Me. fowler has 16 homework papers and 14 exit tickets to return. ms. rivera has 64 homework papers and 60 exit tickets to return. for each teacher write a ratio to represent the umber of homework papers to number of exit tickets they have to return. are the ratios equivalent? explain.

Step-by-step explanation:

Ms Fowler's ratio would be 8:7 and Ms Rivera's would be 16:15, they are not equivalent because the numbers didn't come out to the same ratio when i divided them and 16 and 1 aren't divisible by the same numbers.

here are the steps i took:

1. wrote down the original ratios (16:15 and 64:60)

2. I divided all the numbers by 2 and got them reduced to 8:7 and 30:32

3. I saw that the 8:7 couldn't be divided anymore, so I left it and divided 30 by 2 and 32 by 2 and got 16:15

4. I saw that I couldn't divide those anymore so I compared the ratios and saw that they were not the same so they weren't equal.

hope this helped!

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}