Aaron has a budget of $100 per month to spend on lunch. He made a table showing the total amount of lunch money he will have left after the given number of lunches. Number of lunches 0 5 10 15 Total amount of lunch money left ($) 100 75 50 25 Which equation, in standard form, represents the relationship between the number of lunches, x, and the amount of lunch money Aaron will have left, y? 5x + y = 100 x + 100y = 5 100x + y = 5 x + 5y = 100

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.

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

What is the value of x in the following equation. -x ^3/2 = -27