Randy chooses to survey every 5th student in the cafeteria. He surveys a total of 140 students and finds that 84 support buying new PE equipment. If this is a representative sample, how many total students could he predict would support the purchase of new PE equipment our of the entire student body?

He can predict that 420 students will be in support of the purchase.

Step-by-step explanation:

Since Randy surveyed one student out of every 5 he came across in the cafeteria, it means that if he came across five people, he will survey one, if he came across ten students, he will survey 2 and so on.

If then he surveyed a total of 140 students, then we can actually multiply the number by 5 to know the exact number of students he possibly came across in the cafeteria:

= 140 × 5

= Total of 700 students

If 84 out of the surveyed students supported the purchase, we can find what that figure represents in the total number of students in the cafeteria:

84/140 = x/700

We cross multiply

140 × X = 84 × 700

140X = 58,800

X = 58,800/140

X = 420 students

Therefore, he can predict that 420 students out of a total of 700 students in the cafeteria will be in support of the purchase of the P.E equipment

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.