Nathaniel buys 28 gallons of gas for $56. He will put some more gas in his tank again
and spend $39. How many gallons of gas did he put in the second time? Explain how
you found the answer.

19.5 gallons

Step-by-step explanation:

Hi, to answer this question, we have to use proportions:

Nathaniel buys 28 gallons of gas for $56, so the proportion is:

$56 / 28 gallons.

For $39:

$39 / x gallons

Solving for x (number of gallons)

56/28 = 39/x

x = 39 / (56/28)

x = 19.5 gallons

Feel free to ask for more if needed or if you did not understand something.

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}

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.