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KIM [24]
2 years ago
6

Colin rolls a fair dice and flips a fair coin.

Mathematics
1 answer:
den301095 [7]2 years ago
7 0

Answer:

\frac{1}{12}

Step-by-step explanation:

Coin has 2 outcomes dice has 6 outcomes

A tail is 1/2 and a 3 is 1/6

So a tail and a 3 is 1/2 x 1/6

=1/12

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Marta_Voda [28]

Answer:

7\sqrt{3}

Step-by-step explanation:

Since this is a 30-60-90 triangle, we know that the sides have the following characteristic:

The side opposite to 30 degree angle: n

The side opposite to 60 degree angle: n\sqrt{3}

The side opposite to 90 degree angle: 2n

Since we know that 7 is opposite to 30-degree, and x is opposite to 60 degree, than we know that x = 7\sqrt{3}

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Nata [24]

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Step-by-step explanation:

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If p is a polynomial show that lim x→ap(x)=p(a
Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

 

Solution. Notice that

 

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

 

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

 

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

 

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

 

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

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2 years ago
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