Therefore, Alice cannot prove that the message was sent by Bob.

(b) To compute 530 mod 29 without using a calculator, we can repeatedly subtract multiples of 29 from 530 until we obtain a result less than 29. The remainder will be the result of the modulus operation.

530 - 29 * 18 = 530 - 522 = 8

Therefore, 530 mod 29 = 8.

(c) Factoring an RSA modulus n = pq, where p and q are prime numbers, is a computationally intensive task that is considered difficult in practice. It is not feasible to factorize large prime numbers without using advanced factorization algorithms.

(d) To construct the minimum size LFSR (Linear Feedback Shift Register) that produces an output (1001), we need to determine the feedback polynomial and the number of stages.

Based on the output sequence (1001), we can set up the following equations:

\(1 = a_0 * 2^3 + a_1 * 2^2 + a_2 * 2^1 + a_3 * 2^0\\0 = a_0 * 2^2 + a_1 * 2^1 + a_2 * 2^0 + a_3 * 2^3\\0 = a_0 * 2^1 + a_1 * 2^0 + a_2 * 2^3 + a_3 * 2^2\\1 = a_0 * 2^0 + a_1 * 2^3 + a_2 * 2^2 + a_3 * 2^1\)

Simplifying these equations, we get:

\(1 = 8a_0 + 4a_1 + 2a_2 + a_3\\0 = 4a_0 + 2a_1 + a_2 + 8a_3\\0 = 2a_0 + a_1 + 8a_2 + 4a_3\\1 = a_0 + 8a_1 + 4a_2 + 2a_3\)

Solving these equations, we find the values:

\(a_0 = 0, a_1 = 1, a_2 = 1, a3 = 0\)

Therefore, the feedback polynomial is \(f(x) = x^2 + x + 1,\) and the minimum size LFSR that produces the output sequence (1001) has 4 stages.

(e) For the affine cipher C = aM + b mod 26, where M is a letter of the English alphabet represented as a number between 0 and 25, the keyspace size can be calculated by finding the number of different combinations of values for a and b.

The value of a must be coprime (relatively prime) to 26, which means gcd(a, 26) = 1. Since a is coprime to 26, there are 12 possible values for a (1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25).

The value of b can take any value between 0 and 25, so there are 26 possible values for b.

Therefore, the total keyspace size is given by the product of the number of possible values for a and b, which is 12 * 26 = 312.

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Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

Answer:

cod 3 my dude

Step-by-step explanation:

7. Since they are similar triangles we have:

\( \frac{10}{8} = \frac{x}{12} \\ \\ x = 15\)

So DF is 15

8. They are also similar. So:

\( \frac{14}{7} = \frac{x}{5} \\ x = 10\)

So PR is 10

Answer:

0

I hope its zero.........

Answer:

-1.5

Step-by-step explanation:

-12/6+2

-12/8

-1.5

Answer:

Step-by-step explanation:

This is a trapezium.

The formula od an area of a trapezium:

A = 1/2(a + b) · h

We have:

a = 10, b = 6, h = 8

substitute:

A = 1/2 · (10 + 6) · 8 = 1/2 · 16 · 8 = 8 · 8 = 64

Answer:

A = 64 sq. un

Step-by-step explanation:

6 * 8 + (4 * 8)/2 =

48 + 4 * 4 =

48 + 16 =

64

It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.

A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.

Now, consider an example;

When you wish to build a perpendicular line on a line segment, like line AB, you do the following;

A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.

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Solution:

A negatively skewed distribution is one in which more data values are plotted on the right side of the graph.

In other words, the the tail of the distribution is longer on the left side, and the mean is lower than the median and mode.

Thus, from the options below:

The correct option is C since

Answer:

500 meters above sea level

Step-by-step explanation:

600-100 = 500

The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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Answer: 62.8 cubic feet

Step-by-step explanation:

R is radius

H is height

R=2ft

H=5ft

V=(3.14)(2)^2(5)

V=62.8 cubic feet

Answer:

900%

Step-by-step explanation:

The number of problems that the math team successfully resolved at this year's competition increased from last year by a factor of ten.

Let number of problems resolved by math team last year be x .

So  number of problems resolved by math team this year is 10x.

Percentage increase =  ( 10x - x / x) 100

                                   =  900%      

Answer:

15) 1/3

18) 1/2

21) 25/26

Step-by-step explanation:

15) 2/6=1/3

18) 3/6=1/2

21) 25/26

Answer:

4

Step-by-step explanation:

because The square root of 16 is 4, which is a rational number.

Answer:

4

Step-by-step explanation:

The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Answer:

well how many sides are there in one? then multiply it by the number of the one side to how many sides

Step-by-step explanation:

Answer:

30 inches

Step-by-step explanation:

Equilateral means all the sides are the same

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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(a) The probability that a randomly selected voter voted for Candidate 4 is 0.053.

(b) To find the probability that a randomly selected voter voted for either Candidate 1 or Candidate 5, we need to sum the individual probabilities of voting for each candidate.

Candidate 1: 0.102

Candidate 5: 0.084

Adding these probabilities gives:

0.102 + 0.084 = 0.186

Therefore, the probability that a randomly selected voter voted for either Candidate 1 or Candidate 5 is 0.186.

The probability of a randomly selected voter voting for Candidate 4 is given in the problem as 0.053. This means that out of all the voters, approximately 5.3% voted for Candidate 4.

