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Charra [1.4K]
2 years ago
10

Let f(x)=cos(arctanx). What is the range of f?

Mathematics
1 answer:
Alenkasestr [34]2 years ago
4 0
-π/2 < arctan(x) < π/2

So cos(π/2) < cos(arctan(x)) < cos(0)

0 < cos(arctan(x)) < 1
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From a group of 13 women and ​12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can
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The total number of ways the study can be selected is: 637065

Given,

Total number of women in a group= 13

Total number of men in a group = 12

Number of women chosen = 8

Number of men chosen = 8

∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.

This in the form of combination factor = nCr

                                                     ∴ nCr = n!/(n₋r)! r!

13C₈ = 13!/(13 ₋ 8)! 8!

        = 13!/5!.8!

        = 1287

12C₈ = 12!/(12₋8)! 8!

        = 12!/5! 8!

        = 495

Now multiply both the combinations of men and women

= 1287 × 495

= 637065

Hence the total number of ways the study group is selected is 637065

Learn more about "Permutations and Combinations" here-

brainly.com/question/11732255

#SPJ10

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