NASA launches a rocket at t = 0 seconds. Its position (height), in meters above sea-level, as a function
time, t, is given by s(t): - 4.9t2 + 187t + 192. Use this position function to answer the following
questions. Round solutions to three decimal places, if necessary.
Answers
The rocket splashes down after 39.164 seconds. The rocket reach its peak height 19.081 seconds after launch. The rocket peaks at 1976.13 meters above sea level.
The function of height is given by,
h(t) = -4.9t² + 187t + 192
Once the rocket will be splashed down in sea, means the height of the rocket will be zero. Means
x h(t) = 0
-4.9t² + 187t + 192 = 0
Solving the quadratic equation with quadratic formula, we have two values of t
t = 39.164 and t = -1.001
We will consider the positive value of the time
So the answer is 39.164 seconds.
For getting the maximum value, we should differentiate the function of height and make it equal to zero.
[tex]\frac{dh(t)}{dt} = \frac{d}{dt} (-4.9t^2 + 187 t + 192)[/tex]
For maximum value of h, [tex]\frac{dh (t)}{dt} = 0[/tex]
0 = -4.9 × (2t) + 187
t = 19.081 seconds
At this time, the height of rocket will be maximum.
So putting the vaiue in the given function.
h = -4.9 × (19.081)² + 187 (19.081) + 192
h = 1976.13 meters
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Related Questions
Mar. 1) Egert invested $159,000 cash along with $22,300 in office equipment in the company.
Answers
The transactions of Egert's Company are entered in the general journal as follows:
General JournalDate Account Titles Debit Credit
Mar. 1 Cash $159,00
Office Equipment $22,300
Common stock $181,300
Mar. 2 Prepaid Rent $1,200
Cash $1,200
Mar. 3 Office equipment $3,300
Office supplies $1,580
Accounts Payable $4,880
Mar. 6 Cash $4,300
Service Revenue $4,300
Mar. 9 Accounts Receivable $7,800
Service Revenue $7,800
Mar. 12 Accounts Payable $4,800
Cash $4,800
Mar. 19 Prepaid Insurance $5,300
Cash $5,300
Mar. 22 Cash $4,700
Accounts Receivable $4,700
Mar. 25 Accounts Receivable $4,200
Service Revenue $4,200
Mar. 29 Dividends $5,400
Cash $5,400
Mar. 30 Office supplies $900
Accounts Payable $900
Mar. 31 Utility expenses $800
Cash $800
What is the general journal?The general journal is the first accounting record of a business transaction.
The general journal identifies the accounts involved in each transaction, specifying which will be debited or credited in the general ledger.
Transaction Analysis:Mar. 1 Cash $159,00 Office Equipment $22,300 Common stock $181,300
Mar. 2 Prepaid Rent $1,200 Cash $1,200
Mar. 3 Office equipment $3,300 Office supplies $1,580 Accounts Payable $4,880
Mar. 6 Cash $4,300 Service Revenue $4,300
Mar. 9 Accounts Receivable $7,800 Service Revenue $7,800
Mar. 12 Accounts Payable $4,800 Cash $4,800
Mar. 19 Prepaid Insurance $5,300 Cash $5,300
Mar. 22 Cash $4,700 Accounts Receivable $4,700
Mar. 25 Accounts Receivable $4,200 Service Revenue $4,200
Mar. 29 Dividends $5,400 Cash $5,400
Mar. 30 Office supplies $900 Accounts Payable $900
Mar. 31 Utility expenses $800 Cash $800
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Question Completion:1 Egert invested $159,00 cash along with $22,300 in office equipment in the company in exchange for common stock. 2 The company prepaid $1,200 cash for six months' rent for an office. The company's policy is to record prepaid expenses in balance sheet accounts. 3 The company made credit purchases of office equipment for $3,300 and office supplies for $1,580. Payment is due within 10 days. 6 The company completed services for a client and immediately received $4,300 cash. 9 The company completed a 7,800 project for a client, who must pay within 30 days. Mar. 12 The company paid $4,800 cash to settle the account payable created on March 3. Mar. 19 The company paid $5,300 cash for the premium on a 12-month insurance policy. The company's policy is to record prepaid expenses in balance sheet accounts. Mar. 22 The company received $4,700 cash as partial payment for the work completed on March 9. Mar. 25 The company completed work for another client for $4,200 on credit. Mar. 29 The company paid $5,400 cash in dividends. Mar. 30 The company purchased $900 of additional office supplies on credit. Mar. 31 The company paid $800 cash for this month's utility bill.
Enter the transactions in the general journal.
Heather and her friends want to buy tickets to the Harry Styles concert. Each ticket cost 85$ and parking cost 25$. Write an equation to represent if Heather spends 280$
Answers
answer: 85+85+85+25
Which graph represents the given equation? A. A parabola declines through (negative 1, 4), (negative 1, 3), (0, 2) and (1 point 5, negative 4 point 5) and rises through (2, negative 4), (3, 0) and (4, 6) on the x y coordinate plane. B. A parabola declines through (negative 4, 5), (negative 3 point 5, 2), (negative 3, 0) and (negative 1 point 5, negative 4 point 5) and rises through (0, negative 2), (1, 3) and (1, 4) on the x y coordinate plane. C. A parabola declines through (negative 2 point 3, 5), (negative 2, 2) and (negative 0 point 5, negative 3 point 1) and rises through (0, negative 2), (1, 4) and (1, 5) on the x y coordinate plane. D. A parabola declines through (negative 1, 5), (negative 0 point 5, 2), (0, negative 2) and (0 point 5, negative 3 point 1) and increases through (2, 2), (2 point 5, 5) on the x y coordinate plane.
Answers
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain the graph of a quadratic function?To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:
The x-intercepts, which are the roots of the function.The y-intercept, which is the value of y when the function crosses the y-axis.The vertex, which is the turning point of the function.The function for this problem is defined as follows:
y = 1.5x² + 4x - 2.
Hence the numeric values of the coefficients are listed as follows:
a = 1.5, b = 4, c = -2.
Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:
x = -3.09 -> hence the function passes through point (-3.09, 0).x = 0.43 -> hence the function passes through point (0.43, 0).The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).
The x-coordinate of the vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate of the vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing InformationThe problem asks for the graph of the following function:
y = 1.5x² + 4x - 2.
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Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
Answers
The value of the consecutive numbers are 7 and 8.
What are consecutive integers?Consecutive integers simply means the numbers that follow each others. It should be noted that such numbers have the same difference between them.
From the information given, we want to find two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
Let the numbers be x and x+1.
Therefore, 6x + (x + 1)² = 106
6x + x² + 2x + 1 = 106
Collect like terms
x² + 8x + 1 - 106
x² + 8x - 105
x² + 15x - 7x - 105
x(x + 15) - 7(x - 15) = 0
Therefore x - 7 = 0
x = 0 + 7
x = 7
Therefore x + 1
= 7 + 1
= 8
The numbers are 7 and 8.
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Two tracking stations are on the equator 163 miles apart. A weather balloon is located on a bearing
of N 43°E from the western station and a bearing of N 17°E from the eastern station. How far, to the
nearest mile, is the balloon from the western station? i got 322 miles
Answers
If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
Suppose the selling price of a towel is x, according to the given condition,
5 = x - 15% of x
5=x-0.15x
5=0.85 x
x=5/0.85
x=5.88
Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
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Find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Answers
Step-by-step explanation:
a polynomial of degree 4 must have 4 zeroes.
when we know these zeroes, we can define the polynomial by the factors defining these zeroes.
after all, a multiplication of several factors can only be zero, if at least one of the factors is zero.
we have 3 zeroes at x = -1. and 1 zero at x = 0.
so,
f(x) = (x + 1)(x + 1)(x + 1)x
you see ? this will only be zero, if x = -1 or x = 0. and -1 is built in as zero 3 times.
let's do the multiplications :
(x + 1)(x + 1) = x² + 2x + 1
(x + 1)x = x² + x
(x² + 2x + 1)(x² + x) = x⁴ + x³ + 2x³ + 2x² + x² + x =
= x⁴ + 3x³ + 3x² + x
f(x) = 1x⁴ + 3x³ + 3x² + 1x
Multiply.
1,000 x 550.343978
Answers
Answer:
1,000 x 550.343978 = 550343.978
Joyce paid $120.00 for an item at the store that was 40 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
Answers
what is the ancer to 50+50
Answers
Answer: 100 is the ancer m
Step-by-step explanation: my man
There are 8 roses and 7 daisies in a vase.
