Shawn is starting a woodworking project for which he needs a large number of 2x4s. He plans to buy 2x4s that are 6 feet in length and cut them into the following sizes:

eight pieces that are 12.5 inches long
six pieces that are 8.75 inches long
nine pieces that are 6.25 inches long
Note: A 2x4 ("two by four") is a rectangular piece of wood that is two inches high and four inches wide, as shown in the picture. It can have varying lengths. The 2x4s that Shawn is buying have a length of 6 feet, or 72 inches.

Find the most efficient way for Shawn to cut these pieces. In other words, what is the fewest number of boards he can cut from?

What is the smallest number of 2x4s that Shawn needs to buy in order to cut all of the pieces his project requires?
a0

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

The base of a triangle exceeds the height by 7 centimeters. if the area is 400 square centimeters, find the length of the base and the height of the triangle.

Three baby penguins and their father were sitting on an iceberg 0.50.50, point, 5 meters above the surface of the water. the father dove down 4.74.74, point, 7 meters from the iceberg into the water to catch dinner for his kids. what is the father penguin's position relative to the surface of the water?