A manufacturer of projection TVs must ship a total of at least 1000 TVs to its two central warehouses, x to the first warehouse and y to the second warehouse. Each warehouse can hold a maximum of 750 TVs. The first warehouse already has 150 TVs on hand, whereas the second has 50 TVs on hand. It costs $10 to ship a TV to the first warehouse, and it costs $18 to ship a TV to the second warehouse. How many TVs should be shipped to each warehouse to minimize 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.

The length of the line segment joining the midpoints of sides ab and bc of the parallelogram abcd is 10. find the length of diagnol ac

Convert the mixed numbers into improper fractions. convert the improper fraction to mixed numbers.