Ateam t-shirt costs $3 per adult and $2 per child. on a certain day, the total number of adults (a) and children (c) who bought shirts was 100, and the total money collected was $275. which of the following options represents the number of children and the number of adults who purchased team shirts that day, and the pair of equations that can be solved to find the numbers? 75 children and 25 adults equation 1: a + c = 100 equation 2: 3a − 2c = 275 75 children and 25 adults equation 1: a + c = 100 equation 2: 3a + 2c = 275 25 children and 75 adults equation 1: a + c = 100 equation 2: 3a − 2c = 275 25 children and 75 adults equation 1: a + c = 100 equation 2: 3a + 2c = 275

Eric has challenged himself to walk 24,000 steps in 4 days. if eric walks the same number of steps each day, which function represents the number of steps eric still needs to walk to reach his goal with respect to the number of days since he started his challenge? a. y = 8,000x − 24,000 b. y = -8,000x + 24,000 c. y = 6,000x − 24,000 d. y = -6,000x + 24,000

Astore has clearance items that have been marked down by 60%. they are having a sale, advertising an additional 55% off clearance items. what percent of the original price do you end up paying?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.