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1 year ago

PROVE :sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4

Mathematics

1 answer:

leva [86]1 year ago

3 0

Step-by-step explanation:

$\sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4}$

$\sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30)$

$\frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4}$

$\frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4}$

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Read 2 more answers

An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability tha

TEA [102]

Answer:

The probability is $P(X >300 ) = 0.97219$

Step-by-step explanation:

From the question we are told that

The capacity of an Airliner is k = 300 passengers

The sample size n = 320 passengers

The probability the a randomly selected passenger shows up on to the airport

$p = 0.96$

Generally the mean is mathematically represented as

$\mu = n* p$

=> $\mu = 320 * 0.96$

=> $\mu = 307.2$

Generally the standard deviation is

$\sigma = \sqrt{n * p * (1 -p ) }$

=> $\sigma = \sqrt{320 * 0.96 * (1 -0.96 ) }$

=> $\sigma =3.50$

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

$P(X > k ) = P( \frac{ X -\mu }{\sigma } > \frac{k - \mu}{\sigma } )$

Here $\frac{ X -\mu }{\sigma } =Z (The \ standardized \ value \ of \ X )$

=> $P(X >300 ) = P(Z > \frac{300 - 307.2}{3.50} )$

Now applying continuity correction we have

$P(X >300 ) = P(Z > \frac{[300+0.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > -1.914 )$

From the z-table

$P(Z > -1.914 ) = 0.97219$

$P(X >300 ) = 0.97219$

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3 years ago

Find the sum using the formulas for the sums of powers of integers ( problem attached )

Natasha2012 [34]

Correct Answer: - 550

We can use the distributive property to distribute the summation to the variables and then get the constant out to apply the summation formulas as shown below in the attached image.

The equation editor does not have a summation symbol, so I have attached the solution using the image.

The correct answer to this question is -550. First option is the correct one.

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2 years ago

PROVE :sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4​

PROVE :sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4