Question

Christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. She sets up a tape measure and throws the yoyo 3 times. Her data are charted below.

Answer 1

This is a geometric series.\[a_n = a_1*r ^{n-1}\]

Answer 2

where a_1 is the initial term, 3, and r is the common ratio, 0.7.

Answer 3

this is the formula for a sum of a geometric series:\[S_n = \frac{ a_1(1-r^n) }{ 1-r }\]

Answer 4

Use the formula
\[\large\rm Sum=\frac{initial(1-(\frac{rate}{100})^{times}) }{1-(\frac{rate}{100})}\]

Answer 5

what is r

Answer 6

r is the rate, which is 0.7, since it becomes 70% shorter.

Answer 7

then what is the times

Answer 8

times is the number of throws.

Answer 9

so 10?

Answer 10

yes

Answer 11

that gave me 3.02 which isn't an option

Answer 12

initial is 3
Rate is 70/100
Times is 10
Try again using these values

Answer 13

You divided the rate 0.7 by 100. 0.7 is already divided by 100.

Answer 14

wait np 9.72?

Answer 15

Correct

Answer 16

you guys rock