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  1. #1
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    Unhappy Question

    If anyone can help me with any of these three problems, Its 2 am where I am at.. n I cant sleep until these are finished, i tried looking in my book to further explain, but I am totally stuck any help would be so greatly appreciated... Thank u so much:

    41. What is the probability of rolling a nine
    with a pair of dice consecutively followed
    by rolling a five with a pair of dice?
    Hint: Consecutive events are products of
    individual probabilities.






    57. Find the 5th term of the binomial expansion.

    (2x-3y)^7



    58. Identify and sketch the graph for the
    relation:

    y^2 +x^2 6x + 9 = 25
    Hint: Make a table, let xmin be -2 and xmax be 8, Move all the monomials over to the right hand side except y^2 , then solve for the two values of y when taking the square root, note the positive and negative cases. After making a table, plot the points on graph paper and identify the shape.

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  2. #2
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    For the probability of two dice summing to nine, you can have:

    3 + 6,\,\, 4 +5,\,\, 5 + 4,\,\, 6 + 3

    Each outcome has  P = \frac{1}{6}\,, as the dice are fair.

    So the probability is 4\, \left( \frac{1}{6} \times \frac{1}{6} \right) = \frac{1}{9}

    For the probability of two dice summing to five, you can have:

    1 + 4,\,\, 2 +3,\,\, 3 + 2,\,\, 4 + 1

    Which gives the same probability as for the sum of the dice to 9.
    Because dice rolls are independent, the probability of rolling a 9 with 2 die followed by rolling 5 with 2 die = \left(\frac{1}{9}\right)^2



    For binomial expansions,
    The 5th term will be  _{\,}^7C_4 \,(2x)^3 \,(-3y)^4 (binomial expansion formula).
    Last edited by nzmathman; December 4th 2008 at 01:47 AM.
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  3. #3
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    For the last question,

    y^2 + x^2 - 6x + 9 = 25

    You need to complete the square for x (the y term is already a perfect square)

    y^2 + (x - 3)^2 = 25

    Now this is the standard equation for a circle. The centre will be at (3,0), and the radius is \sqrt{25} = 5

    To sketch this, place the compass point at (3,0) and draw a circle of radius 5 units.
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  4. #4
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    Quote Originally Posted by Steph07 View Post
    What is the probability of rolling a nine
    with a pair of dice consecutively followed
    by rolling a five with a pair of dice?
    Hint: Consecutive events are products of
    individual probabilities.
    Pr(rolling a 9) x Pr(rolling a 5).

    Use this dice table to help calculate each probability: Dice table
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