A hyperbola centered at (4, –1) has a vertex at (4, 6) and a focus at (4, 24). Write the equation of the hyperbola by completing the statements below. \
The quantity ? squared over a squared will be written first in the equation.
The quantity ? squared over b squared will be written second in the equation.
The value of a is ?
The value of b is ?

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

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?

Factor the polynomial by its greatest common monomial factor.