The following section is a statement from the rental agreement tim signed when he rented his car this past weekend. "upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. the approximate fuel level will be recorded on the check-out sheet and verified with initials by the vehicle renter. one copy of the check-out sheet will be given to the customer. another copy will be kept with the on-site records of the vehicle. "the rented vehicle must be returned with a minimum fuel level the same as that indicated on the check-out sheet. a vehicle returned with a fuel level less than the approximate level indicated on the check-out sheet will be completely refueled with on-site pumps. the price of the fuel used to refuel the vehicle will be added to the renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge." tim forgot to refuel the vehicle when he returned it. his check-out sheet indicates that the vehicle had about 1/2 of a tank left. the tanks is now nearly empty. if it takes 11.75 gallons of gas to refuel the car tim rented, how much extra should he expect to pay because he forgot to get gas? a. $26.44 b. $31.44 c. $52.88 d. $57.88

Option D. $57.88

Solution:

The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet.

Tim's Check-Out sheet indicates that the vehicle had about 1/2 of a tank left.  Tim forgot to refuel the vehicle when he returned it. The tanks is now nearly empty.

A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps.

Renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge.

It takes 11.75 gallons of gas to refuel the car Tim rented.

How much extra should he expect to pay because he forgot to get gas?

Extra pay of Tim: P=?

P=($4.50/gallon) n + $5

Number of gallons: n=11.75 gallons

Replacing n by 11.75 gallons in the equation above:

P=($4.50/gallon)(11.75 gallons)+$5

P=$52.875+$5

P=$57.875

P=$57.88

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}

54.864 meters

step-by-step explanation: