We have two stacks of styrofoam cups. One stack has 6 cups, and its height is 15 cm. The other stack has 12 cups, and its height is 23 cm. How many cups are needed

37.5 cups

Step-by-step explanation:

Given data

First stack (n)= 6cups ,

height = 15cm

Second stack(n) = 12 cups

Height = 23cm.

Solution:

First we need to calculate for the average

= H1 - H2 / n1 - n2

= 15 - 23 / 6 - 12

= -8 / - 6

= 4/3.

Next we need to obtain the height of 50cm using our average gotten.

= 50 / 4/3

= 75/2

= 37.5

37.5 cups would be needed to get a height of 50cm.

took the test it's 94

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}