Your brother has a bag of marbles containing 1 red marble, 2 blue marbles, and 47 green marbles. He claims he'll give you $10 if you pull the red marble but just $5 if you pull a blue marble. However, if you pull a green marble, you will owe him $3. What is the expected value each time you pull a marble? Round to the nearest cent. Do not round until your final answer.

Write the expression as a constant , a single trigonometric function, or a power of a trigonometric function. sin x cos x/ tan x

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.

Select the margin of error that corresponds to the sample mean that corresponds to each population: a population mean of 25, a standard deviation of 2.5, and margin of error of 5%