Proposition 2.30. suppose x and y are topological spaces, and f : x → y is any map. (a) f is continuous if and only if f (a c f(a) for all asx. (b) f is closed if and only if f (a) 2 f(a) for all a cx. (c) f is continuous if and only if f -(int b) ) for all b cy. (d) f is open if and only if f-'(int b) 2 int f-'(b) for all b c y.

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

What’s 8y+48 and factor each expression completely

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.