100,000,000 microbes in a speck of mold
A) The length of the longer leg is x-1
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
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5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
5x = 2x + 9, where 5x > 0 and 2x + 9 > 0 ;
Then, 3x = 9 ;
Then, x = 3 ;
Verify : 5 × 3 = 2 × 3 + 9 ;correct !
5 × 3 > 0 ; correct !
2 × 3 + 9 > 0; correct !
1. D - Since it's random, everyone has an equal chance of being picked
2. B - Since the people are already registered voters it would be easier to get a response from them. Plus, picking ever 10th person makes it random.
3. false - a fair question wouldn't make assumptions about the population
4. B - "Don't you think" causes the answerer to be pushed towards saying yes
hope this helps :)