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Radda [10]
3 years ago
11

Urgent!!! Please simplify

Mathematics
1 answer:
Fofino [41]3 years ago
5 0

Answer:

The answer is

<h2>3x² - 2x³</h2>

Step-by-step explanation:

First factor (x+1)² out of the expression

That's

\frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} -  {x}^{3}   \times 2 \sin( \frac{\pi}{2} )  }{ ({x + 1})^{2} }

Reduce the expression by (x + 1)²

We have

6 \cos( \frac{\pi}{3} )  \times  {x}^{2}  -  {x}^{3}  \times 2 \sin( \frac{\pi}{2} )

Using trigonometric values table

\cos( \frac{\pi}{3} )  =  \frac{1}{2}

\sin( \frac{\pi}{2} )  = 1

So we have

6 \times  \frac{1}{2}  \times  {x}^{2}  -  {x}^{3}  \times 2 \times 1

Simplify

We have the final answer as

{3x}^{2}   - 2 {x}^{3}

Hope this helps you

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A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta
Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

                             P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of women who find success with this new treatment = \frac{7}{14} = 0.50

          n = sample of women = 14

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                            level of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

<u />

<u>95% confidence interval for p</u> = [\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }]

= [ 0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } } , 0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } } ]

 = [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

4 0
4 years ago
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