Q3 Mathematical foundations of cryptography 15 Points Answer the following questions on the mathematical foundations of cryptography. Q3.1 Primality testing 7 Points Alice wants to test if n 319 is a prime number. Show that n = 319 is a Fermat pseudo-prime in the base a = 144. Enter your answer here Use the Miller-Rabin test to decide whether n = 319 is a strong pseudo-prime in base a = 144. Detail the steps of the algorithm. Enter your answer here Compute (319) where is Euler's totient function. Include details of the computation. Enter your answer here
Answers
n = 319 is not a strong pseudo-prime in base a = 144.Q3.1 Primality testing:
To determine whether n = 319 is a Fermat pseudo-prime in the base a = 144, we need to check if a^(n-1) ≡ 1 (mod n).
Calculating a^(n-1) (mod n):
a = 144
n = 319
a^(n-1) ≡ 144^(319-1) (mod 319)
We can simplify the exponent using Euler's totient function (φ):
φ(n) = φ(319) = (p-1)(q-1) = 318, where p and q are the prime factors of n.
Therefore, we need to calculate 144^318 (mod 319).
Now, let's perform the calculations step by step:
Step 1:
144^2 ≡ 144 * 144 ≡ 20736 ≡ 4 (mod 319)
Step 2:
144^4 ≡ 4^2 ≡ 16 (mod 319)
Step 3:
144^8 ≡ 16^2 ≡ 256 (mod 319)
Step 4:
144^16 ≡ 256^2 ≡ 65536 ≡ 99 (mod 319)
Step 5:
144^32 ≡ 99^2 ≡ 9801 ≡ 173 (mod 319)
Step 6:
144^64 ≡ 173^2 ≡ 29929 ≡ 131 (mod 319)
Step 7:
144^128 ≡ 131^2 ≡ 17161 ≡ 55 (mod 319)
Step 8:
144^256 ≡ 55^2 ≡ 3025 ≡ 255 (mod 319)
Step 9:
144^318 ≡ 144^256 * 144^64 * 144^32 * 144^16 * 144^2 ≡ 255 * 131 * 173 * 99 * 4 ≡ 1 (mod 319)
Since we obtained a congruence of 1 (mod 319), this shows that n = 319 is a Fermat pseudo-prime in the base a = 144.
Now, let's use the Miller-Rabin test to determine whether n = 319 is a strong pseudo-prime in base a = 144.
Miller-Rabin Test:
Step 1: Write n-1 as 2^s * d, where d is an odd number.
319 - 1 = 318 = 2^1 * 159
Step 2: Choose a random base, a = 144.
Step 3: Calculate a^d (mod n).
144^159 ≡ 92 (mod 319)
Step 4: Check if a^d ≡ 1 (mod n) or a^((2^r) * d) ≡ -1 (mod n) for any r from 0 to s-1.
In this case, r = 0.
a^d ≡ 92 ≢ 1 (mod 319)
a^((2^0) * d) ≡ 92 ≢ -1 (mod 319)
Since neither of the conditions is satisfied, we can conclude that n = 319 is not a strong pseudo-prime in base a = 144.
Please note that the Miller-Rabin test is probabilistic, and repeating the test with different bases would further strengthen the conclusion.
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Related Questions
Assignment 4: Evens and Odds
Instructions
Write a program that will ask a user for how many numbers they would like to check. Then, using a for loop, prompt the user for a number, and output if that number is even or odd. Continue doing this as many times as the user indicated. Once the loop ends, output how many even numbers were entered and how many odd numbers were entered.
Hint: For a number to be even, when the number is divided by 2, there should be no remainder - so you will want to use the modulus (%) operator.
Hint: You will need two count variables to keep track of odd and even numbers.
Sample Run 1
How many numbers do you need to check? 5
Enter number: 20
20 is an even number.
Enter number: 33
33 is an odd number.
Enter number: 4
4 is an even number.
Enter number: 77
77 is an odd number.
Enter number: 8
8 is an even number.
You entered 3 even number(s).
You entered 2 odd number(s).
Sample Run 2
How many numbers do you need to check? 3
Enter number: 10
10 is an even number.
Enter number: 3
3 is an odd number.
Enter number: 400
You entered 2 even number(s).
You entered 1 odd number(s).
Sample Run 2
How many numbers do you need to check? 3
Enter number: 10
10 is an even number.
Enter number: 3
3 is an odd number.
Enter number: 400
You entered 2 even number(s).
You entered 1 odd number(s).
Benchmarks
1. Create and initialize two count variables - one for odd and one for even.
2. Prompt the user to answer the question, “How many numbers do you need to check?"
3. Based on the previous input, create a for loop that will run that exact number of times.
1. Prompt the user to “Enter number: “
2.If that number is even, output “[number] is an even number.”
3.Update the even count variable.
4.Or else if the number is odd, output “[number] is an odd number.”
5.Update the odd count variable.
4.Output “You entered [number] even number(s).”
5.Output “You entered [number] odd number(s)."
Answers
Identify the data type of each variable as either int, float, string, list, or boolean.
Answers
Data type of each variable is:
i-int
j-string
k-string
m-boolean
n-list
p-float
q-integer
r- boolean
s-int
t- string
u-string
v- float
w-string
What are data types?Data is categorized into different types by a data type, which informs the compiler or interpreter of the programmer's intended usage of the data. Numerous data types, including integer, real, character or string, and Boolean, are supported by the majority of programming languages. Today, binary data transfer is the most widely used type of data transport for all devices.
A collection of 0s and 1s arranged in a precise order makes up a binary kind of data. Every piece of information is translated to binary form and used as needed. Another set of binary data is connected to this binary form to define the type of data being carried since this binary form does not specify what it is carrying. Variables are specific storage units used in computer programming that hold the data needed to carry out tasks.
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Help!!
So I think that someone is tracking my truck with an apple airtag but I don't know for sure. The only apple product I have is an iPad and I don't know how to check if an airtag is near by!!
Answers
Answer:
Explanation:
In iOS 13 or iPadOS 14 or later go to Settings > account name > Find My > Find My iPhone/iPad, and disable Find My network.
In macOS 10.15 Catalina or later, go to the Apple ID preference pane, select the iCloud link at left, click the Options button to the right of the Find My Mac item, and uncheck Offline Finding or Find My network (the text varies by macOS version).
Data ________ is important because it establishes an organization's rules for sharing, disseminating, acquiring, standardizing, and classifying data.
Answers
Data protection policy is important because it establishes an organization's rules for acquiring, standardizing and disseminating data.
What is Data protection policy?These are policies adopted by organizations that help to ensure data is adequately protected.
When data isn't protected , it could get to the hands of criminals which could use it for different types of cybercrime and also to ensure compliance with data protection laws in the country.
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You work as the IT security administrator for a small corporate network. You recently placed a web server in the DMZ. You need to configure the perimeter firewall on the network security appliance to allow access to the web server from the LAN and the WAN. You would also like to improve security by utilizing the attack security features provided by the firewall.
Answers
As an IT security administrator, you may configure the network security appliance's perimeter firewall to enable access to the web server in the DMZ from both the LAN and the WAN. To do this and boost security by utilizing the firewall's attack security capabilities, take the following steps:
1. Determine the IP address of the web server in the DMZ as well as the precise ports that must be opened (e.g., port 80 for HTTP and port 443 for HTTPS).
2. Log in to the firewall's administration interface and browse the firewall rules or policies setup area.
3. Set a new firewall rule or policy that allows inbound LAN and WAN traffic to the web server's IP address and specified ports.
4. Activate the attack security elements of the firewall, such as an Intrusion Detection System (IDS) or Intrusion Prevention System (IPS), to monitor and defend the web server from potential attacks.
5. Set up the IDS/IPS rules or signatures to identify and prevent typical web server threats including SQL injection, cross-site scripting (XSS), and Distributed Denial of Service (DDoS).
6. Make the modifications and test the web server's connectivity from both the LAN and the WAN to confirm it is accessible and functional.
By following these steps, you can configure the perimeter firewall to enable access to the web server in the DMZ from the LAN and WAN while simultaneously boosting security by utilizing the firewall's attack security capabilities.
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How many of the colonists of Jamestown died before they made it to shore, due to the difficult voyage?
half
almost all
one third
nonE
Answers
2. What changes, if any, could Lisa make to her income?
Ramsey classroom
Answers
Answer: what changed if any could lisa make to her income
Explanation:
What is the name of the compound, c9 h18?
a. 1,3 diethylcyclopentane
b. 3,1 diethylcyclopentane
c. 1,3 dimethylcyclopentane
d. 3,1 dimethylcyclopentane
Answers
The correct name of the compound c9 h18 is: b) 1,3 diethylcyclopentane.
This name is derived from the structure of the molecule, which consists of a cyclopentane ring with two ethyl groups attached to the 1 and 3 positions. The prefix "di-" indicates that there are two ethyl groups, while the numbers 1 and 3 specify their locations on the ring. Naming organic compounds is an important aspect of organic chemistry, as it helps chemists to communicate effectively about the structure and properties of different molecules.
The rules for naming organic compounds are based on a set of guidelines developed by the International Union of Pure and Applied Chemistry (IUPAC), which help to ensure that names are clear, concise, and unambiguous. By following these guidelines, chemists can accurately name and identify a wide range of organic compounds. So the answer is: b) 1,3 diethylcyclopentane.
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Activity 15: enhance an ajax application so it uses an expanded json file the goal of this activity is to modify the json application so it uses an expanded json file. The resulting page should look like this:
Answers
Only supplied the Pham-Activity13.js file. The remaining HTML, JSON, and CSS files were not modified by me. The same folder or directory must include all of your JSON, HTML, and CSS files.
DynamoDB is a fully-managed NoSQL server platform that enables the creation of server tables with unlimited data storage and recovery capabilities. An AWS server platform called DynamoDB encourages software designs and key-priced web resources. DynamoDB can support peaks of over 20 million queries per second and can handle more than 10 billion requests per day.
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what do you think of the FNAF plus trailer? if you have seen it tell me who looks better
Answers
Answer:
Explanation:
bonnie looks the best, freddy looks better, and chica looks awsome, in my opinion this looks better than the original fnaf
Answer:
honestly Bonnie looks best
Explanation:
What is one difference between low- and high-level programming languages? (5 points)
O a
Ob
Low-level programming languages are challenging for humans to read, while high-level programming languages are easier.
Low-level programming languages are more human-friendly, while high-level programming languages are more challenging for
humans to understand.
Ос
Low-level programming languages require interpreters and compilers, while high-level programming languages do not.
Od
Low-level programming languages use program code to communicate with computers, while high-level programming languages
use machine code.
Answers
Answer: Low-level programming languages are computer code at its most basic. They are difficult or sometimes impossible for humans to read, while high-level languages are designed to be easy for humans to understand. I believe the answer is A.
Answer:
Low-level programming languages require interpreters and compilers, while high-level programming languages do not.
Explanation: I AM SURE IT IS CORRECT 100% CORRECT
Below is the initial setup for a set of processes and resources. The initial setup is safe.
Suppose P2 wants an additional R1, is it still safe? Show your work and explain your result.
R1 R2 R3 R1 R2 R3
P1 3 2 3 P1 2 1 2
P2 2 3 2 P2 0 1 1
P3 2 1 2 P3 1 1 0
Claim matrix Allocation matrix
R1 R2 R3 R1 R2 R3
4 4 4 1 1 1
Answers
Yes, it would still be safe if P2 requests an additional R1.
Explanation:
The initial state of the system:
Available resources (total resources - allocated resources): (4-1, 4-1, 4-1) = (3, 3, 3)
If P2 requests an additional R1, the new state would be:
Allocation matrix:
P1 2 1 2
P2 1 1 1
P3 1 1 0
Available resources: (3-1, 3-1, 3-1) = (2, 2, 2)
Now, let's check if the system is still safe after the request:
1. P3's claim can be fulfilled as the available resources are greater than or equal to its needs (2, 1, 2) >= (1, 1, 0).
2. After P3 finishes and releases its resources, the available resources become (3, 3, 2).
3. P1's claim can now be fulfilled as the available resources are greater than or equal to its needs (3, 3, 2) >= (3, 2, 3).
4. After P1 finishes and releases its resources, the available resources become (5, 5, 5).
5. Finally, P2's claim can be fulfilled as the available resources are greater than or equal to its needs (5, 5, 5) >= (2, 3, 2).
Since all processes can eventually finish executing without causing any deadlocks, the system remains in a safe state even after P2 requests an additional R1.
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Which of the following is not an option for sorting data sets on the Data tab? Choose the correct answer
a. last modified
b. owner
c. name
d. quality
Answers
The option that is not available for sorting data sets on the Data tab is "quality".
On the Data tab in various applications, you can sort data sets by different criteria such as last modified, owner, and name. For example, in Microsoft Excel, you can sort data by clicking on the "Sort" button and selecting the column by which you want to sort the data. Sorting data can help you analyze and manage large data sets more efficiently. However, "quality" is not an option for sorting data in most applications and is not a commonly used criterion for data management.
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Student leadership activities can:
Answers
Student leadership activities can provide numerous benefits to students.
What are the benefits to students?First, they can help develop important skills such as communication, teamwork, problem-solving, and decision-making.
Additionally, they can foster a sense of responsibility, confidence, and self-esteem in students. Through these activities, students can also learn how to manage their time effectively and prioritize tasks.
Furthermore, leadership activities can allow students to connect with peers who share similar interests and goals. Finally, these activities can help students build a sense of community and create a positive impact within their school or local community.
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What are the benefits of a student leadership to students?
Start your answer with, "Student leadership activities can..."
The science of how an object reacts to its motion through air is called
(12 letters)
Answers
Answer:
The science of how an object reacts to its motion through air is called aerodynamics
Explanation:
Aerodynamics is the science 〔ç) of studying, designing, and manufacturing vehicles such that they can operate in atmospheric conditions. Aerodynamic efficiency has many aspects respect to generating flight including maneuverability and make use of minimum amount of fuel needed for lift. Aerodynamics also deal with the flow around objects or what a rotational fluid must do as it flows along a curved surface or moves past a blunt body that creates turbulence.
The science of how an object reacts to its motion through air is called aerodynamics.
What is motion?Motion is the shift in such an item's location with regard to time. Translocation, the act or process of changing or shifting locations or positions. It is described as a movement that occurs repeatedly at set intervals of time.
The examination of forces and how they cause anything to move through the air is known as aerodynamics. We can estimate the strengths of lift, whose enable an aircraft to defy logic, and drag, that is the opposition an aircraft "feels" as it traverses the air, by observing the movements of the air over an item. By directing air in this method, a component referred as drag attributable to lift is created, which slows the forward speed of the aircraft.
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BRAINLIEST!!!!!!
I nEeD your HeLp
Answers
Answer:
\(option \:1 . \: is \: cd \\ option \:2. \: is \: hard \: disk \: drive \\ primary \: memory \: is \: \: a \: memory \: dirctly \\ \: accessed \: by \: the \: cmp \\ why \: secondary \: is \: not \: directly \: accessed\)
\(\boxed{1.)}\;Your\;answer\;is\;indeed\;cd.\\\\\\\boxed{1's\;explanation...\;>See\;Below<}\\\\\\An\;SSS\;device\;is\;a\;Solid-state \;storage \;device.\;It\;collects\;storage.\;Therefore,\;your\\\;answer\;is\;B,\;cd.\)
\(\boxed{-----------------------------------}\)
\(\boxed{2.)}\;Your \;answer\; is\; HDD.\\\\\\\boxed{2's \;Explanation...}\\\\\\A\;HDD\;is\;a\;drive\;located\;inside\;of\;a\;computer.\;Therefore,\;your\;answer\;is\;B.\\\\\\\boxed{------------------------------------}\\\\\\\boxed{Hope\;it\;helps!}\\\\\\\huge\boxed{Thanks,razorple.}\)
True/false? in the palindromes program, the inner loop evaluates one string to see if it is a palindrome.
Answers
False. The inner loop checks the characters in a given string to determine if it is a palindrome.
In the palindrome program, the inner loop evaluates whether the given string is a palindrome or not by comparing the first and last characters of the string and moving towards the middle of the string until all characters have been compared. The inner loop does not evaluate one string to see if it is a palindrome, but rather checks the given string to determine if it is a palindrome or not.
In a palindrome program, the algorithm checks whether a given string is a palindrome or not by comparing the first and last characters of the string. If the characters match, the algorithm continues to check the next pair of characters towards the middle of the string. If all pairs of characters match, the string is a palindrome. Otherwise, it is not a palindrome. The algorithm may use nested loops to compare each pair of characters in the string, with the outer loop iterating over the entire length of the string and the inner loop iterating from the start and end of the string simultaneously.
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Which three statements describe characteristics of permanent memory in a
computer?
A. It loses data when the computer is powered off.
B. It holds a large amount of data.
C. It is slower to access than RAM.
D. It is inexpensive.
Answers
Answer:
it's used for further cahce
b
TRUE / FALSE.
views can include website data from before the view was created
Answers
Views can include website data from before the view was created is a FALSE statement.
What is views?When you create a view in a database, it will not show any data that was gathered before the view was made. Views are ways to see information that has been organized and created from the tables or other views in a database. When you make a view, it shows you the information that's currently in the tables it's based on.
Views are like questions that don't have answers until you ask them. They don't store any information by themselves, but instead, they search for answers when you open them.
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changing the layout of a document or the text is called....
Answers
The Answer is:
Formatting.
what is the 'key exchange' problem in modern information security? encryption keys are too long. there are too many encryption keys to keep track of. two parties need to privately share the secret encryption key before communicating. the encryption key is too complicated to calculate.
Answers
The 'key exchange' problem in modern information security refers to the challenge faced by two parties who need to privately share a secret encryption key before communicating securely. Encryption is a method of converting data into an unreadable format, so that only authorized parties with the correct decryption key can access the information.
Key exchange is crucial for ensuring secure communication because it allows the involved parties to establish a shared secret key that can be used for encryption and decryption. However, exchanging keys securely can be a challenge, especially when communication is happening over an unsecured channel where eavesdroppers can intercept the messages.
One common solution to the key exchange problem is using asymmetric encryption algorithms, such as RSA or Elliptic Curve Cryptography (ECC), which involve the use of public and private key pairs. In this system, each party has a public key that can be shared openly and a private key that is kept secret. The sender encrypts the message with the recipient's public key, and the recipient decrypts it with their private key.
While asymmetric encryption provides a solution to the key exchange problem, it is generally slower than symmetric encryption methods, which use a single shared key for both encryption and decryption. To achieve the best of both worlds, many secure communication protocols combine both techniques, using asymmetric encryption to securely exchange a symmetric key that is then used for encrypting the actual data.
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What is an example of an action that takes advantage of cloud computing?
Answers
The cloud gives you total access to and control over your data. Choosing which users have access to what data and at what level is a simple process.
What is the importance of cloud computing?The ability to scale, preserve flexibility, and concentrate resources on business operations rather than managing complicated IT infrastructure are the key benefits of cloud computing for businesses.
Therefore, working with a cloud partner is one of the greatest methods to maximize cloud computing for your company.
Resources are instantly accessible with cloud computing, allowing businesses to react to new market developments much more quickly.
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the problems with scale in the profitability index can be corrected by using
Answers
The problems with scale in the profitability index can be corrected by using discounted cash flow (DCF).
What is the profitability index?
The profitability index (PI) is a capital budgeting technique that compares the present value of cash inflows to the initial investment required to make them. It can be used to assess various investment opportunities that may have differing initial investments.
The profitability index is calculated by dividing the present value of future cash flows by the initial investment. In mathematical terms,
PI = Present Value of Future Cash Flows / Initial Investment
A profitability index greater than one means that the project is worth pursuing, while a profitability index less than one means that the project is not profitable.
How can the scale problem in the profitability index be corrected?
There is a scale problem in the profitability index that must be addressed. When calculating the profitability index, the scale problem arises when comparing the profitability index of two projects with different scales.
For example, suppose you're comparing the profitability index of a $100,000 project with a $500,000 project. The project with a larger scale would have a greater profitability index because it would generate more cash flows than the smaller project, even if the smaller project has a higher return on investment (ROI).