(a) What is the ratio of roses to all flowers in the vase?
(b) What is the ratio of daisies to all flowers in the vase?
Answers
b) 7:15
Hope it helps
Suppose the probability that it will rain is 3 over 10.
What is the probability that it will not rain?
What are the odds in favor of rain occurring?
Answers
Answer: the probability that it will not rain is 70% (you might need to do 7/10)
the odds in favor of the rain occuring is 30% (again, you might need to do 3/10)
Step-by-step explanation:
since the probability that it will rain is 3/10, there is only 7/10 left, so it is more likely to not rain than to rain.
Since it will rain 3/10 times, it is 30% for the second problem
Give me brainliest please!
What is the smallest distance between the origin and a point on the graph of y = 1/2*(x^2 - 8)?
Answers
The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Given, a function
y = 1/2(x² - 8)
We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).
Now, the point on the graph be,
( x , 1/2(x² - 8) ) and origin be (0 , 0)
Let the function of the distance between both the points be,
D = √(x - 0)² + (1/2(x² - 8) - 0)²
D = √x² + 1/4(x² - 8)²
D² = x² + 1/4(x² - 8)²
On differentiating, we get
2DD' = 2x + x(x² - 8)
x³ + 2x - 8x = 0
x³ - 6x = 0
x(x² - 6) = 0
So, x = 0 , √6 , -√6
and the distance is minimum for x = √6
Therefore, using distance formula, we get
Distance = √(x1 - x2)² + (y1 - y2)²
Distance = √(0 - √6)² + (0 - (-1))²
Distance = √6 + 1
So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
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What is the constant of proportionality, ?
I
y
30+
28+
26+
-24+
22+
20+
18+
16+
14+
12+
10+
8+
6+
4+
2+
2
3
4
5
6
7
8
I
Answers
Answer:50.8%
Step-by-step explanation:
Samantha invested $1000 in an account that pays 5% interest
compounded annually. Assuming no deposits or withdrawals are
made, find how much money Samantha would have in the account 18
years after her initial investment. Round to the nearest tenth (if
necessary).
Answers
The amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
The principal amount = $1000
The interest rate = 5%
Time period = 18 years
The interest is compounded annually
The compound interest
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Where A is the final amount
P is the principal amount
r is the interest rate
t is the time period
n is the number of times the interest applied
A = [tex]1000(1+0.05)^{18}[/tex]
A = 1000 × 2.40661
Multiply the terms
A = $2406.61
Hence, the amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
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(x+1)² using identity
please help on this question
Answers
Answer:
[tex]x^2+2x+1[/tex]
Step-by-step explanation:
Note that [tex](a+b)^2=a^2+2ab+b^2[/tex].
Let [tex]a=x[/tex] and [tex]b=1[/tex].
[tex](x+1)^2=x^2+2(x)(1)+1^2=x^2+2x+1[/tex]
the distance between two cities is 4 kilometeres. how many meters apart are the two cities
Answers
Answer: 4000
Step-by-step explanation: x by 1000
what is 500,000x100=
Answers
The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]
We have,
The product of 500,000 multiplied by 100.
= 500,000 x 100
= 50,000,000
This can be written as:
= 5 x [tex]10^7[/tex]
Therefore,
The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]
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Simplify.
-6√7.4√5
-2√35
24√√35
-24 √√35
Answers
The simplified form of the expression is -24√35
Expression
Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
Here we have the expression -6√7.4√5
Now, we have to simplify the expression.
While we looking into the given expression, we have identified that the expression is in the form of multiplication,
So, the first step in solving the expression is to group the similar element,
So, the grouped form of the expression is,
=> (-6 x 4).(√7 x √5)
Now, we have to perform the multiplication on it, then we get,
=> -24√35
Therefore, the simplified form of the expression is -24√35
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Which fraction has the same value as 44.4¯%?
Answers
Answer: 111/250
Step-by-step explanation:
Step 1: Write down the percent divided by 100 like this:
44.4% = 44.4/100
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,
44.4/100 = (44.4 x 10)/(100 x 10) = 444/1000.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(444,1000) = 4. So,
The farmer has 8.9kg of animal feed. In a day, he used 350g for the chickens, 675g for the cows and 1.3kg for the horses. How much feed will he have left?
Answers
Answer:
-1027.4
Step-by-step explanation:
that is the answer i got from my calculations. I hope this is right
programing problem :
Scenario: The county tax office calculates the annual taxes on property using the following formula:
Property tax = property value × 0.0065
Every day, a clerk in the tax office gets a list of properties and must calculate the tax for each property on the
list. You have been asked to design a program that the clerk can use to perform these calculations.
In your interview with the tax clerk, you learn that each property is assigned a lot number, and all lot numbers
are 1 or greater. You decide to write a loop (while) that uses the number 0 as a sentinel value. During each
loop iteration, the program will ask the clerk to enter either a property’s lot number, or 0 to end.
Answers
The program to illustrate the information will be:
This function gets the value of the property from the user,
# calculates the tax, then displays the value of the tax
def show_tax():
# getting the value of the property from the user
property_value = float(input("Enter the property value: "))
# calculating the tax
property_tax = property_value * 0.0065
# displaying the value of the tax
print("Property tax: $ {0:.2f}".format(property_tax))
How to illustrate the information?This program will receive the lot number from the user, while the lot number does not equal 0, then it gets the value of the property from the user, calculates the tax, then displays the value of the tax
The main() function will receive the lot number from the user,
# while the lot number does not equal 0,
# call the show_tax() function then ask for the next lot number.
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I need help
y= 350x + 1.25
Answers
Answer: 351.25
Step-by-step explanation:
unless there is more to the question that I am not seeing that is the answer.
a magician charges a $30 fee to cover travel and expenses, plus $19.99 per hour. Write an equation to represent the relationship between h, the number of hours, and t, the total charge for the magician.
Answers
The equation to represent the relationship between h and t is
t = 30 + 19.99h.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the magician charges a $30 fee one time and a $19.99 fee per hour.
The total charge, t, for the magician for h hours is,
t = 30 + 19.99h
Hence, the equation to represent the relationship between h and t is
t = 30 + 19.99h.
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Ted is a freshman attending a 4-year college. He has been approved for an $8,000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education subsidize in interest costs during his 4.5-year non-payment period?
Answers
Answer:
$1544.40
Step-by-step explanation:
You want to know the amount of interest cost subsidized by the Department of Education during the 4.5-year non-payment period on an $8000 subsidized federal loan at 4.29%.
InterestThe interest accrued on the loan amount is found by the simple interest formula:
I = Prt
The principal is $8000, the rate is 4.29%, and the time period is the non-payment period, 4.5 years. The interest is ...
I = $8000·0.0429·4.5 = $1544.40
The DoE will subsidize $1544.40 in interest during the non-payment period.
__
Additional comment
For the purpose of this problem, the 10-year period of the loan is irrelevant, as we're only concerned with the 4.5 year period before repayment starts. Because the loan is subsidized, that interest is never "capitalized" and is not due to be repaid by the borrower.
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15. Tim can finish painting his barn in 10 hours. It takes
his wife JoAnn only 8 hours to do the same job. If they
work together, how long will it take them to complete the
job?
Answers
Answer:
4 4/9
is the time it will take
A waterskier skis over the ramp shown in the figure at a speed of 30 ft/s. How fast is she rising as she leaves the ramp?
Answers
The waterskier has a final speed of approximately 25.350 feet per second.
What is the final speed of the waterskier?
In this question we need to determine the final speed of the waterskier, that is, the final speed of the waterskier when she leaves the ramp. This can be done by means of the principle of energy conservation, where the total energy is the result of combining translational kinetic energy (K), in pounds-feet per second, related to the speed of the waterskier, and gravitational potential energy (U), in pounds-feet per second.
The equation that represents the situation is described below:
K = U + K'
0.5 · m · v² = m · g · h + 0.5 · m · v'²
0.5 · v² = g · h + 0.5 · v'²
v'² = v² - 2 · g · h
Where:
K' - Final translational kinetic energy, in pounds-feet per second.K - Initial translational kinetic energy, in pounds-feet per second.m - Mass of the waterskier, in pounds.v - Initial speed of the waterskier, in feet per second. v' - Final speed of the waterskier, in feet per second.g - Gravitational acceleration, in feet per square second. h - Final height of the waterskier, in feet.If we know that v = 30 ft / s, g = 32.174 ft / s² and h = 4 ft, then the final speed of the waterskier is:
v' = √[(30 ft / s)² - 2 · (32.174 ft / s²) · (4 ft)]
v' ≈ 25.350 ft / s
The final speed of the waterskier is approximately 25.350 feet per second.
