Answer:
Option 4: r ≥ 6
Step-by-step explanation:
5(6+3r) + 7 ≥ 127
30 + 15r + 7 ≥ 127
37 + 15r ≥ 127
15r ≥ 90
r ≥ 6
Answer:
12−3xStep-by-step explanation:
Answer:
3.08 km/h.
Step-by-step explanation:
We know that,
Ali traveled at a speed of s km/h for 2.5 hours.
Let d be the distance and t be the time.
...(1)
On his return journey, he increased his speed by 4 km/h and saved 15 minutes. So, distance is d and times is t-15.
...(2)
From (1) and (2), we get
Put t=40 in (1).
So, t=40 and d=100.
Now,
Total distance = d + d = 100 + 100 = 200
Total time = t + t - 15 = 40 + 40 - 15 = 65
So, the average speed is
Therefore, the average speed is 3.08 km/h.
Answer:
![-0.048](https://tex.z-dn.net/?f=-0.048%3CP_1-P_2%3C0.036)
Do not reject ![H_0:P_1-P_2=0](https://tex.z-dn.net/?f=H_0%3AP_1-P_2%3D0)
Step-by-step explanation:
From the question we are told that
Sample size ![n_1=350](https://tex.z-dn.net/?f=n_1%3D350)
Sample size ![n_2=250](https://tex.z-dn.net/?f=n_2%3D250)
Sample proportion 1 ![\hat P= \frac{25}{350} =>0.07](https://tex.z-dn.net/?f=%5Chat%20P%3D%20%5Cfrac%7B25%7D%7B350%7D%20%3D%3E0.07)
Sample proportion 2 ![\hat P= \frac{19}{250} =>0.076](https://tex.z-dn.net/?f=%5Chat%20P%3D%20%5Cfrac%7B19%7D%7B250%7D%20%3D%3E0.076)
95% confidence interval
Generally for 95% confidence level
Level of significance
![\alpha = 1-0.95=>0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%201-0.95%3D%3E0.05)
![\alpha /2=\frac{0.05}{2} =>0.025](https://tex.z-dn.net/?f=%5Calpha%20%2F2%3D%5Cfrac%7B0.05%7D%7B2%7D%20%3D%3E0.025)
Therefore
![Z_a_/_2=1.96](https://tex.z-dn.net/?f=Z_a_%2F_2%3D1.96)
Generally the equation for confidence interval between
is mathematically given as
![(\hat P_1-\hat P_2)\pm Z_a_/_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=%28%5Chat%20P_1-%5Chat%20P_2%29%5Cpm%20Z_a_%2F_2%5Csqrt%7B%5Cfrac%7B%5Chat%20P_1%281-%5Chat%20P_1%29%7D%7Bn_1%7D%2B%5Cfrac%7B%5Chat%20P_2%281-%5Chat%20P_2%29%7D%7Bn_2%7D%20%20%7D)
![(0.07-0.076)\pm 1.96\sqrt{\frac{0.07(1-0.07)}{350}+\frac{0.076(1-0.076)}{250} }](https://tex.z-dn.net/?f=%280.07-0.076%29%5Cpm%201.96%5Csqrt%7B%5Cfrac%7B0.07%281-0.07%29%7D%7B350%7D%2B%5Cfrac%7B0.076%281-0.076%29%7D%7B250%7D%20%20%7D)
![(0.07-0.076)\pm 1.96\sqrt{4.66896*10^-^4 }](https://tex.z-dn.net/?f=%280.07-0.076%29%5Cpm%201.96%5Csqrt%7B4.66896%2A10%5E-%5E4%20%20%7D)
![(-0.006)\pm 0.042](https://tex.z-dn.net/?f=%28-0.006%29%5Cpm%200.042)
![(-0.006)+ 0.042=>0.036](https://tex.z-dn.net/?f=%28-0.006%29%2B%200.042%3D%3E0.036)
Therefore
Confidence interval is
![-0.048](https://tex.z-dn.net/?f=-0.048%3CP_1-P_2%3C0.036)
Conclusion
Given the confidence interval has zero
Therefore do not reject ![H_0:P_1-P_2=0](https://tex.z-dn.net/?f=H_0%3AP_1-P_2%3D0)