Determine whether each integral is convergent or divergent.

1- 1/(x-2)^3/2 dx, limits ( infinite to 3)

2- (1/3-4x)dx, limits (0 to -infinite)

3- e^(-5p) dx, limits ( infinite to 2)

4- (x^2/(sqrt(1+x^3)))dx , limits ( infinite to 0)

5- lnx/x dx , limits(infinite to 1)

6- 1/(x^2 +x)dx , limits (infinite to 1)

7- 3/x^5 dx ,limits (1 to 0)

8- dx/(x+2)^1/4 , limits (14 to -2)

9- 1/(x-1)^1/3 , limits (9 to 0)

10- e^x /((e^x) -1), limits (1 to -1)

11- z^2 lnz dz ,limits( 2 to 0)

12- s={(x, y) | x>= 1,0 <= y <=e^-x}

The data shown in the table below represents the weight, in pounds, of a little girl, recorded each year on her birthday. age (in years) weight (in pounds) 2 32 6 47 7 51 4 40 5 43 3 38 8 60 1 23 part a: create a scatter plot to represent the data shown above. sketch the line of best fit. label at least three specific points on the graph that the line passes through. also include the correct labels on the x-axis and y-axis. part b: algebraically write the equation of the best fit line in slope-intercept form. include all of your calculations in your final answer. part c: use the equation for the line of best fit to approximate the weight of the little girl at an age of 14 years old.

Given: and prove: what is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).