Answer:
The answer is "(0.73,0.87)".
Step-by-step explanation:
Given:
number of girls![= 64](https://tex.z-dn.net/?f=%3D%2064)
number of boys![= 16](https://tex.z-dn.net/?f=%3D%2016)
Total number of children![= 64+16= 80](https://tex.z-dn.net/?f=%3D%2064%2B16%3D%2080)
So,![n=80](https://tex.z-dn.net/?f=n%3D80)
Calculating the value of the proportion which is given by girls:
![\hat{p}= \frac{\text{number of girls}}{\text{total number of childrens}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%20%5Cfrac%7B%5Ctext%7Bnumber%20of%20girls%7D%7D%7B%5Ctext%7Btotal%20number%20of%20childrens%7D%7D)
![=\frac{64}{80}\\\\=\frac{8}{10}\\\\= 0.8](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B80%7D%5C%5C%5C%5C%3D%5Cfrac%7B8%7D%7B10%7D%5C%5C%5C%5C%3D%200.8)
Therefore the confidence interval is:
![\to \hat{p}\pm z_{(1-\frac{\alpha }{2})}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to 0.8 \pm 1.75\sqrt{\frac{0.8(1-0.8)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.8(0.2)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.16}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{0.002}\\\\\to 0.8 \pm 1.75 (0.04)\\\\\to 0.8 \pm 0.07\\\\\to (0.73,0.87)](https://tex.z-dn.net/?f=%5Cto%20%5Chat%7Bp%7D%5Cpm%20z_%7B%281-%5Cfrac%7B%5Calpha%20%7D%7B2%7D%29%7D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%5Csqrt%7B%5Cfrac%7B0.8%281-0.8%29%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B%5Cfrac%7B0.8%280.2%29%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B%5Cfrac%7B0.16%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B0.002%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%280.04%29%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%200.07%5C%5C%5C%5C%5Cto%20%280.73%2C0.87%29)
![\therefore \\\\\text{The lower confidence limit} = 0.73\\\\\text{The upper confidence limit} = 0.87\\](https://tex.z-dn.net/?f=%5Ctherefore%20%5C%5C%5C%5C%5Ctext%7BThe%20lower%20confidence%20limit%7D%20%3D%200.73%5C%5C%5C%5C%5Ctext%7BThe%20upper%20confidence%20limit%7D%20%3D%200.87%5C%5C)
You need to get the denominator at the same number first. The Lowest common denominator is 6. So multiple 7/3 by 2 and 5/2 by 3 to get 14/6 and 15/6. 15/6 is greater. 15/6 is 5/2, so the answer is 5/2. I hope this helps!
Sin32=opposite/hypotenuse, which is 12.87/23.96. (12.87/23.96)/12.87=
12.87/(23.96*12.87)=1/23.96.
For the right side to be equal, it must have 22.35 on the top (to cancel out) and 23.96 on the bottom. Since 23.96 is the hypotenuse, we have that, and since 22.35 needs to be on the top, sin67 fulfills that
Answer:
P ( x ) = -0.7 (x - 2)²(x + 3)
Step-by-step explanation:
<u>We are given</u> :
P ( x ) , has a root of multiplicity 2 at x = 2
and a root of multiplicity 1 at x = − 3
Then
P ( x ) = a (x - 2)²(x + 3) ; where ‘a’ is a real number.
P ( x ) = a (x - 2)²(x + 3)
= a (x² - 4x + 4)(x + 3)
= a [x³ - 4x² + 4x + 3x² - 12x + 12]
P (0) = -8.4
⇔ a [(0)³ - 4(0)² + 4(0) + 3(0)² - 12(0) + 12] = -8.4
⇔ 12 a = -8.4
⇔ a = (-8,4) ÷ 12
⇔ a = -0,7
<u>Conclusion</u> :
P ( x ) = -0.7 (x - 2)²(x + 3)