Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000143 mm, while the length of the second strain measures 0.0000000937 mm. How much larger is the first strain than the second?

1.53 times

Step-by-step explanation:

Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000143 mm, while the length of the second strain measures 0.0000000937 mm. How much larger is the first strain than the second?

We would have:

First strain : Second strain

0.000000143 mm : 0.0000000937 mm

How much larger is the first strain than the second?

We divide both by the length of the second strain

0.000000143/0.0000000937 : 0.0000000937 / 0.0000000937

1.52614727855 times

Approximately = 1.53 times

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}

the answer is two. hope this !