Notes, summaries, assignments, exams, and problems for Other courses

Residual claim: shareholders get only what is left-over after everyone has been paid. Discount rate: the rate at which present and future values are traded off. Future value of cash flow: C x (1+ r)^n. R= (FV/PV)^1/n - 1. Present value= C/(1+ r)^n. Compound interest: exponential growth in wealth, initial amount of money + the interest that has been added the previous years. Perpetuity, Growing Perpetuity, Annuity: multiple payments overtime, same amount, regular interest. NPV: the difference between and investment's value and its cost. Positive NPV=investment yes; NPV=0 project earns the required rate. . IRR measures the average return on the investment: accept project if IRR is greater than the discount rate(minimum return you want). Payback

Rajputs: Origins, Governance, and Legacy

Theories of Rajput Origin

1. Foreign Origin Theory: This theory suggests that the Rajputs were of foreign origin, specifically from Central Asia or Scythia.
2. Indigenous Origin Theory: This theory proposes that the Rajputs were of indigenous origin, emerging from the local population of India.
3. Mixed Origin Theory: This theory suggests that the Rajputs were of mixed origin, with both foreign and indigenous elements.

Rajput Administration System

1. Monarchical System: The Rajputs followed a monarchical system, with the king holding supreme power.
2. Feudal System: The Rajputs also followed a feudal system, with the king granting land and titles to his nobles and vassals.
3. Council of Ministers: The king was advised by a council

Preparing for Your Upcoming Staff Meeting

Dear Team,

I hope this email finds you well. This message provides important instructions to help you prepare for our staff meeting, scheduled for [date and time].

Key Preparation Steps

• Review the Agenda: Please review the attached meeting agenda carefully. Note any items requiring your input or preparation for discussion.
• Prepare Updates & Reports: Ensure all relevant updates or reports are ready to share during the meeting.
• Finalize Presentations: If you are responsible for presenting, finalize your slides and upload them to the shared drive by [deadline]. Please ensure your content is clear, concise, and focuses on key points.
• Gather Supporting Documents: Bring any necessary documents, such as reports

Letter to a Friend About a Trip

From: [Your Name]

To: [Friend’s Name]

Subject: My Trip to Canada

Hi [Friend’s Name],

How are you? I have amazing news! I’m going to Canada for three weeks to study English!

I’ll be arriving on January 15th and staying at a student residence close to the school. My course has 20 lessons a week, and I’ll take morning classes. In the afternoons, I plan to join some activities, like city tours and maybe trying fun things like ice skating. I also want to explore and enjoy Canadian food. It’s going to be so exciting!

I hope you’re doing well. Do you think I should pack anything special for the trip? Let me know!

Take care,

[Your Name]

Family Vacation in La Serena, Chile

I went on vacation in February with my family... Continue reading "Canada Trip & Family Vacation: Travel Stories & Johnny Depp Bio" »

Les Misérables: Key Plot Points and Character Arcs

Chapter 1: Release and the Bishop's Kindness

Jean Valjean is released from prison after serving 19 years for stealing bread. Marked as a dangerous ex-convict, he is rejected everywhere until he finds shelter at the bishop’s house, where he is treated with kindness and taught the value of redemption.

Chapter 2: The Act of Mercy and Javert's Pursuit

Valjean steals the bishop’s silver, but when caught, the bishop defends him, claiming it was a gift. This profound act of mercy sets Valjean on a path toward true redemption. Meanwhile, Inspector Javert begins searching for the escaped convict.

Chapter 3: Fantine and the Thénardiers

Fantine, a young mother, leaves her daughter Cosette with the cruel... Continue reading "The Epic Story of Les Misérables: Redemption and Revolution" »

Essential Algorithms and Data Structures

Longest Increasing Subsequence (LIS):

• Subproblem: dp[i] = length of LIS ending at index i
• Recursion: dp[i] = max(dp[j] + 1 for j < i and arr[j] < arr[i])
• Base case: dp[i] = 1 (every element is a subsequence of length 1)
• Time Complexity: O(n^2), O(n log n) with binary search optimization.

Longest Alternating Subsequence (LAS):

• Subproblem: dp[i][0] (increasing), dp[i][1] (decreasing)
• Recursion: dp[i][0] = max(dp[j][1] + 1 for j < i and arr[j] < arr[i]), dp[i][1] = max(dp[j][0] + 1 for j < i and arr[j] > arr[i])
• Base case: dp[0][0] = 1, dp[0][1] = 1
• Time Complexity: O(n^2)

0/1 Knapsack Problem:

• Subproblem: dp[i][w] = maximum value for the first i items and weight limit w
• Recursion: dp[i][w] = max(

Arithmetic Progressions (AP)

Sum of terms = n[(1st term + last term)]/2

Geometric Progressions (GP)

Sum of terms = [1st term(1 - quotientⁿ)/(1 - quotient)] (Swap positions of 1 & quotient if quotient > 1)

Logarithms

• log_a(x/y) = log_ax - log_ay
• log_axⁿ = nlog_ax
• log_ab = (log_cb/log_ca)

Permutations

For a set of n objects: The total number of permutations is n!

For arranging 'r' objects from a set of 'n' objects: The number of permutations is nPr = n! / (n-r)!. (e.g., ways to arrange 3 objects from a set of 5 is 5 * 4 * 3, since there are 5 possibilities for the first object, followed by 4, then 3.)

Combinations

For selecting 'r' objects from a set of 'n' objects: The number of combinations is nCr = n! / (r! * (n-r)!). (Divide by r! since there are r! ways

Key Concepts in Language Acquisition and Child Development

Questions & Answers

1. According to Chomsky, language is... A (We possess an innate capacity for language.)
2. Which of the following statements is true? C (Learners need a supportive environment.)
3. Behaviorism relies on... A (Skinner's theory of operant conditioning.)
4. According to Krashen... C (Comprehensible input is important.)
5. According to constructivism... A (Children of a similar age think similarly.)
6. The term "concentration span" refers to... A (The time and capacity for focused attention.)
7. Comprehensible input means... B (The teacher uses facial expressions and gestures.)
8. Language acquisition does not require... D (All of the above.)
9. What is the zone of proximal development? A (The zone

Present Simple Affirmative Sentences

1. They work at the same company.
2. I practice yoga to relieve stress.
3. I drink coffee every morning.
4. She watches TV in the evenings.
5. They play soccer on weekends.
6. He reads a book before going to bed.
7. She listens to music while working.
8. They take the bus to work every day.
9. He brushes his teeth twice a day.
10. He cooks dinner for his family every night.

Present Simple Interrogative Sentences

1. Do you like coffee?
2. What do you usually eat for breakfast?
3. Where do you live?
4. How often do you exercise?
5. Do you have any pets?
6. What time do you usually wake up?
7. What is your favorite TV show?
8. Do you enjoy reading books?
9. How do you usually get to work or school?
10. What do you like to do in your free time?

Present Continuous Affirmative Sentences

1. I am currently