Aformal description of the problems: the input is a set x of n points: x = {x1 < x2 < . . < xn}, where each xi (1 ≤ i ≤ n) represents a house. we need to select a subset y ⊆ x such that: (1) for every point xi ∈ x, there is a point xj ∈ y with |xi − xj | ≤ 5, and (2) the 2 size of y is minimum, subject to condition (1). describe a polynomial time greedy algorithm for solving this problem. you need to prove the correctness of the algorithm.

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

Abarbecue sold 26 hamburgers and hot dogs. hamburgers sell for $3.50 each and hot dogs sell for $2.00 each. if the barbecue made $70 in sales, determine and state the number of hot dogs sold.

Write the equation in logarithmic form 8^x=64