Probability
When rolling two fair dice, this is the total number of possible outcomes in the sample space.
36
A set is considered ________ if there's nothing in it.
Empty
p-> -q
what is a locus ?
A set of points that follow a rule .
Expand (x - 1)^3.
x^3 - 3x^2 + 3x - 1
The probability of rolling a sum of 8 where both dice show even numbers is this simplified fraction.
1/12
The symbol of a universal set.
U
p->-q
what shape is formed by all points the same distance from one point ?
A circle
Expand (x - 5)^4.
x^4 - 20x^3 + 120x^2 - 500x +625
You roll two fair dice, but a partition prevents you from seeing one of them. If the die you can see is a six, this is the probability that the total sum is 12.
1/6 (The outcome of the unseen die is independent of the first)
{Clock 8,+}
5+6
3
state the contrapositive of -p ->q
-q->p
What is the locus of points equally distant from two points ?
The perpendicular bisector .
Find the second term of the expansion: (x - 3a)^5.
-15x^4a
There are exactly this many ways to roll "doubles" (the same number on both dice) using a standard pair of dice.
6
{Clock 5,+}
(2x3)+3
4
What is a Tautology
A Tautology is a statement that is always true in every possible scenario or interpretation
what is the locus of points equally distant from two intersecting line ?
The angle bisector .
Find the middle term of the expansion: (y - 7)^6.
-6860a^3
When rolling a single die twice, this is the probability that you roll a 6 at least once.
11/36
All possible subsets of {q,r,s,t}
{q,r,s,t}, {q,r,s}, {q,s,t}, {r,q,s}, {r,s,t}, {s,q,r}, {s,t,r}, {t,q,r}, {t,r,s}, {q,r}, {q,s}, {q,t}, {r,q}, {r,s}, {r,t}, {s,q}, {s,r}, {s,t}, {t,q}, {t,r}, {t,s}, {q}, {r}, {s}, {t}, {}.
Let H be the sentence "Laura is hungry and e be the sentence "Laura eats". write this sentence in symbolic form
"If Laura is hungry, then Laura eats"
H->E
A point moves so it is always 5 units away from a fixed point . What figure is created ?
A circle radius 5 .
Expand (1 - z^3)^3.
1 - 3z^3 + 3z^6 - z^9.