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Math Help - Need Help With All these Algebra Problems.

  1. #1
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    Need Help With All these Algebra Problems.

    Sorry, I'm just stupid when it comes to math.

    1) Rationalize the denominator of expression


    2)A baseball player has a batting average of 0.175. What is the probability that he has exactly 3 hits in his next 7 at bats?
    The probability is ________

    3)Evaluate the expression and write the result in the form a+bi

    4)Solve the following inequality. Write the answer in interval notation.


    5)NASA launches a rocket at seconds. Its height, in meters above sea-level, as a function of time is given by
    Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
    The rocket splashes down after _______seconds
    How high above sea-level does the rocket get at its peak?

    The rocket peaks at _________meters above sea-level.

    6)The equation has two solutions A and B where A<B and A=________ and B=_________

    If you don't want to show the work on how you got it, it's fine. I understand that it's a lot of problems.
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  2. #2
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    Quote Originally Posted by badandy328 View Post
    Sorry, I'm just stupid when it comes to math.

    1) Rationalize the denominator of expression

    \frac{2}{{4 + \sqrt 5 }} = \frac{2}{{4 + \sqrt 5 }} \cdot \frac{{4 - \sqrt 5 }}{{4 - \sqrt 5 }} = \frac{{2(4 - \sqrt 5 )}}{{(4 + \sqrt {5)(4 - \sqrt 5 )} }} = \frac{{2(4 - \sqrt 5 )}}{{4^2  - 5}} = \frac{{2(4 - \sqrt 5 )}}{{11}}
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  3. #3
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    Quote Originally Posted by badandy328 View Post

    2)A baseball player has a batting average of 0.175. What is the probability that he has exactly 3 hits in his next 7 at bats?
    The probability is ________
    This is binomial probability.
    p=.175
    The probability of failure is,
    p=1-.175=.825
    Thus,
    {7\choose 3}(.175)^3(.825)^4


    4)Solve the following inequality. Write the answer in interval notation.
    That means,
    x-2\geq 5
    Or,
    x-2\leq -5
    Thus,
    x\geq 7
    Or,
    x\leq -3
    In interval notation,
    x=(-\infty,-3]\cup[-5,+\infty)
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  4. #4
    Senior Member OReilly's Avatar
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    Quote Originally Posted by badandy328 View Post
    6)The equation has two solutions A and B where A<B and A=________ and B=_________
    \begin{array}{l}<br />
 3x^2  + 15x + 3 = 0 \\ <br />
 x_{1/2}  = \frac{{ - 15 \pm \sqrt {15^2  - 4(3 \cdot 3)} }}{{2 \cdot 3}} = \frac{{ - 15 \pm \sqrt {225 - 36} }}{6} = \frac{{ - 15 \pm \sqrt {189} }}{6} = \frac{{ - 15 \pm 3\sqrt {21} }}{6} \\ <br />
 B = x_{1 = } \frac{{ - 15 + 3\sqrt {21} }}{6} = \frac{{3( - 5 + \sqrt {21} )}}{{3 \cdot 2}} = \frac{{ - 5 + \sqrt {21} }}{2} \\ <br />
 A = x_{2 = } \frac{{ - 15 - 3\sqrt {21} }}{6} = \frac{{3( - 5 - \sqrt {21} )}}{{3 \cdot 2}} = \frac{{ - 5 - \sqrt {21} }}{2} \\ <br />
 \end{array}<br />
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  5. #5
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    [QUOTE=ThePerfectHacker;29042]This is binomial probability.
    p=.175
    The probability of failure is,
    p=1-.175=.825
    Thus,
    {7\choose 3}(.175)^3(.825)^4


    I still do not get what the answer would be? What is multipleied into the 3 and 7?
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  6. #6
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    Hello, badandy328!

    3)Evaluate the expression (8 + 5y)(-3+3i) and write the result in the form a+bi
    (8 + 5i)(-3+3i) \;=\;-24 + 24i - 15i + 15i^2 \;= \;-24 + 9i - 15 \;= \;-39 + 9i
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  7. #7
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    Quote Originally Posted by ThePerfectHacker View Post

    That means,
    x-2\geq 5
    Or,
    x-2\leq -5
    Thus,
    x\geq 7
    Or,
    x\leq -3
    In interval notation,
    x=(-\infty,-3]\cup[-5,+\infty)
    There is error in solution.

    TPH made typo (intentionaly so that you be confused ).
    Solution is x=(-\infty,-3]\cup[7,+\infty)
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  8. #8
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    Quote Originally Posted by OReilly View Post
    There is error in solution.

    TPH made typo (intentionaly so that you be confused ).
    Solution is x=(-\infty,-3]\cup[7,+\infty)
    That explains why it was saying it was wrong.
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  9. #9
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    [QUOTE=badandy328;29047]
    Quote Originally Posted by ThePerfectHacker View Post
    This is binomial probability.
    p=.175
    The probability of failure is,
    p=1-.175=.825
    Thus,
    {7\choose 3}(.175)^3(.825)^4


    I still do not get what the answer would be? What is multipleied into the 3 and 7?
    Can someone explain this to me?
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  10. #10
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    Hello again, badandy328!

    5) NASA launches a rocket.
    Its height, in meters above sea-level, is given by: h(t) \;=\;-4.9t^2 + 349t + 332

    At what time does splashdown occur?

    How high above sea-level does the rocket get at its peak?

    Splashdown occurs when h(t) = 0.

    We have: . -4.9t^2 + 349t + 332 \:=\:0

    Quadratic Formula: . t \;=\;\frac{-349 \pm\sqrt{349^2 - 4(\text{-}4.9)(332)}}{2(\text{-}4.9)} \;\approx\;\{-8.3,\:72.2\}

    Splashdown occurs about \boxed{72.2\text{ seconds}} after liftoff.


    The maximum height occurs at the vertex of the parabola.

    The vertex is at: . t \:=\:\frac{-b}{2a} \:=\:\frac{-349}{2(\text{-}4.9)} \:\approx\:35.6 seconds

    Then: . h(35.6)\;=\;-4.9(35.6)^2 + 349(35.6) + 332 \;=\;6546.336

    The rocket peaks at about \boxed{546\text{ feet}}

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  11. #11
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    Quote Originally Posted by badandy328 View Post

    Can someone explain this to me?
    That means you choose 3 out of 7
    _7C_3 is another way to write it.
    It means multiply by 3 factors and divide by 3!
    Thus,
    \frac{7\cdot 6\cdot 5}{3!}=35
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