Is a measure of 24 inches "far away from a mean of 16 inches? As someone with knowledge of statistics, you answer it depends" an
d request the standard deviation of the underlying data
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 24 inches from 16 inches?
(b) Is 24 inches far away from a mean of 16 inches?
(c) Suppose the standard deviation of the underlying data is 5 inches. Is 24 inches far away from a mean of 16 inches?
(a) 24 inches is
standard deviation(s) away from 16 inches.
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In order to construct this equation, we will use the variables: V to represent mixture volume (40 ml) C to represent mixture concentration (0.32) v₁ to represent volume of first solution (40 / 4 = 10 ml) c₁ to represent concentration of first solution (0.2) v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml) c₂ to represent the concentration of the second solution
We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus: VC = v₁c₁ + v₂c₂ 40(0.32) = 10(0.2) + 30c
For this exercise it is important to know the definition of "Vertical Angles".
When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".
By definition, Vertical angles are congruent, which means that the have the equal measure.
In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.
You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below: