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2 years ago

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A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the out

come in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?

1 answer:

const2013 [10]2 years ago

4 0

Hujhsusjsvsjhdjdjjdd

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Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)

masha68 [24]

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad 1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\$

$\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}$

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2 years ago

At the school cafeteria, you can get 3 slices of pizza for $5.94. At this rate, how much would 7 slices cost, in dollars and cen

gavmur [86]

Answer:

$13.86

Step-by-step explanation:

$5.94 / 3 = $1.98

1 slice = $1.98

7 slices = $1.98 x 7 = $13.86

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

Which shows the following expression after the negative exponents have been eliminated?

Sati [7]

B. Negative exponent flip from denominator to numerator and numerator to denominator.
B is the second option.

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2 years ago

A phone company offers two packages of service. Package A is $35.00 per month with an additional charge of $0.15 per minute for

ella [17]

Answer: 200 minutes have to be used for the costs of both plans to be the same.

Step-by-step explanation:

Let x represent the number of minutes that have to be used for the costs of both plans to be the same.

Package A is $35.00 per month with an additional charge of $0.15 per minute for long distance. This means that the cost of using package A for x minutes in a month would be

35 + 0.15x

Package B is $45.00 per month with an additional charge of $0.10 per minute for long distance. This means that the cost of using package A for x minutes in a month would be

45 + 0.1x

For both costs to be the same, it means that

35 + 0.15x = 45 + 0.1x

0.15x - 0.1x = 45 - 35

0.05x = 10

x = 10/0.05

x = 200

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2 years ago