Auniversal studios admission ticket is on sale for 20% off the original price of $115. if there is 7.5% sales tax, what is the final price of the ticket.

Medium sodas cost $1.25 and hot dogs cost $2.50. natalie’s group brought in pizzas but is buying the drinks at concession stand. how many medium sodas can natalie’s group buy with $20? make a table to show answer.

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.

Find the exact value of each of the following. in each case, show your work and explain the steps you take to find the value. (a) sin 17π/6 (b) tan 13π/4 (c) sec 11π/3