Search
Four balls are drawn in succession without replacement from an urn containing 4 red balls, 3 blue balls and 3 yellow balls. Let Z be the random variable representing the number of blue balls.
USE THE METHOD OF DIRECT TO PROVE:
If a is an odd integer, then a’2 + 3a +5 is odd.
A mean of 3 out of 5 students request for tomato sauce with their meal in a canteen. A random sample of 8 students is selected, what is the probability that less than 4 students request for tomato sauce with their meal?
There are three grades in a report card that you want to interpret in terms of performance: mathematics 75, english 85, and science 90. This means are 72,83 and 88, respectively. The standard deviation are 3, 10, and 15, respectively.
{F} Construct the Combinatorial Circuit of the given output.
- (p∨q) 2. (p∧ ~q)
- (p→~q)→(p∨q)
{F} 2.
Find the transitive closures of these relations on {1, 2, 3, 4}.
a) {(1, 2), (2,1), (2,3), (3,4), (4,1)}
b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4, 3)}
c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3, 4)}
d) {(1, 1), (1,4), (2,1), (2,3), (3,1), (3, 2), (3,4), (4, 2)}
3.
Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is
a) reflexive and transitive.
b) symmetric and transitive.
c) reflexive, symmetric, and transitive.
4.
Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(0, 0), (1, 1), (2, 2), (3, 3)}
b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)}
c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}
d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)}
e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0),(2, 2), (3, 3)}
The lifetime of a light bulb is normally distributed with 800 hours and standard deviation 50 hours. A random light bulb is selected. What is the probability that it will last for more than 950 hours?
If a certain number x is subtracted from 8,it will be equal to two less than four times the same number
{F} Work Out
1. Solve by crammer's rule, the following equations.
3X + 3Y - Z = 11
2X - Y + 2Z = 9
4X + 3Y - 27 = 25
2. solve the above equations using graphical method.
Determine which of the following is not the solution set of the linear equations below.
3x-y+z=2
2x-z=2
