In a school poetry contest, 4 out of the 12 students who entered will wins small prize. half of the remaining students receive a certificate. how many students get certificate?

1/3 of the students

Step-by-step explanation:

4/12 of the students wins the small prize

so, 8/12 of the students will not get a small prize

1/2 of 8/12 = 4/12 = 1/3

1/3 of the students will get the certificate.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

answer: a.   one is a factor of every whole number since every number is divisible by itself.