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Jay and Ted observed two points, P and Q, on a number line.
A number line is shown from negative 1 to positive 1 with increments of 1 over 8. The numbers negative 1, negative 6 over 8, negative 4 over 8, negative 2 over 8, 0, 2 over 8, 4 over 8, 6 over 8 are labeled on the number line. A point P is shown at the first tick mark to the left of 0, and a point Q is shown at the first tick mark to the right of 0.
Jay said that the absolute values of the numbers represented by the two points are the same.
Ted said that the absolute values of the numbers represented by the two points are different.
Which of the following explains who is correct? (1 point)
Jay, because each point is fraction 1 over 8 unit from 0
Jay, because the distance between the points is fraction 1 over 8 unit
Ted, because the points are on different sides of 0
Ted, because the points are at different locations on the number line
Answers
Jay, because each point is fraction 1 over 8 unit from 0.
What is absolute length?
One way to think about a number's absolute value is as its distance from zero on the real number line.In addition, the distance between two real numbers is the absolute value of their difference.For instance, the absolute value of 12:
Since each number is 12 units away from zero, it is clear that 12 and -12 both have the same absolute value, which is 12. In order to determine the absolute value of a negative number, simply remove the minus sign. Absolute value is always positive.Absolute value is the length from which the number is from 0 in this they are adding two so it would mean that they are both 1/8 away from 0.
Hence, Jay, because each point is fraction 1 over 8 unit from 0.
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Equipment was acquired at the beginning of the year at a cost of $36,000. The equipment was depreciated using the double-declining-balance method based on an estimated useful life of ten years and an estimated residual value of $700.
Question Content Area
a. What was the depreciation for the first year?
fill in the blank
b. Assuming the equipment was sold at the end of year 2 for $8,860, determine the gain or loss on the sale of the equipment.
fill in the blank
Answers
The depreciation for the first year is $28,800.
If the equipment is sold for $8,860 at the end of year 2, the loss on the sale is $-14,180.
What is the depreciation in year 1 and the loss on the sale?
Depreciation is the method used in expensing the cost of an asset. The double declining method is an exponential method that is used to expense the cost of an asset.
Depreciation expense using the double declining method = Depreciation factor x cost of the asset
Depreciation factor for the double declining method = 2 x (1/useful life)
Depreciation expense in year 1 = (2 / 10) x $36,000 = $7,200
Book value at the beginning of year 2 = cost of the asset - depreciation in year 1
$36,000 - $7,200 = $28,800
Depreciation in year 2 = (2/10) x $28,800 = $5,760
Book value at the end of year 2 = book value at the end of year 1 - depreciation in year 2
$28,800 - $5,760 = $23,040
Loss = sales price - cost price
Loss = $8,860 - $23,040 = $-14,180
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Question 3(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O4, 8, 11
O6, 8, 13
O√3, √5, 8
O√3, √13, 4
PLEASE HELP WILL GIVE BRAINLIST
Answers
Answer:
ok i got you its two;)
Step-by-step explanation:
A tourist from the U.S. is vacationing in Greece. One day, he notices that gasoline costs 1.28 euro per liter. On that same day, euro is worth 1.09 dollars. How much does the gas cost in dollars per gallon? First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of the equation.
Answers
The cost of the gas in dollars per gallon would be = $5.3 per gallon.
What is the conversation of liters to gallon?Liters can be converted to gallon as 1 liter = 0.264 gallon.
On the first day, the cost of gasoline = 1.28 euro per liter
On the first day, the worth of £1 = $ 1.09
Which means, if £1 = $1.09
£ 1.28 = $x
Make $x the subject of formula;
$x = 1.28 × 1.09/1
$x = $1.40
Which means that on the first day, the cost of gasoline in dollars = $1.40
To convert liters to gallon;
1 liter = 0.264 gallon
If $1.40 = 0.264 gallon
$x = 1 gallon
make $x the subject of formula;
$x = 1×$1.40/0.264
$x = 5.3
Therefore, the cost of gasoline in dollar per euro = $5.3 per gallon.
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