Answer and explanation:
1. It is commonly referred to as the arithmetic average: the mean measure of central tendency is also referred to as the arithmetic mean or arithmetic average or just average.
It is algebraically defined (that is, there is an equation you can use to calculate its value): the mean can be represented by the algebraic equation
a1+a2+a3...ai/n
2. There can be more than one median where there are an even number of data points and not odd number, in which the two middle number are divided by 2
It can be found when there are undetermined scores: median can be found with undetermined scores
3. It corresponds to an actual score in the data: the mode is an actual value in the data that appears more frequently than other values
There can be more than one: there can be more than one mode(bimodal,trimodal,multimodal) where 2 or more values appear the same number of times
1 Inch = 25.4 mm
4.5 Inches = ? mm
mm in 4.5 inches = 4.5*25.4 mm = 114.3 mm
<span>n = 5
The formula for the confidence interval (CI) is
CI = m ± z*d/sqrt(n)
where
CI = confidence interval
m = mean
z = z value in standard normal table for desired confidence
n = number of samples
Since we want a 95% confidence interval, we need to divide that in half to get
95/2 = 47.5
Looking up 0.475 in a standard normal table gives us a z value of 1.96
Since we want the margin of error to be ± 0.0001, we want the expression ± z*d/sqrt(n) to also be ± 0.0001. And to simplify things, we can omit the ± and use the formula
0.0001 = z*d/sqrt(n)
Substitute the value z that we looked up, and get
0.0001 = 1.96*d/sqrt(n)
Substitute the standard deviation that we were given and
0.0001 = 1.96*0.001/sqrt(n)
0.0001 = 0.00196/sqrt(n)
Solve for n
0.0001*sqrt(n) = 0.00196
sqrt(n) = 19.6
n = 4.427188724
Since you can't have a fractional value for n, then n should be at least 5 for a 95% confidence interval that the measured mean is within 0.0001 grams of the correct mass.</span>
Answer:
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Step-by-step explanation:
Required
Show that:
To make the proof easier, I've added a screenshot of the triangle.
We make use of alternate angles to complete the proof.
In the attached triangle, the two angles beside are alternate to and
i.e.
Using angle on a straight line theorem, we have:
Substitute values for (1) and (2)
Rewrite as:
<em></em><em> -- proved</em>
Because 44 is a bigger number than 4 it is 11 times bigger so the difference is larger than a proportional number