Which number is a factor of 15, but not a multiple of 3
2 answers:
We know that factors are numbers we can multiply together to get another number.
So 1 and 15 are factors of 15.
Also,
So 3 and 5 are factors of 15.
We have got 1, 3, 5, 15 all are factors of 15.
Multiple is a number that can be divided by another number without a remainder.
So we know that 3 is a multiple of 3, as and also 15 is a multiple of 3, as
.
But 1 and 5 are not multiples of 3.
We have got the required answer.
1 and 5 are factors of 15 but not multiples of 3.
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Given:
A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.
To find:
The total surface area of the prism.
Solution:
We have,
Height of prism = 7½ = 7.5
Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because
So, the base of the prism is a right triangle.
Area of a triangle is
The area of the base is equal to the area of the top, i.e., sq units.
Perimeter of the base is
The curved surface area of the prism is
Now, the total area of the prism is
Therefore, the total surface area of the triangular prism is 285 square units.
Answer:
Explain the circumstances for which the interquartile range is the preferred measure of dispersion
Interquartile range is preferred when the distribution of data is highly skewed (right or left skewed) and when we have the presence of outliers. Because under these conditions the sample variance and deviation can be biased estimators for the dispersion.
What is an advantage that the standard deviation has over the interquartile range?
The most important advantage is that the sample variance and deviation takes in count all the observations in order to calculate the statistic.
Step-by-step explanation:
Previous concepts
The interquartile range is defined as the difference between the upper quartile and the first quartile and is a measure of dispersion for a dataset.
The standard deviation is a measure of dispersion obatined from the sample variance and is given by:
Solution to the problem
Explain the circumstances for which the interquartile range is the preferred measure of dispersion
Interquartile range is preferred when the distribution of data is highly skewed (right or left skewed) and when we have the presence of outliers. Because under these conditions the sample variance and deviation can be biased estimators for the dispersion.
What is an advantage that the standard deviation has over the interquartile range?
The most important advantage is that the sample variance and deviation takes in count all the observations in order to calculate the statistic.