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anonymous

  • 5 years ago

Does anyone have any questions Something challenging

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  1. anonymous
    • 5 years ago
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    solve for x (3 dp) a) 3^x=19. b) 2^1-x=7 c) (1/4)^x=75. How to do this?

  2. anonymous
    • 5 years ago
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    You need to use logarithms

  3. anonymous
    • 5 years ago
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    a) if 3 ^ x = 19 x = log 19 to the base 3 x = 2.68

  4. anonymous
    • 5 years ago
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    for b) 2^1 = 2 2 - x =7 -x = 7-2 x = -5

  5. anonymous
    • 5 years ago
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    for c) if (1/4) ^ x = 75 x = log 75 to the base 0.25 x = -3.11

  6. anonymous
    • 5 years ago
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    I think for b, I got 1.807.. and for a and c I got the same answer as yours.

  7. anonymous
    • 5 years ago
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    your answer gets to 7.28 My answer gets to 18.99 To check your answer for part b), substitute it in 3^x = 19

  8. anonymous
    • 5 years ago
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    the formula is if x^y = z y = log z to the base x

  9. anonymous
    • 5 years ago
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    hm.. ok.

  10. anonymous
    • 5 years ago
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    You understand logarithms right

  11. anonymous
    • 5 years ago
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    hm.. yup I understand it.

  12. anonymous
    • 5 years ago
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    So then you should show this as your method

  13. anonymous
    • 5 years ago
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    adam an eve take turns flipping a coin. the first one to flip 'heads' wins. if eve goes first, what it the probability she wins?

  14. anonymous
    • 5 years ago
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    1/2 ?

  15. anonymous
    • 5 years ago
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    nope. she has the advantage of going first, so it must be greater than 1/2.

  16. anonymous
    • 5 years ago
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    I dont think so The probability of her getting heads is half The probability of Adam getting heads and her cetting tails is 0.5 * 0.5 thats 1/4 So she should be 1 - 0.25 = 0.75

  17. anonymous
    • 5 years ago
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    no that is not it either but it is getting closer. two methods (which really amount to the same thing) a linear equation, or write out sample space of 'eve wins' and sum the geometric series.

  18. anonymous
    • 5 years ago
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    No i think it should just be 0.75 I can't think of anything else

  19. anonymous
    • 5 years ago
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    Whats your answer and method

  20. anonymous
    • 5 years ago
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    how could she win? get heads on first try, done. i represent as (h) and probability is 1/2 eve gets tails, adam gets tails, and then eve gets heads. represent as (t t h) and probability is 1/8 eve gets tails, adam gets tails, eve gets tails, adam gets tails, eve gets heads (t t t t h) probability is 1/32 etc these events are mutually exclusive, so add them up \[\frac{1}{2}+\frac{1}{8} +\frac{1}{32}+...\]

  21. anonymous
    • 5 years ago
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    that is method one. method 2: put P = probability eve wins. write a linear equation in P as follows. she could win on first try with probability 1/2 OR she flips tails, adam flips tails [this happens with probability 1/4], AND she gets another turn. now if she gets another turn that is just like starting the game over, so her probability of winning has not changed. OR means we add the probabilities, AND means we multiply (assuming they are independent, which they are) and so we get an equation in P \[P = \frac{1}{2} + \frac{1}{4}P\] If you sum the geometric series you see that it is identical so solving the linear equation for P

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