Answer: E
Step-by-step explanation: In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. ... Many mathematical theorems are conditional statements.
Answer:
3−y
2. 8
4.2bh
Step-by-step explanation:
5(2x+y)=15
2 Divide both sides by 55.
2x+y=\frac{15}{5}2x+y=
5
15
3 Simplify \frac{15}{5}
5
15
to 33.
2x+y=32x+y=3
4 Subtract yy from both sides.
2x=3-y2x=3−y
5 Divide both sides by 22.
x=\frac{3-y}{2}x=
2
1. 3−y
2. 8
2.Add 2y2y to both sides.
x=-8+2yx=−8+2y
2 Regroup terms.
x=2y-8x=2y−8
Answer:
The statement is false.
Step-by-step explanation:
To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.
Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.
The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.
Answer:
80/81
Step-by-step explanation:
If a head is twice as likely to occur as a tail, then the probability of getting heads is 2/3 and the probability of getting tails is 1/3.
The probability of getting at least 1 head involves 4 scenarios:
1) 1 Head and 3 Tails
2) 2 Heads and 2 Tails
3) 3 Heads and 1 Tail
4) 4 Heads
Instead of calculate all these scenarios, you could calculate the opposite scenario: 4 Tails. The sum of all possible scenarios is 1, so:
P(at least one head) + P(no heads) = 1
Then, P(at least one head) = 1 - P(no heads)
The probability of 4 tails is:
P(no heads) = P(TTTT) = (1/3)(1/3)(1/3)(1/3)=1/81
Then, P(at least one head) = 1 - 1/81=80/81
Answer:
21
Step-by-step explanation:
