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The mean height of the grade nine students at a certain high school is 164 centimeters and the

standard deviation is 10 centimeters. Assuming the heights are normally distributed, what

percent of the heights is greater than 168 centimeters?


The following data are the heights of four students in centimeter; 110, 125, 120, and 130. Suppose sample size of 2 is to be taken from the population of four students. What will be the probability when the sample mean is 115?


Find the magnitude and direction of the vector represented by each of the following pairs of components:


(a) 𝐴π‘₯ = 3.0 π‘π‘š, 𝐴𝑦 = βˆ’4.0 π‘π‘š;


(b) 𝐴π‘₯ = βˆ’5.0 π‘š, 𝐴𝑦 = βˆ’12.0 π‘š;


(c) 𝐴π‘₯ = βˆ’2.0 π‘˜π‘š, 𝐴𝑦 = 3.0 π‘˜π‘š.



1.Β Write a program to declare a structure and inside it is a non-static method that returns the area of a rectangle.

Β 

Test Data and Sample Output:

Input the dimensions of a rectangle:

Length: 60

Width: 30

Expected Output:

Length: 60

Width: 30

Area: 1800



The equation of motion:


r = -10i + 15t j + 5t2k


Q: (1)The average velocity from t=Is to t=2s


(2) The instantaneous velocity and acceleration at t=2s.


Show that ( p β†’ q) ∧ ( q β†’ r) β†’ ( pβ†’ r) is a tautology by using truth table or rules of



logical equivalence


A tall fat and skinny girl athlete of mass 55 kg throws a ball of mass 0.80kg against a wall. The ball strikes the wall horizontally with a speed of 25m/s and it bounces back with the same speed. The ball is in contact with the wall 0.050s. Determine the magnitude of the average force exerted on the wall by the ball?

1.Which of the following is the solution of the equation below?

0x + 0y = 0

1. (0,0,0).

2. (1,0,0).

3. No such solution exists

4. Infinitely many solution or (-1,2,1).


Read about doing multiplication using Karatsuba method

(https://en.wikipedia.org/wiki/Karatsuba_algorithm ).

Write a C++ program which:

β€’ Prompts user to enter two large integer numbers (x, y).

β€’ Make a function called Karatsuba() which takes these two integers and returns the

multiplication result using Karatsuba algorithm.

o Your function should do parameter validation. Both numbers must be more

than 4 digits and less than 10 digits (don’t use strings). If parameters are not

valid then the function should return 0;

o The entered numbers could be negative or positive. For example: 820778 and

-58712979 where x is 6-digit positive number and y is 8-digit negative

number.


β€’ You might need to make another helper function called getDigits() which will get an

integer as input and returns number of digits of that integer. getDigits() will help you

find the value of m and Bm.

β€’ Finally, display result in the main function


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