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solve for x: 3tan^3x-tanx=0
Suppose a box contains 4 red balls and 3 black balls. Compute the probability that the second ball drawn is red if the first ball drawn was black.
Give the most compact theta notation for the number of times the statement
x = x + 1 is executed in the following pseudo-code:
for i = 1 to i = 3n − 1{
for j = 1 to j = n{
x = x + 1
}
}
x = x + 1 is executed in the following pseudo-code:
for i = 1 to i = 3n − 1{
for j = 1 to j = n{
x = x + 1
}
}
Let f(n) and g(n) be functions with domain {1, 2, 3, . . .}. Prove the following:
If f(n) = Ω(g(n)), then g(n) = O(f(n)).
If f(n) = Ω(g(n)), then g(n) = O(f(n)).
abdullah has decided to make loot bags for his birthday party. Balloons are sold in bags of 20 party horns are sold in bags of 10 and candy bars are sold in packages of 8.He invited his 36 classmates. How many of each should he buy so there are an equal number of balloons horns and candy bars in each basket? he does not want any leftovers
Math
what is 3082.24 divided by 24
Which ordered pair is the solution to the system?
x+5y=−15
y=15x+1
a. (−5, −2)(−5, −2)
b. (−10, −1)(−10, −1)
c. (−7, −0.4)(−7, −0.4)
d. (−8, −1.2)
x+5y=−15
y=15x+1
a. (−5, −2)(−5, −2)
b. (−10, −1)(−10, −1)
c. (−7, −0.4)(−7, −0.4)
d. (−8, −1.2)
D. Solving a System of Linear Equation.
Direction: Use an inverse matrix to solve each system of linear equation.
1. (a) x+2y=-1
x-2y=3
(b) x+2y=10
x-2y=-6
2. (a) 2x-y=-3
2x+y=7
(b) 2x-y=-1
2x+y=-3
3. (a) x+2y+z=2
x+2y-z=4
x-2y+z=-2
(b) x+2y+z=1
x+2y-z=3
x-2y+z=-3
E. Let A, B and C be:
A = [1 2 -3; 0 1 2; -1 2 0]
B = [-1 2 0; 0 1 2; 1 2 -3]
C = [0 4 -3; 0 1 2; -1 2 0]
1. Find an elementary matrix E such that EA=B
2. Find an elementary matrix E such that EC=A
3. Find an elementary matrix E such that EB=A
F. Find the LU Factorization of the matrix.
4. A = [1 0; -2 1]
5. B = [-2 1; -6 4]
6. C = [3 0 1; 6 1 1; -3 1 0]
Direction: Use an inverse matrix to solve each system of linear equation.
1. (a) x+2y=-1
x-2y=3
(b) x+2y=10
x-2y=-6
2. (a) 2x-y=-3
2x+y=7
(b) 2x-y=-1
2x+y=-3
3. (a) x+2y+z=2
x+2y-z=4
x-2y+z=-2
(b) x+2y+z=1
x+2y-z=3
x-2y+z=-3
E. Let A, B and C be:
A = [1 2 -3; 0 1 2; -1 2 0]
B = [-1 2 0; 0 1 2; 1 2 -3]
C = [0 4 -3; 0 1 2; -1 2 0]
1. Find an elementary matrix E such that EA=B
2. Find an elementary matrix E such that EC=A
3. Find an elementary matrix E such that EB=A
F. Find the LU Factorization of the matrix.
4. A = [1 0; -2 1]
5. B = [-2 1; -6 4]
6. C = [3 0 1; 6 1 1; -3 1 0]
A. Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination.
1.-x+y+2z=1
2x+3y+z=-2
5x+4y+2z=4
2. 2x+3y+z=10
2x-3y-3z=22
4x-2y+3z=-2
B. Finding the Inverse of a Matrix.
Find the inverse of the matrix.
1. [2 0; 0 3]
2. [-1 1; 3 -3]
3. [1 2; 3 7]
C. Finding the inverse of the Square of a Matrix.
Direction: Compute A^-2.
1. A = [0 -2; -1 3]
2. A = [2 7; -5 6]
3. A = [-2 0 0; 0 1 0; 0 0 3]
1.-x+y+2z=1
2x+3y+z=-2
5x+4y+2z=4
2. 2x+3y+z=10
2x-3y-3z=22
4x-2y+3z=-2
B. Finding the Inverse of a Matrix.
Find the inverse of the matrix.
1. [2 0; 0 3]
2. [-1 1; 3 -3]
3. [1 2; 3 7]
C. Finding the inverse of the Square of a Matrix.
Direction: Compute A^-2.
1. A = [0 -2; -1 3]
2. A = [2 7; -5 6]
3. A = [-2 0 0; 0 1 0; 0 0 3]
in a card game with my friend, I pay a certain amount of money each time I lose. i win $4 if I draw a jack or a queen and I win $5 if I draw a king or ace for an ordinary pack of 52 playing cards. if I draw other cards I lose. what should I pay so that we come out even? (that is if the game is fair).
