And what’s the question?????
Using the distributive property, you’ll get the equation 56i+63.
You’ll distribute (multiply) 7 to 8i, and 7 to 9
the coordinates where the bridges must be built is
and
.
<u>Step-by-step explanation:</u>
Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:
Basically we need to find values of x for which f(x) = g(x) :
⇒ ![f(x)-g(x)=0](https://tex.z-dn.net/?f=f%28x%29-g%28x%29%3D0)
⇒ ![3x^2- 24x + 39-(3x - 15 ) =0](https://tex.z-dn.net/?f=3x%5E2-%2024x%20%2B%2039-%283x%20-%2015%20%29%20%3D0)
⇒ ![3x^2- 24x + 39-3x + 15 =0](https://tex.z-dn.net/?f=3x%5E2-%2024x%20%2B%2039-3x%20%2B%2015%20%20%3D0)
⇒ ![3x^2- 27x + 54 =0](https://tex.z-dn.net/?f=3x%5E2-%2027x%20%2B%2054%20%20%3D0)
⇒ ![x^2- 9x + 18 =0](https://tex.z-dn.net/?f=x%5E2-%209x%20%2B%2018%20%20%3D0)
⇒ ![x^2- 6x-3x + 18 =0](https://tex.z-dn.net/?f=x%5E2-%206x-3x%20%2B%2018%20%20%3D0)
⇒ ![x(x- 6)-3(x - 6) =0](https://tex.z-dn.net/?f=x%28x-%206%29-3%28x%20-%206%29%20%20%3D0)
⇒ ![(x-3)(x- 6) =0](https://tex.z-dn.net/?f=%28x-3%29%28x-%206%29%20%20%3D0)
⇒ ![x=3 , x=6](https://tex.z-dn.net/?f=x%3D3%20%2C%20x%3D6)
Value of g(x) at x = 3 : y=3x -15 = 3(3)-15 = -6
Value of g(x) at x = 6 : y=3x -15 = 3(6)-15 = 3
Therefore , the coordinates where the bridges must be built is
and
.
Answer:
![-0.061 < P_1 -P_2< 0.025](https://tex.z-dn.net/?f=-0.061%20%3C%20P_1%20-P_2%3C%200.025)
Step-by-step explanation:
Give data:
![n_1 = 350](https://tex.z-dn.net/?f=%3C%2Fstrong%3En_1%20%3D%20350%3Cstrong%3E)
![n_2 =250](https://tex.z-dn.net/?f=%3C%2Fstrong%3En_2%20%3D250%3Cstrong%3E)
![x_1 = 23](https://tex.z-dn.net/?f=%3C%2Fstrong%3Ex_1%20%3D%2023%3Cstrong%3E)
![x_2 = 21](https://tex.z-dn.net/?f=%3C%2Fstrong%3Ex_2%20%3D%2021%3Cstrong%3E)
![\hat{P} 1 = \frac{x_1}{n_1} = \frac{23}{350} = 0.066](https://tex.z-dn.net/?f=%3C%2Fstrong%3E%5Chat%7BP%7D%201%20%3D%20%5Cfrac%7Bx_1%7D%7Bn_1%7D%20%3D%20%5Cfrac%7B23%7D%7B350%7D%20%3D%200.066%3Cstrong%3E)
![\hat{P} 2 = \frac{x_2}{n_2} = \frac{21}{250} = 0.084](https://tex.z-dn.net/?f=%3C%2Fstrong%3E%5Chat%7BP%7D%202%20%3D%20%5Cfrac%7Bx_2%7D%7Bn_2%7D%20%3D%20%5Cfrac%7B21%7D%7B250%7D%20%3D%200.084%3Cstrong%3E)
for 95% confidence interval
![\alpha = 1 - 0.95 = 0.05 and \alpha/2 = 0.025](https://tex.z-dn.net/?f=%3C%2Fstrong%3E%5Calpha%20%3D%201%20-%200.95%20%3D%200.05%20and%20%5Calpha%2F2%20%3D%200.025%3Cstrong%3E)
from standard z- table
confidence interval for P_1 and P_2 is
![\hat{P} 1 - \hat{P} 2 \pm z_{\alpja/2} \sqrt{\frac{\hat{P} 1(1-\hat{P} 1)}{n_1} +\frac{\hat{P} 2(1-\hat{P} 2)}{n_2}}](https://tex.z-dn.net/?f=%3C%2Fstrong%3E%5Chat%7BP%7D%201%20-%20%5Chat%7BP%7D%202%20%5Cpm%20z_%7B%5Calpja%2F2%7D%20%5Csqrt%7B%5Cfrac%7B%5Chat%7BP%7D%201%281-%5Chat%7BP%7D%201%29%7D%7Bn_1%7D%20%2B%5Cfrac%7B%5Chat%7BP%7D%202%281-%5Chat%7BP%7D%202%29%7D%7Bn_2%7D%7D%20%3Cstrong%3E)
![(0.066 - 0.084) \pm 1.96 \sqrt{\frac{0.066(1-0.066)}{350} +\frac{0.084(1-0.084)}{250}}](https://tex.z-dn.net/?f=%3C%2Fstrong%3E%280.066%20-%200.084%29%20%5Cpm%201.96%20%5Csqrt%7B%5Cfrac%7B0.066%281-0.066%29%7D%7B350%7D%20%2B%5Cfrac%7B0.084%281-0.084%29%7D%7B250%7D%7D%3Cstrong%3E)
![-0.018 \pm 0.043](https://tex.z-dn.net/?f=%3C%2Fstrong%3E-0.018%20%5Cpm%200.043%3Cstrong%3E)
confidence interval is
![-0.018 - 0.043 < P_1 -P_2](https://tex.z-dn.net/?f=%3C%2Fstrong%3E-0.018%20-%200.043%20%3C%20P_1%20-P_2%3C-0.018%2B0.043%3Cstrong%3E)
![-0.061 < P_1 -P_2< 0.025](https://tex.z-dn.net/?f=-0.061%20%3C%20P_1%20-P_2%3C%200.025)