Bryce has two small buckets each containing numbered tiles. the tiles in bucket a are the odd numbers from 1 to 31, one tile per number. the tiles in bucket b are the even numbers from 2 to 32, one tile per number. bryce draws one tile from bucket a. on the number line below "bucket a," select the point that represents the probability of drawing a tile that is a prime number from bucket a. he then draws one tile from bucket b. on the number line below "bucket b," select the point that represents the probability of drawing a tile that is evenly divisible by 6 from bucket b.

total number of prime numbers in bucket A = 10(  3 5 7 11 13 17 19 23 29 31)

Probability = favorable outcomes/ total outcomes = 10/31

total number of numbers evenly divisible by 6 in bucket B = 5(6 12 18 24 30)

probability = 5/31

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.

the bolded word " farsighted" could be replaced with visionary.