Grace starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 14
1
4
each week for a number of weeks, w. she writes the expression 100(14
1
4
)w to find the amount of radioactive substance remaining after w weeks.

ryan starts with 1 milligram of a radioactive substance. the amount of the substance decreases by 40% each week for a number of weeks, w. he writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks.

use the drop-down menus to explain what each part of grace’s and ryan’s expressions mean.

Given: ∆mop p∆mop =12+4 3 m∠p = 90°, m∠m = 60° find: mp, mo

Design an er diagram for keeping track of information about votes taken in the u. s. house of representatives during the current two-year congressional session. the database needs to keep track of each u. s. state's name (e. g., texas', new york', california') and include the region of the state (whose domain is {northeast', midwest', southeast', southwest', west'}). each congress person in the house of representatives is described by his or her name, plus the district represented, the start date when the congressperson was first elected, and the political party to which he or she belongs (whose domain is {republican', democrat', 'independent', other'}). the database keeps track of each bill (i. e., proposed law), including the bill name, the date of vote on the bill, whether the bill passed or failed (whose domain is {yes', no'}), and the sponsor (the congressperson(s) who sponsored - that is, proposed - the bill). the database also keeps track of how each congressperson voted on each bill (domain of vote attribute is {yes', no', abstain', absent'}). additional information:

1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. subtraction property of equality 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 substitution 3. m∠1 + m∠2 = m∠3 + m∠2 definition of complementary 4. m∠1 = m∠3 given