Rewrite with only sin x and cos x. cos 2x + sin x

1 + 3 sin x
1 + 3 sin2x
1 - 2 sin2x + sin x
1 + 2 sin2x + sin x

Select the correct answer from the drop-down menu. this graph represents the inequality x+2< 4,2x> 3,x+6< 12,2x> 12

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.

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?