In the figure below, lines m and n are parallel: Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.

In the diagram shown, ∠2 measures 77 degrees. What is the measure of ∠4?

5 degrees
77 degrees
103 degrees
180 degrees

Question part points submissions used suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. of these 100 tickets, only 12 are winning tickets. the generalized pigeonhole principle guarantees that there must be a streak of at least l losing tickets in a row. find l.

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.

7. if the value of x varies directly with the value of y, and x = 3 when y = 21. what is the valu y, and x = 3 when y = 21. what is the value of x when y = 105?