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mwlevin
Answers (11)
There are 26^3 * 10 ways to select characters for the passwords, and 26*2 * 10 ways to select characters for which 2 letters repeat. Assuming order matters, there are (4 C 1) 26^3 * 10 possible passwords (we have to choose the position of the number) and
a) Choose any x, you can easily find a y that makes P(x,y) false. b) ∃ and ∀ switch with negation; ∀x∃y ~P(x,y)
Many of the symbols aren't showing up. Try rewriting using ∧ and ∨, or & and |.
Yes, but you still need to simplify the terms.
Let x be Sam's age and y be Angel's age. "Sam is 9 years older than Angel." x = y + 9 "Six years from now..." x + 6 "...thrice the age of Angel 3 years ago". 3(y - 3) x + 6 = 3(y - 3)
Those are equalities, not inequalities. You know exactly what temperature is needed and how long it takes to get there. Which takes less time, 110 min to heat it up or 120 min to cool it down?
(x-1)^12 has a degree of 12. It's equal to x^12 + some other terms. Similarly, (x+1)^3 = x^3 + ... has a degree of 3. When they are multiplied, x^12 * x^3 = x^15 is the highest power term, so the degree is 15.
Let x be the units digit and y be the tens digit. "The units of a number is 4 more than the tens digit" x = y + 4 "If the digits are reversed the new number..." The original number is x + 10y. The reversed number is 10x + y. "...is 1 less than twice the
It depends on whether you're looking for the sum or just individual rolls, and for individu rolls, whether order matters.
That's right.
Distribute over everything in the parentheses. 2(x - y) = 2x - 2y -(x + y) = -x + -y = -x - y 2x - x - 2y - y = x - 3y
