Calculate the sample mean of x without the use of mean(), sd(), sum(), or . Hint: Recall that vectors in R are column vectors. (Although when you display them, they often look like row vectors.) You may need to create a second vector, which is allowed, and should also look into the function crossprod(). Essentially, you need to use matrix algebra to recreate the formulas above. You may use mean() to check your answer.

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For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.

How would you cite different books by the same author on the works cited page? moore, jack h. folk songs and ballads. salem: poetry press, 1999. print. moore, jack h. ballads in poetry – a critical review. dallas: garden books, 1962. print. moore, jack h. folk songs and ballads. salem: poetry press, 1999. print. –––. ballads in poetry – a critical review. dallas: garden books, 1962. print. moore, jack h. ballads in poetry – a critical review. dallas: garden books, 1962. print. moore, jack h. folk songs and ballads. salem: poetry press, 1999. print. moore, jack h. ballads in poetry – a critical review. dallas: garden books, 1962. print. –––. folk songs and ballads. salem: poetry press, 1999. print.