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4 years ago

Solve 3sinx-4sin^3 x= -1

1 answer:

5 0

Hello,

Since 3sin x-4sin^3x=sin (3x) (*****)
3sin x-4sin^3x=-1
==>sin (3x)=-1
==>3x=3π/2 +2kπ
==>x=π/2+2kπ/3, k being an integer

(*****)
sin (3x)=sin(x+2x)=sin x cos2x+cos x sin 2x
=sin x(cos²x-sin²x)+2cos²x sin x
=sin x(cos²x+2cos²x-sin²x)
=sinx(3(1-sin²x)-sin²x)
=3sin x-4sin^3x

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According to the last census (2010), the mean number of people per household in the United States is LaTeX: \mu = 2.58 Assume a

Veseljchak [2.6K]

Answer:

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, $\mu$ = 2.58 and Standard deviation, $\sigma$ = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar $\leq$ 2.50)

P(Xbar < 2.66) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{2.66-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z < -1.68) = 1 - P(Z 1.68)

= 1 - 0.95352 = 0.04648

P(Xbar $\leq$ 2.50) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{2.50-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z $\leq$ -3.92) = 1 - P(Z < 3.92)

= 1 - 0.99996 = 0.00004

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

7 0

3 years ago

The width of a math textbook is 0.75 inches. How many math textbooks can be placed standing up on a shelf that is 18 inches wide

larisa [96]

Since the width of each math textbook is 0.75 you have to find a number that multiplied by 0.75 will be equal 18

so, 0.75 x 24 = 18

18 books can be placed in the shelf

5 0

3 years ago

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A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.

tatuchka [14]

1/12. There are 12 possibilities, and only one number under 2.

5 0

3 years ago

Suppose that the salaries, in thousands of dollars, of the managers for a industry are normally distributed with an unknown mean

Marrrta [24]

Answer: t _(α/2) = 2.060

Step-by-step explanation:

Given that;

sample size n = 26

confidence interval = 95%

level of significance α = ( 1 - 95/100 ) = 0.05

but from the question the salaries (26) are use to estimate the mean of the population so, its a two tail test

therefore our level if significance α will be divided by 2 = 0.05/2 = 0.025

now our degree of freedom df = 26 - 1 = 25

FROM standard t-table value

the critical value of t for the level of significance 0.025

and 25 degree of freedom is 2.060

therefore, t _(α/2) = 2.060

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3 years ago

75% of a number is 120. what is 40% of the number?

balandron [24]

75%= 3/4
120*4=480
480/3=160
160/10=16
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Hope you understand it

4 0

4 years ago