Answer:
The upper limit of a 95% confidence interval for the population mean would equal 83.805.
Step-by-step explanation:
The standard deviation is the square root of the variance. Since the variance is 25, the sample's standard deviation is 5.
We have the sample standard deviation, not the population, so we use the t-distribution to solve this question.
T interval:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of 0.95(
). So we have T = 1.761
The margin of error is:
M = T*s = 1.761*5 = 8.805.
The upper end of the interval is the sample mean added to M. So it is 75 + 8.805 = 83.805.
The upper limit of a 95% confidence interval for the population mean would equal 83.805.
Sin (A + B) = sin A cos B + cos A Sin B
<span>Cos (A - B) = cos A cos B + sin A sin B </span>
<span>=> (SinACosB+ CosASinB) (CosACosB +SinASinB) </span>
<span>=>SinACosACos^2B+Sin^2ACosBSinB+Cos^2A... </span>
<span>=>SinACosA(Cos^2B+Sin^2B) +SinBCosB(Sin^2A+Cos^2A) </span>
<span>we know that Sin^2+Cos^2=1 </span>
<span>=>SinACosA(1)+SinBCosB(1) </span>
<span>=SinACosA+SinBCosB </span>
<span>Proved
</span>
Answer:
5π
Step-by-step explanation:
just need to find half of the circumference
The order you apply the adjustments does make a difference because the percents that are applied will be applied to different amount.
For example, 80% of 100 = $80. The price would be $180.
Decreasing this by 25% 25% of 180 = $45; 180-45 = $135.
25% of 100 is not the same as 25% of 180.
ALL of their points are common. If you multiply each side of the first equation by 2, you'll see that they're both the same line.
