Description
Find the smallest number x such that tan e ^x is undefined.
Round your answer to five decimal places.
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Explanation & Answer
e^x = pi
turns into..
ln pi = x
tan(t) = sin(t) / cos(t)
tan(t) is undefined where cos(t) = 0
tan(t) is zero where sin(t) = 0
cos(t) = 0 at t = pi/2 + n pi; n integer
sin(t) = 0 at t = n pi; n integer
e^x = exp(x) >= 0 for all x
so t < 0 aren't included.
So the smallest t are those closest to, but not equal to zero.
For sin(t) = 0, t = pi
For cos(t) = 0, t = pi/2
so
tan(exp(x)) = 0 when x = ln(pi)
tan(exp(x)) undefined when x = ln(pi/2)
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Learning Resources
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Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.
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Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.
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Required Media
Laureate Education (Producer). (2016d). Descriptive statistics [Video file]. Baltimore, MD: Author.
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population mean for the 100 listing prices was $671,185.14. Population Standard Deviation is a measure of how spreads out numbers are. Researchers use statistics to estimate parameters, refer to a numerical property of a population. The real estate population Standard Deviation was σ= $274,980.89.2. Divide the 100 listing prices into 10 samples of n=10 each. Each of your 10 samples will tend to be random if the first sample includes houses 1 through 10 on your spreadsheet, the second sample consists of houses 11 through 20, and so on.Compute the mean of each of the 10 samples and list them:Answer- n=10 (Sample 1: listings 1-10) Mean = $561,808.90 n=10 (Sample 2: listings 11-20) Mean = $602,175.00 n=10 (Sample 3: listings 21-30) Mean = $783,299.50 n=10 (Sample 4: listings 31-40) Mean = $738,140.00 n=10 (Sample 5: listings 41-50) Mean = $842,058.80 n=10 (Sample 6: listings 51-60) Mean = $817,098.80 n=10 (Sample 7: listings 61-70) Mean = $626,167.60 n=10 (Sample 8: listings 71-80) Mean = $671,445.00 n=10 (Sample 9: listings 81-90) Mean = $498,889.00 n=10 (Sample 10: listings 91-100) Mean = $570,768.80 3. Compute
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not, to the population mean of the 100 listing prices
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the 10 means to the population standard deviation of all 100 listing
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