Math Answers

Q2. Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900

2x1 + 4x2 ≤ 1000

x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.

The random variable X represents the number of taxi cabs a doctor meets on his way to the hospital. The probability distribution of X is given in the following distribution table.

X P(x)

0 0.01

1 0.15

2 0.20

3 0.25

4 0.30

5 0.09

Find the expected value and variance of X.

Two balls are pick in succession without replacement, 4 white balls and 5 green balls. let Y be the random variable representing tge gree balls. Find the values of a random variable Y. Complete the table gelow.

Sketch the curve y = x³-3x.

Find the equations of the tangent and the normal of y = 3x²-2x+1 at point (1,2).

Find the first derivative of y with respect to x. Use the given relation in its

implicit form.

a. x² + y² = a²

b. X² + 4y² = 4ay

Find the second derivative of y = (x2+x+1)2

Find the first derivative of y = (3x+4)2

X 3 6 9 12 15

P(X) 4/9 2/9 1/9 1/9 1/9

Daniel went to the perya and played a game. The rule says that the outcome of the game is a random variable 

from 1 to 14 and that if the outcome is even, he wins ₱50. If the outcome is odd, he wins nothing. Assuming that 

playing is for free, what is Daniel’s expected gain, if there is any?