1. A) Is there a number x ∈ R, so cos x = 0.8 and sin x = 0.2? b) Same question for cos x = 0.8 and sin x = 0.6 2. Show that for any x ∈ R: a) sin^{3}x + cos^{3} = (sin x + cos x)(1- sin x * cos x) b) sin^{4} x + cos^{4} x = 1 - 2sin^{2} x * cos^{2}x

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?

Acompany charges $0.10 for each letter engraved. bobby plans to spend no more than $5.00 on the engraving on a jewelry box. write and solve an inequality to find the maximum number of letters he can have engraved.

5. (04.07)which of the following exponential functions goes through the points (1, 12) and (2, 36)? (2 points)f(x) = 3(4)^xf(x) = 4(3)^-xf(x) = 3(4)^-xf(x) = 4(3)^x