Theorem: in any circles the same ratio of arc length to radius determines a unique central angle that the arcs subtend; and conversely, equal central angles determine the same ratio of arc length to radius. prove the theorem above using the definition of the radian measure of an angle.

Given the parent function of [tex]f(x)=x^4[/tex], what change will occur when the function is changed to [tex]f(\frac{1}{2} x)[/tex]?

Mrs. avila is buying a wallpaper border to go on all of her kitchen walls. she wants to buy 5 extra feet of wallpaper border than she needs to be sure she has enough. she buys 55.5 feet of the border. the store owner selling the border uses the width of mrs. avila's kitchen to determine that the length of her kitchen must be 14.5 feet.

Ur environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 4.04.0 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 2525 samples is 4.44.4 ppm with a standard deviation of 0.80.8. assume the population is normally distributed. a level of significance of 0.020.02 will be used. make the decision to reject or fail to reject the null hypothesis. answer tables