Answer:
The last one.
Step-by-step explanation:
Answer:
![0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.2870.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613](https://tex.z-dn.net/?f=0.45%20-%201.96%5Csqrt%7B%5Cfrac%7B0.45%281-0.45%29%7D%7B36%7D%7D%3D0.2870.45%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.45%281-0.45%29%7D%7B36%7D%7D%3D0.613)
we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613
Step-by-step explanation:
The estimated proportion of interest is ![\hat p=0.45](https://tex.z-dn.net/?f=%5Chat%20p%3D0.45)
We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by
and
.
And the critical value is:![z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D-1.96%2C%20z_%7B1-%5Calpha%2F2%7D%3D1.96)
The confidence interval for the true population proportion is interest is given by this formula:
![\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}](https://tex.z-dn.net/?f=%5Chat%20p%20%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%20%281-%5Chat%20p%29%7D%7Bn%7D%7D)
Replacing the values provided we got:
![0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287\\\\0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613](https://tex.z-dn.net/?f=0.45%20-%201.96%5Csqrt%7B%5Cfrac%7B0.45%281-0.45%29%7D%7B36%7D%7D%3D0.287%5C%5C%5C%5C0.45%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.45%281-0.45%29%7D%7B36%7D%7D%3D0.613)
And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613
Answer:
a. 53.4
b. 24.4
Step-by-step explanation:
a+j=77.8
j=a-29
a+j=77.8
-a+j=-29
2j=48.8
j=24.4
a+24.4=78.8
a=53.4
Answer:
39.6 cm
Step-by-step explanation:
Applying
s = 2πrθ/360................ Equation 1
Where s = length of an arc or distance traveled by the minutes hand of the clock during the 42 munites, r = length of the minutes hand of the clock, θ = Angle traveled by the minute hand of the clock for every 42 minutes
From the question,
Given: r = 9 cm, θ = 252°
Constant: π = 22/7 = 3.14
Substitute these values into equation 1
s = (2×3.14×9×252)/360
s = 39.564
s = 39.6 cm
14a^2bc^4/21abc^6 = 2a/3b^2