<h2>5%</h2>
Step-by-step explanation:
let % be X
30 = x% of 600
30 = x × 600 / 100
x = 30 × 100 /60
x = 5
follow me
Slope is rise over run or Y2 - Y1 divided X2 - X1. The X's and Y's are your coordinate points. It doesn't matter which Y you put down first but remember to choose the X in the same place. Your coordinate points are (0, -1) and (-4, 2)
Your equation will be:
-1 - 2 / 0 - (-4)
-3 / 0 + 4
-3 / 4
Your slope is negative 3/4
you can compare the length of sides of both the triangles...
The sample proportion
.
<h3>
How to estimate the sample proportion?</h3>
We know that the confidence interval for sample proportion exists estimated as;
90% confidence interval = Sample proportion Margin of Error
Here, let
= sample proportion
Level of significance = 1 - 0.90 = 0.
10 or 10% Critical value of z at 5% (two-sided) level of significance exists 1.645.
So, 90% confidence interval ![$=\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$](https://tex.z-dn.net/?f=%24%3D%5Chat%7Bp%7D%20%5Cpm%201.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%24)
![$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots(1)$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%20%5Cldots%281%29%24)
![$0.28=\hat{p}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots (2)](https://tex.z-dn.net/?f=%240.28%3D%5Chat%7Bp%7D%2B1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%20%5Cldots%20%282%29)
From (1) and (2) , we get;
![$&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\](https://tex.z-dn.net/?f=%24%260.22%2B1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%3D0.28-1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%20%5C%5C)
Simplifying the equation, we get
![$&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22 \\](https://tex.z-dn.net/?f=%24%261.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%2B1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%3D0.28-0.22%20%5C%5C)
![$&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06 \\](https://tex.z-dn.net/?f=%24%262%20%5Ctimes%201.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%3D0.06%20%5C%5C)
![$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645} \\](https://tex.z-dn.net/?f=%24%26%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%3D%5Cfrac%7B0.06%7D%7B2%20%5Ctimes%201.645%7D%20%5C%5C)
![$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.02](https://tex.z-dn.net/?f=%24%26%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%3D0.02)
Now, squaring both sides, we get;
![$\frac{\hat{p}(1-\hat{p})}{n}=0.0004 \\](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%3D0.0004%20%5C%5C)
![$n=\frac{\hat{p}(1-\hat{p})}{0.0004}](https://tex.z-dn.net/?f=%24n%3D%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7B0.0004%7D)
Now, putting value of n in (1), we get;
![$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%24)
![$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{\hat{p}(1-\hat{p})} \times 0.0004}$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-1.645%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%20%5Ctimes%200.0004%7D%24)
Simplifying the equation, we get
![$0.22=\hat{p}-1.645 \times \sqrt{0.0004}$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-1.645%20%5Ctimes%20%5Csqrt%7B0.0004%7D%24)
![$0.22=\hat{p}-(1.645 \times 0.02)$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-%281.645%20%5Ctimes%200.02%29%24)
![$0.22=\hat{p}-0.033$](https://tex.z-dn.net/?f=%240.22%3D%5Chat%7Bp%7D-0.033%24)
.
The sample proportion
.
Therefore, the correct answer is option D. 0.25.
To learn more about confidence interval refer to:
brainly.com/question/17212516
#SPJ9
9514 1404 393
Answer:
- 17 minutes 8.6 seconds (17 1/7 min)
- 2 hours 51 minutes 26 seconds (2 h 51 3/7 min)
Step-by-step explanation:
The relationship between time, speed, and distance is ...
time = distance/speed
__
a) For 1 km, the time in hours is ...
time = (1 km)/(3.5 km/h) = 1/3.5 h = 2/7 h
In minutes, that is ...
(60 min/h)(2/7 h) = 120/7 min = 17 1/7 min . . . . time for 1 km
__
b) The time for 10 km is 10 times the time for 1 km, so will be ...
(10)(2/7 h) = 20/7 h = 2 6/7 h
In hours and minutes, that is 2 hours and (6/7)(60 min) = 360/7 min = 51 3/7 min.
The time for 10 km is 2 hours 51 3/7 minutes.