Match each of 1 -6 with its appropriate definition from the list A - F below. 1. Axiom
2. Corollary
3. Contradiction
4. Tautology
5. Theorem
6. Lemma

a. An elementary mathematical truth that is assumed self-evident and not in need of proof.
b. A theorem that is an immediate consequence (and perhaps special case) of another theorem.
c. A proposition that is always false.
d. A proposition that is always true.
e. An important true mathematical statements.
f. A theorem that is needed as a stepping stone to prove a greater theorem.

In a sample of 2023 u. s. adults, 373 said franklin roosevelt was the best president since world war ii. two u. s. adults are selected at random from the population of all u. s. adults without replacement. assuming the sample is representative of all u. s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

The only way to identify an intercept is as an ordered pair. true false

X+ y = 5 ; x - y =3 solve using linear combination