Let p=2n+1 for n=10, 20, 30, or 40. For which value of n does p2−1 have the most factors?

For n= 40 p has 7 factors

For n= 20 p has 7 factors

For n= 10 p has 6 factors

For n= 30 p has 6 factors

Step-by-step explanation:

p = 2n + 1

Putting the value of n= 10

p1= 20+1= 21

Putting the value of n= 20

p2= 40+1= 41

Putting the value of n= 30

p3= 60+1= 61

Putting the value of n= 40

p4= 80+1= 81

p2- 1= (p+1)(p-1)

         = (81+1)(81-1)

         =( 82)(80)

          = 6560

             = (1312)5

             = 328)4)5

             = 41 (2)(2)(2)(2)(2)(5)

p2- 1= (p+1)(p-1)

         = (61+1)(61-1)

          =( 62)(60)

          =3720

            = (465)(8)

            = (93)(5)(8)

             = (31)(3)(5)(2)(2)(2)

p2- 1= (p+1)(p-1)

         = (41+1)(41-1)

          =( 42)(40)

          = 1680

           = (7)(3)(5*2)(2*2*2)

p2- 1= (p+1)(p-1)

         = (21+1)(21-1)

         =( 22)(20)

         = 440

         = (11)(2)(5)(2)(2)

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.