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Thus ;
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The price of a silk scarf is $32. The sales tax is $1.92. What is the sales tax rate?
2 answers:
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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.
Confused what the question is. Are you looking for the product or the zeroes?
If you are looking for the product, then:
Use foil to get: sec²(1) - sec²(-csc²) -1(1) -1(-csc²)
= sec² + sec²csc² - 1 + csc²
= sec²csc² + sec² + csc² - 1
= sec²csc² + 1 - 1 (NOTE: sec² + csc² = 1 is an identity)
= sec²csc²
Answer: sec²csc²
***************************************************
If you are looking for the zeroes, then:
Using the zero product property, set each factor equal to zero and solve.
<u>First factor:</u>
sec²Θ - 1 = 0
sec²Θ = 1
secΘ = 1, -1
remember that secΘ is
= 1
= -1
cross multiply to get:
cosΘ = 1 cosΘ = -1
use the unit circle (or a calculator) to find that Θ = 0 and π
<u>Second factor:</u>
1 - csc²Θ = 0
1 = csc²Θ
1, -1 = cscΘ
remember that cscΘ is
= 1
= -1
cross multiply to get:
sinΘ = 1 sinΘ = -1
use the unit circle (or a calculator) to find that Θ = and
Answer: 0, π, ,