Discounted cash flow (DCF) is used to correct the scale problem in the profitability index. In capital budgeting, discounted cash flow (DCF) is a valuation method that involves forecasting the future cash flows of a project and discounting them back to their present value using a discount rate. The present value of future cash flows is calculated as follows:
PV = FV / (1 + r)n
Where:
PV = Present ValueFV = Future Valuer = Discount RateN = Number of YearsThat's how the scale problem in the profitability index can be corrected by using discounted cash flow (DCF).
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Part 2: Code the Program Use the following guidelines to code your program. 1. Use the Python IDLE to write your program. 2. Using comments, type a heading that includes your name, today’s date, and a short description. 3. Set up your def main(): statement. (Don’t forget the parentheses and colon.) 4. Use at least two variables and two print statement to display your message to the screen. 5. Conclude the program with the main() statement. 6. Follow the Python style conventions regarding indentation in your program. 7. Run your program to ensure it is working properly. Fix any errors you may observe. Example of expected output: The output below is an example of a “Favorite TV Show” message. Your specific results will vary depending on the choices you make about your message. Output My favorite TV show is MythBusters. I like it because I learn a lot and they do crazy experiments. When you've completed writing your program code, save your work by selecting 'Save' in the Python IDLE. When you submit your assignment, you will attach this Python file separately.
Answers
# Replace this with your name, date, and a short description
def main():
x = "My favorite book is python for dummies."
y = "I like it because it introduces new python topics."
print(x)
print(y)
if __name__ == "__main__":
main()
what type of events do the following components generate?
Answers
The type of events for components generate is:
1. Button: The button component generates events such as onClick and onDoubleClick.
2. TextField: The TextField component generates events such as onKeyPress and onKeyUp.
3. CheckBox: The CheckBox component generates events such as onChange and onCheckedChanged.
4. RadioButton: The RadioButton component generates events such as onCheckedChanged and onClick.
5. ComboBox: The ComboBox component generates events such as onSelectedIndexChanged and onDropDownOpened.
The components you listed will generate different types of events. For example, a button component may generate a 'click' event, while an input component may generate a 'change' event.
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Troy wants to list his technical skills on his résumé. What formatting would be best for that?
A)Block Format
B)Chronological Order
C)Bullet Form
D)Bold Text
Answers
is a solar energy technology that uses unique properties of semiconductors to directly convert solar radiation into electricity.
Answers
The given statement is the definition of a solar energy technology that uses unique properties of semiconductors to directly convert solar radiation into electricity. The technology referred to in the statement is solar cell technology or photovoltaic technology.
The conversion of solar radiation into electrical energy takes place in a solar cell or photovoltaic cell, which is a device that generates electrical energy directly from sunlight. Solar cells use a photovoltaic effect to convert light energy into electrical energy. Photovoltaic cells consist of semiconductor materials that absorb light energy and create a current of electrons that can be used as electricity.
The solar cell consists of a thin layer of silicon, which is a semiconductor material, and when sunlight falls on it, the energy from the photons is absorbed and the energy from these photons releases electrons, which then create an electric current. This current is then used to power electronic devices or store it in batteries. It is a long answer because it explains the entire process of the conversion of solar radiation into electricity using solar cell technology.
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when creating a sql query, which join clause returns all matching records in two or more database tables?
Answers
Answer:
Inner Join
Explanation:
Clause in SQL Server creates a new table (not physical) by combining rows that have matching values in two or more tables. This join is based on a logical relationship (or a common field) between the tables and is used to retrieve data that appears in both tables.
Choose the term that makes the sentence true.
When you enlarge a raster image, the painting program uses ___
to add the needed pixels.
Answers
When you enlarge a raster image, the painting program uses interpolation to add the needed pixels.
What is Interpolation?Interpolation is a technique used by painting programs to add pixels to an image when it is enlarged, by estimating the color values of the new pixels based on the color values of existing pixels.
Hence, it can be seen that when making an image edit and you want to make an enlargement of a raster image, there is the use of interpolation to add the needed pixelation.
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Which one is called the Information Super Highway? a. E-mail b. Mobile phone c. Internet d. Land phone
class 6
Answers
Answer:
c
Explanation:
Explanation: