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Design an Optimal Binary Search Tree for 7 nodes with their probability is given respectively as


(2,8,7,6,4,3,9). Also find the leaf nodes, root, internal nodes, external nodes, height of OBST, Depth


of the last leaf, Level of the second last leaf node

How large a force parallel to a 300 incline is needed to give a 5.0 kg an acceleration 0.20 m/s2 up the incline a) if friction is negligible? b) if the coefficient is 0.30?


Determine the complexity of the expression



(I) 5n² + 3nlogn + 2n + 5 that log n <= n for n >= 1



(II) 5n⁴ + 3n³ + 2n² + 4n + 1

Draw the chemical structure for the 5-isopropyl-2-sec-butyl-cyclonon-1-ene. 


  1. Write algorithms/pseudocode on:
  • Linear Search
  • Binary Search
  • Bubble Sort
  • Quick Sort

2.After the algorithm/pseudocode ends, provide the time complexity for each of them



The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 52kg and 66kg?  


How did we get our answer for this problem above? 



Suppose that you have a computer with a memory unit of 24 bits per word. In this computer, the assembly program’s instruction set consists of 198 different operations. All instructions have an operation code part (opcode) and an address part (allowing for only one address). Each instruction is stored in one word of memory. a. How many bits are needed for the opcode? b. How many bits are left for the address part of the instruction? c. How many additional instructions could be added to this instruction set without exceeding the assigned number of bits? Discuss and show your calculations. d. What is the largest unsigned binary number that the address can hold?


A population consists of the values {1, 2, 3, 4, 5). Consider samples of size 3 that can be drawn




from this population.




a. List down all the possible samples and corresponding sample mean




Sample




Sample Means




5




b. Construct the sampling distribution of the sample means.




Sample Means Frequency




Probability P(x)




c. Draw a histogram of the sampling distribution of the sample mean.

Based on the inheritance hierarchy/tree, write a C++ program to get the width, length and




height from users and call the calculateArea() member function of the Calculate




drived class to determine and return the volume of the user’s input. Before the program




ends, display all values read from users and the calculated area.





2. Make a C++ program that will calculate the total expenses and Cash left of Miss Carla after spending the following : 

Cash - 4,050.00 

  B&W perfume - 700.50

  B&W lotion - 560.85

  Dresses - 2072.50 


Note : the program must display the cash left and total expenses. 


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