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2 years ago

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Mathematics

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Thepotemich [5.8K]2 years ago

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Answer:

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A fair coin is flipped twelve times. What is the probability of the coin landing tails up exactly nine times?

seraphim [82]

Answer:

$P\left(E\right)=\frac{55}{1024}$

Step-by-step explanation:

Given that a fair coin is flipped twelve times.

It means the number of possible sequences of heads and tails would be:

2¹² = 4096

We can determine the number of ways that such a sequence could contain exactly 9 tails is the number of ways of choosing 9 out of 12, using the formula

$nCr=\frac{n!}{r!\left(n-r\right)!}$

Plug in n = 12 and r = 9

$=\frac{12!}{9!\left(12-9\right)!}$

$=\frac{12!}{9!\cdot \:3!}$

$=\frac{12\cdot \:11\cdot \:10}{3!}$ ∵ $\frac{12!}{9!}=12\cdot \:11\cdot \:10$

$=\frac{1320}{6}$ ∵ $3!\:=\:3\times 2\times 1=6$

$=220$

Thus, the probability will be:

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$=\frac{220}{4096}$

$=\frac{55}{1024}$

Thus, the probability of the coin landing tails up exactly nine times will be:

$P\left(E\right)=\frac{55}{1024}$

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2 years ago

If m∠D = 18°, and m∠C = 45°, what is ?

Fynjy0 [20]

<span>the question is, If m∠D = 18° and m∠C = 45° what is arc BC? your answer is B. 54 degrees </span>

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3 years ago

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The sum of 27 and a number n

Jobisdone [24]

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Its X And The Sum Of N Is Going To Be 27

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2 years ago

Share successful learning strategies that you have applied in previous mathematic courses

marshall27 [118]

Sure, I have this strategy to make a sheet with questions of that chapter and do that before I study the chapter so I can see if I know a little or a lot of that chapter

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2 years ago

140 fluid ounces increased by 45%

Radda [10]

$100\%\ increased\ by\ 45\%=100\%+45\%=145\%\\\\method\ \#1\\\\p\%=\frac{p}{100}\to145\%=\frac{145}{100}=\frac{145:5}{100:5}=\frac{29}{20}\\\\145\%\ of\ 140=\frac{29}{20}\cdot140=29\cdot7=\boxed{203\ (ounces)}\leftarrow answer$

$method\ \#2\\\\\begin{array}{ccc}140&-&100\%\\x&-&145\%\end{array}\ \ \ cross\ multiply\\\\\\100\cdot x=140\cdot145\ \ \ \ |divide\ both\ sides\ by\ 100\\\\x=\frac{140\cdot145}{100}\\\\\boxed{x=203\ (ounces)}$

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3 years ago