Let U be the group of units in Z109 together with the usual multiplication mod 109. Show that U is an abelian group of order 108. (Hint: First note that 109 is a prime number. How many element in U satisfy a2 = 1?)

Factor the expression using the gcf. the expression 21m−49n factored using the gcf

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?

3. a sum of $2700 is to be given in the form of 63 prizes. if the prize is of either $100 or $25, find the number of prizes of each type.