Abicycle manufacturing company makes a particular type of bike. each child bike requires 4 hours to build and 4 hours to test. each adult bike requires 6 hours to build and 4 hours to test. with the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. if c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week.

no, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

no, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Calculate the missing value. round the answer to on decimal place. start with 70, increase it by 21%, and end up with

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?