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Dahasolnce [82]
4 years ago
10

What is the probability of rolling a 6 sided die and getting a 2 or an odd number?

Mathematics
2 answers:
mr_godi [17]4 years ago
3 0
The correct answer is 1/6 for a two and 1/2 for an odd number so all together it would be 2/3
djyliett [7]4 years ago
3 0

Answer: \dfrac{2}{3}

Step-by-step explanation:

When we roll a 6-sided dis , the total possible of outcomes : 1, 2, 3, 4, 5, 6

Thus , the total number of outcomes =6

The favorable outcomes: 2, 1, 3 , 5

Thus , the number of favorable outcomes = 4

Now, the required probability :-

\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{4}{6}=\dfrac{2}{3}

Hence, the probability of rolling a 6 sided die and getting a 2 or an odd number=\dfrac{2}{3}

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​Find all roots: x^3 + 7x^2 + 12x = 0 <br> Show all work and check your answer.
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The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

<u>Solution:</u>

We have been given a cubic polynomial.

x^{3}+7 x^{2}+12 x=0

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

x^{3}+7 x^{2}+12 x=0

x\left(x^{2}+7 x+12\right)=0   ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

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Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

x^{2}+7 x+12=0

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

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By substituting the values of a,b and c in the quadratic equation we get;

\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}

<em><u>Therefore, the two roots are:</u></em>

\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}

And,

\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

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3 years ago
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svet-max [94.6K]

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