To find the probability of a randomly selected voter voting for either Candidate 1 or Candidate 5, we sum the individual probabilities of each candidate. The probability of voting for Candidate 1 is given as 0.102, which means approximately 10.2% of voters chose Candidate 1. Similarly, the probability of voting for Candidate 5 is given as 0.084, representing approximately 8.4% of voters. Adding these probabilities together gives the combined probability of 0.186 or 18.6%.

By understanding the given frequency distribution and the probabilities associated with each candidate, we can calculate the probabilities of different voting outcomes. These probabilities provide insight into the voting patterns of the population and can help analyze and understand the election results.

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Answer:

4/3 x - 7/3

Step-by-step explanation:

Hope it helps!

Answer:

Hope this helps

Step-by-step explanation:

a) x^2 + 3x = x(x+3)

b) 2x^2 - 8x = 2x(x - 4)

c) 6x + 9x^3 = 3x(2 + 3x^2)

d) 12x^3 - 4x^2 = 4x^2(3x - 1)

Answer:

12 sides.

Step-by-step explanation:

the sum of every pair of interior and exterior angle is always 180 degrees.

x = exterior angle.

the interior angle is then x+120.

so then exterior and interior angle together must be 180.

x + x + 120 = 180

2x + 120 = 180

2x = 60

x = 30 degrees

how many sides ?

the sum of all exterior angles must be 360 degrees.

all exterior angles are the same (because all the interior angles must be the same due to "regular polygon").

so, how many times does 30 fit into 360 ?

360/30 = 36/3 = 12

it has 12 corners and also sides.

Answer:

Domain: real numbers greater than or equal to -3

Range: equal to -4, 2 and 3

Step-by-step explanation:

Answer:

Domain:

✔ real numbers greater than or equal to –3

Range:

✔ equal to –4, 2, and 3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given the 2 equations

x + y = 3 → (1)

2x - y = 6 → (2)

Adding the 2 equations term by term eliminates the y- term, that is

3x = 9 ( divide both sides by 3 )

x = 3

The inequality that models the situation is:

x + 2y ≥ 12

We know that a Mecnahinc named Zeke plans to work a maximum of 12 hours (12 hours is an allowed value) tomorrow.

And we know that he works doing tune-ups and oil changes.

Let's define the variables:

We know that It takes 1 hour to perform a tune-up and 2 hours to perform an oil change.

Then the total number of hours worked by Zeke is given by the expression:

x*1 + y*2

And that must be equal to or smaller than 12, so we will get the inequality:

x + 2y ≥ 12

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To find which fractions are equal to each other, we must simplify or multiply to both denominator and numerator:

          \(\frac{2}{6} =\frac{1*2}{3*2} =\frac{1}{3}*\frac{2}{2}=\frac{1}{3}*1= \frac{1}{3} \\\\\frac{8}{1}=8\\ \\\frac{2}{4} =\frac{1*2}{2*2} =\frac{1}{2}*\frac{2}{2} =\frac{1}{2} *1= \frac{1}{2} =\frac{1}{2}*1 =\frac{1}{2}*\frac{4}{4} =\frac{1*4}{2*4}=\frac{4}{8} \\\\\frac{2}{8} =\frac{1*2}{4*2}=\frac{1}{4}*\frac{2}{2} =\frac{1}{4} *1 =\frac{1}{4} \\\\\frac{4}{4} =1\)

Hope that helps!

Answer:

2/6 = 1/3

8/1 = 8

2/4 = 4/8

2/8 = 1/4

4/4 = 1

Step-by-step explanation:

2/2 = 1 and 6/2 = 3 so that would make the equivalent fraction 1/3

for 8/1 it is the same as just 8

2*2 = 4 and 4*2 = 8 so that would make the equivalent fraction 4/8

and 2/8 is 1/4

and 4/4 is just 1  

PLEASE RATE!! I hope this helps!!

If you have any questions let me know

Given Information:

Principle amount = P = $9,129

Interest rate = r = 4% = 0.05

Period in years = t = 5

Required Information:

Balance in 5 years = ?

Answer:

Balance in 5 years = $11,651.17

Step-by-step explanation:

Using the formula given in the question,

\(B = P(1 + r )^{t}\)

Where B is the final amount, P is the initial amount, r is the interest rate and t is the number of years

\(B = P(1 + r )^{t}\\\\B = 9,129(1 + 0.05)^{5}\\\\B = 11,651.17\)

Therefore, Zack will have $11,651.17 in 5 years by investing $9,129 in a savings account at 5% annual interest.

Answer:

2 < x < 12

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the interval

difference of 2 sides < x < sum of 2 sides , that is

7 - 5 < x < 7 + 5

2 < x < 12

third side could be 3, 4, 5, 6, 7, 8, 9, 10, 11

Answer:

23/6400 ml or 0.003594 ml

Step-by-step explanation:

Steps to determining the answer

Soy sauce in one bottle = total soy sauce in one bottle / total number of bottles

4/800 ÷ 32 =

4/800 x 1/32 = 1 / 6400

soy sauce in 23 bottles

1/6400 x 23 = 23/6400 ml or 0.003594 ml

Answer:

2-5p

1-p

Step-by-step explanation:

put the whole equation into one one fraction. then you simplify. first do the bottom

1. first do 3-2=1

2. then the variable numbers i forget the fancy term

p-2p = -p

3. add together 1 - p

then do the top

its the same thing so then you put the new fraction together

4. 2-5p

1-p

I forget if there's anymore steps but I hope this helps