Show that the given curve c(t) is a flow line of the given velocity vector field f(x, y, z).
c(t) = (t^2, 2t − 6, 3sqrt( t > 0; f(x, y,z) = ( y+6, 2, 9/2z)
c'(t) = ?
f(c(t)) = ?

What is the value of x in the equation (2)3) (x+6)= -18 a. -36 b. -33 c. -24 d. -18

Arestaurant charges $100 to rent its banquet room for an event. it also charges $15 to serve dinner to each guest. write an equation for the total cost of the banquet room in terms of the number of guests. deine your variables. what is the total cost of the banquet room for 20 guests?

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).