Let P (n) be the statement that 1³ + 2³ + · · · + n³ = (n(n + 1)/2)² for the positive integer n. a) What is the statement P (1)? b) Show that P (1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f ) Explain why these steps show that this formula is true whenever n is a positive integer.

About 60% of the normal humanbeing's body weight is composed ofwater. how much of a 125 poundperson is water weight? f 72 pounds h 76 poundsg 75 pounds i 80 pounds

Awater truck is filling a swimming pool. the equation that represents this relationship is y=19.75x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool.

Sara has been reading about different types of financial grants, including federal pell grants, academic competitiveness grants, smart grants, and teach grants. which statement about these grants is true? filling out a fafsa will not her apply for these grants. she will not have to pay back any funds she receives from these grants. these grants only go to students with less than a 3.0 gpa. she will have to pay back all the funds she receives from these grants.