Rika works in the perfume department at hoover’s department store. she is giving away samples of a new fragrance and a new scented hand lotion to customers that pass by her station. she is required to hand out a total of 114 samples during her shift. she has already handed out 36 samples, which represents 1/3 of the number of fragrance samples and 1/4 of the number of hand lotion samples that she must hand out.

write a system of equations for this problem situation. let x represent the number of fragrance samples, and let y represent the number of hand lotion samples.

Witch represents the inverse of the function f(x)=1/4x-12

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Helll ! 1,400 tons of wheat of two different varieties was delivered to the silo. when processing one variety, there was 2% of waste and 3% during the processing of the second variety of wheat. after the processing, the amount of remaining wheat was 1,364 tons. how many tons of each variety of wheat was delivered to the silo?