This is very spread out just to show properly but you could get it smaller haha
Answer:
Longest possible length for each of the shorter lengths of ribbon is 9 cm because greatest common factor for both 36 and 45 is 9.
Step-by-step explanation:
Alannah has two ribbons one length is 36cm and other is 45cm.
It asked to find shorter length of ribbons that each cut into equal pieces with out no ribbon left over.
So, let's find greatest common factor for both 36 and 45.
Let's prime factor each number
36= 2*2*3*3
45= 3*3*5
So, GCF is product of common factors for both numbers.
GCF= 3*3 =9
So, longest possible length for each of the shorter lengths of ribbon is 9 cm.
Learn more about GCF in brainly.com/question/21612147.
Answer: The conditional statements are not in the correct form to make a conclusion using the law of syllogism. “If p, then q and if p, then r” cannot be used to draw a conclusion using the law of syllogism. The law of syllogism could be used if the hypothesis in the second statement was "if two pairs of congruent angles are formed."
Step-by-step explanation:
"If p, then q and if p, then r" cannot be used to draw a conclusion using the law of syllogism.
Neither of the conclusions of the conditional statements are the hypothesis of the other.
"If two pairs of congruent angles are formed" could be the hypothesis of the second statement.
** Both can be used to answer the question :)
Expected Mean, E(X), is obtained by multiplying each pair of

and its

and add up the answers
E(X) = (0×0.7) + (1×0.2) + (2×0.1) = 0.4
The formula to calculate the variance, Var(X), is given by E(X)² - (E(X))²
E(X²) = (0²×0.7) + (1²×0.2) + (2²×0.1) = 0+0.2+0.4 = 0.6
(E(X))² = (0.4)² = 0.16
Var(X) = 0.6 - 0.16 = 0.44
Translating these answers into the context we have
E(Y) = 0.4×500 = $200
Var(Y) = $110