Amanufacturing company receives orders for engines from two assembly plants. plant i needs at least 45 engines, and plant ii needs at least 32 engines. the company can send at most 120 engines to these assembly plants. it costs $30 per engine to ship to plant i and $40 per engine to ship to plant ii. plant i gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant ii gives similar $10 rebates. the manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. how many engines should be shipped to each plant to minimize shipping costs? what is the minimum cost?

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Aflute is on sale for 20% off. including the discount and 8% tax, the sales price is $216.

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?