Liam and Evan are mixing paint. Liam uses 2 quarts of yellow paint and adds 314 jars of blue paint. Evan uses 12 quart of yellow paint and adds 512 jars of red paint. They end up with the same volume of paint. Part A Which equation represents the situation? 2x+314x=12x+512x 2+314x=12+512x 2x+314y=12a+512b 2+512x=12+314x Part B What volume of paint did each boy mix? −23 quart 23 quart 112 quarts 416 quarts

In the equations, a and b represent the price per night for a room in hotel a and hotel b, respectively, w weeks after september 1 last autumn. what was the price per night in hotel a when it was equal to the price per night in hotel b? a = 240 − 20w b = 320 − 30w

Acommunity group sells 2,000 tickets for its raffle. the grand prize is a car. neil and 9 of his friends buy 10 tickets each. when the winning ticket number is announced, it is found to belong to neil's group. given this information, what is the probability that the ticket belongs to neil? a.1/5 b.1/10 c.1/200 d.1/4

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.