One third of the students in the marching band signed up for the pep band. Then five students changed their mind. If there are 31 students in the pep band, how many students are in the marching band?

10 1/3 students

Step-by-step explanation: 31 times 1/3 is 31/3, which is then simplified to 10 1/3.

Hope this helps! :-)

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.