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natita [175]
3 years ago
11

I know that 700 divided by 70 =10 because the 7 in 700 represents 100 times what it represents in

Mathematics
2 answers:
dedylja [7]3 years ago
4 0
The 7 in 700 represents 7 multiplied by 100 because of the two other digits
Ronch [10]3 years ago
3 0

"in" represent 10 because

7 * 10 = 700

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Seventy cards are numbered 1 through 70 , one number per card. One card is randomly selected from the deck. What is the probabil
Vanyuwa [196]

Answer:

Probability = \frac{2}{35}

Step-by-step explanation:

Given

Total = 70

First, we need to list the multiples of 5

M_5 = \{5,10,15,20,25,30,35,40,45,50,55,60,65,70\}

Then, multiples of 3M_3 = \{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69\}

Next, is to list out the common elements in both

M_3\ n\ M_5 = \{15,30,45,60\}

n(M_3\ n\ M_5) = 4

The required probability is then calculated as thus:

Probability = \frac{n(M_3\ n\ M_5)}{Total}

Probability = \frac{4}{70}

Probability = \frac{2}{35}

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3 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
At Rick's Pizza, they always put exactly 6 pieces of pepperoni on each slice of pizza. Each pizza has 10 slices. How many pieces
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Answer:

360

Step-by-step explanation:

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Solve the following equation:
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Complete the square.

z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0

\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4

Use de Moivre's theorem to compute the square roots of the right side.

w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)

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Now, taking square roots on both sides, we have

z^2 + \dfrac12 = \pm w^{1/2}

z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2

Use de Moivre's theorem again to take square roots on both sides.

w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)

\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}

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\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}

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1 year ago
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