1. ben said: for every $60 the sixth graders plan to raise, the seventh graders plan to raise $90. he looks at the principal's thermometers and sees that $60 is at the same place on the sixth-grade thermometer as $90 is on the seventh-grade thermometer.
ben also makes the claim: for every $30 the sixth graders plan to raise, the seventh graders plan to raise $45.
do you agree with this claim? explain your reasoning.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure