A gas station sells unleaded regular and unleaded premium gasoline. The price per gallon charged by the station is$1.299 for unleaded regular and $1.379 for unleaded premium. The cost per gallon from supplier is$1.219 for unleaded regular and $1.289 for unleaded premium. If equals the number of gallons sold of regular and equals the number of gallons sold of premium:(a) Formulate the revenue function from selling and gallons of the two grades of gasoline respectively?(b) Formulate total cost for purchasing and gallons?(c) Formulate the total profit? d) what is the total profit expected to equal if the station sells 100,000 gallons of unleaded and regular and 40000 of unleaded premuim?

Answers

Answer 1

Answer:

a) Revenue function = 1.299r + 1.379p

where: r = gallon of unleaded regular gasoline and p = gallon of regular unleaded premium gasoline

b) cost function = 1.219f + 1.289p

c) profit function = (1.299r + 1.379p) - (1.219f + 1.289p) = 1.299r - 1.219r + 1.379p - 1.289p = 0.08p + 0.09p

d) total profit = (0.08 x 100,000) + (0.09 x 40,000) = $8,000 + $3,600 = $11,600


Related Questions

A small town has two local high schools. High School A currently has 850 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 60 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine after how many years, t,t, the number of students in both high schools would be the same.

Answers

An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

The required equation will be in the form y = Ae^kt

where:

k is the growth constantA represents the number of students in High School A in t years.B represents the number of students in High School B after t years.

If High School A currently has 850 students and is projected to grow by 35 students each year, hence;

A = 850k = 35 (growth factor)

Substituting into the formula, we will have:

y = 850e^35t

If High School B currently has 700 students and is projected to grow by 60 students each year, hence;

A = 700k = 60 (growth factor)

Substituting into the formula, we will have:

y = 700e^70t

An equation for each situation, in terms of t, is y = 850e^35t and

y = 700e^70t

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The temperature increases from 18° F to 27° F.
What is the percent increase of the temperature?
A
3%
B
9%
С
33%
D
50%

Answers

Either 50% or 9%
Because it can be both

The percent increase in the temperature is 50%.

To understand more, check below explanation.

Percentage increase:

The temperature increases from 18° F to 27° F.

       Increase in temperature = 27 - 18 = 9

The percent increase in the temperature is computed as,

                                  [tex]=\frac{27-18}{18}*100\\ \\=\frac{9}{18}*100\\ \\=\frac{1}{2}*100=50\%[/tex]

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There were 42 mangoes in each crate. 12 such crates of mangoes were delivere to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many mangoes were left after the 4 rotten ones were thrown away? * Your answer​

Answers

Answer: 50

Step-by-step explanation: 42x12=504. 504-4=500. 500/10=50.

Answer:

Total Mangoes = 50

Rotten =  46

Step-by-step explanation:

50 divided by 10 = 5.

50 minus 4 is 46.

What is the point slope form of a line that has a slope of 3 and passes through point (1, 4)?

Answers

Answer:

3x - y = -1

Step-by-step explanation:

y - y₁ = m(x - x₁)

substitute (1,4) in for (x₁, y₁) respectively and the slope of 3 in for m

y -4 = 3(x - 1)

distribute 3 to (x - 1)

y - 4 = 3x -3

isolate 3x by itself by adding 3 to both sides

y - 1 = 3x

subtract y from each side

-1 = 3x - y

and just flip around the equation to make it look nicer

3x - y = -1

D=
R=
Function?
Find the domain and range of each relation. Then, determine if the relation is a function.

Answers

Answer:

Step-by-step explanation:

D = { - 4 , 0 , 2 , 7 }

R = { - 8 , - 1 , 3 }

Yes the relation is a function.

A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?

Answers

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

success (reaching 4 before 0) and failure (reaching 0 before 4).

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

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At Cheng's Bike Rentals, it costs 31 to rent a bike for 6 hours.
How many hours of bike use does a customer get per dollar?

Answers

Answer:

0.2hrs/dollars

Step-by-step explanation:

Given parameters:

Cost of bike = $31

Time duration  = 6hrs

Unknown:

Hours customers get per dollar = ?

Solution:

The number of hours customer gets per dollar is;

      Number of hrs/dollar = [tex]\frac{time duration }{cost}[/tex]

    Number of hrs/dollar  = [tex]\frac{6hrs}{31}[/tex]  

    Number of hrs/dollar = 0.2hrs/dollars

Is the relation in the mapping below a function? Explain.
Domain
1,3,5,7
Range
2,4,6

Answers

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help

Answers

Answer:

22 units

Step-by-step explanation:

Known Quantities:

AB = CD and AC = BD

Calculations:

AB = 8AC = 3CD = 8BD = 3

Final Calculations:

perimeter = 2 x (3+8)perimeter = 22

What is 400,000 in scientific notation?
O A) 40 x 104
OB) 400 x 103
OC) 4 x 106
OD) 4 x 105

Answers

Answer:

4 x 10⁵

so that i think will be OD)

A rock is thrown from a cliff into a ravine. The function ℎ() = −16^2 + 19 + 2560 describes the height, in feet, of the rock from the ground seconds after it is thrown. What is the height of the rock, in feet, 2 seconds after it is thrown?

Answers

Answer:

d

Step-by-step explanation:

Simplify.

Rewrite the expression in the form 4^x.

4^4 x 4^3 = ??

Answers

Answer:

[tex]4^{7}[/tex]

Step-by-step explanation:

To simplify the expression [tex]4^{4}\times4^{3}[/tex], we can use the first law of the law of indices which states that the exponent is added together when multiplying numbers with the same base. Eg: [tex]a^{x}\times a^{y} = a^{x+y}[/tex].

[tex]4^4 \times4^3=4^{4+3}[/tex]

[tex]=4^{7}[/tex]

Hope this helps :)

How many solutions exist for the given equation? (x + 12) = 4x - 1 o zero infinitely many ​

Answers

Time of the 20 to the x then get 420

Answer this question and get it right I will mark right one Brainliest
I am thinking of a number from 1-10 what is it ?

Answers

Answer:

6

Step-by-step explanation:

6 is the most common lol

Answer:

I'll say 5

Step-by-step explanation:

Hoped this helped!

Byron's MP3 player holds 75 songs. He has space for 26 more songs. Write an equation to find how many songs are already on Byron's MP3 player.A.) 75 + s = 26 B.)75/s = 26 C.) 26s = 75 D.)s + 26 = 75

Answers

Answer:

D

Step-by-step explanation:

let the number of songs Byron have be s songs.

s + 26 = 75

Answer:

D

Step-by-step explanation:

s= number of songs played.

s+26=75

s-26=75-26

s=49

How do I solve this equation?

Answers

Answer:

x = ± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]|a|= \left \{ {a,if{a\geq 0} \atop-a, if {a<0}} \right.[/tex]

~~~~~~~~~~~~

7 | 3x | + 2 = 16

7 | 3x | = 14

| 3x | = 2

1). 3x = 2

x = [tex]\frac{2}{3}[/tex]

2). - 3x = 2

x = - [tex]\frac{2}{3}[/tex]

what is the value of q in the equation 4/5q = 32

Answers

Answer:

40

Step-by-step explanation:

4/5 * q = 32

First you divide 4/5 by itself so you can eliminate it from the equation and then you have to divide 32 by 4/5 n when you do that you get 40. So q = 40.

Anna makes unique jewelry. The owner of the "Unique" store agreed with Anna to deliver 20 bracelets a week. At the moment, Anna has 80 bracelets made, and can make 17 bracelets a week. For how many consecutive weeks will Anna be able to supply her bracelets to the "Unique" store?

Answers

Answer:

7 weeks

Step-by-step explanation:

80 ÷ 20 = 4

She over those four week she makes 17 per week. So,

17 × 4 = 68

Next, divide the product by 20:

68 ÷ 20 = 3.4

But 3.4 is only 3 full weeks so then its 3.

Lastly, add the 3 weeks we just solved for the the 4 weeks from before and you get 7 weeks.

So, Anna will be able to supply the "Unique" store for 7 weeks.

I HOPE I HELPED!!!!!!!!!! :))))))

On a spelling quiz, Lily got 16 out of 20 questions correct. Select all the expressions that show the ratio of Lily’s correct answers to incorrect answers.

Answers

Where’s the options?

Answer:

ACD

Step-by-step explanation:

VNQLW3M2L,Q;KJ52KQ

Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Answers

FGH and m FGH =(7x-9)
m HGJ = (2x + 36)
Find m FGH

X = 14
7x16 112

2x16 32+36 68
68+112= 180

The answer is x = 16

Give brainest pls

if the cost of 8 mobile set is rs 40,000.how many mobile sets can be purchased for Rs 100,000​

Answers

Answer:

20 mobile sets.

Step-by-step explanation:

Every mobile set costs:

40000 / 8

= 5000 Rs.

Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:

100,000 / 5000

= 20 mobile sets.

Hope this helped!

write 9.68 in expanded form

Answers

Answer:

9+0.6+0.08

Step-by-step explanation:

The given decimal number in expanded form is 9+0.6+0.08.

The given decimal number is 9.68.

What is expanded from of a decimal number?

Unlike whole numbers, decimal numbers can also be written in the expanded form. For writing the decimals in expanded form, we multiply each of the decimal digits with increasing exponent values of (1/10).

Now, the expanded form of 9.68 is

9×1 + 6×1/10 + 8×1/100

= 9+0.6+0.08

= 9.68

Therefore, the given decimal number in expanded form is 9+0.6+0.08.

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What's 6+2x^2 in factored form?

Answers

Answer:

2 ( x^2 + 3 )

Step-by-step explanation:

Kiran's family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran's family, there will be 10 people at the gathering.
A bottle of sparkling water contains 22 ounces and costs $1.50. A package of pretzels contains 16 ounces and costs $2.99. Let LaTeX: nn represent number of people watching the football game, LaTeX: ss represent the ounces of sparkling water, LaTeX: pp represent the ounces of pretzels, and LaTeX: bb represent Kiran's budget in dollars. Which equation best represents Kiran's budget?

Answers

The answer to your question is 16$ and 50 cents

A cuboid with a volume of 925cm^3 has dimensions.
4cm, (x + 1) cm and (x + 11) cm.
Show clearly that x^2 + 12x - 220 = 0
Solve the equation by factorising, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.

Answers

Answer:

Step-by-step explanation:

Volume of the cuboid = Length * Width * Height

Given

Length = 4cm

Width = (x+1)cm

Height = (x-11)cm

Volume of the cuboid = 4(x+1)(x+11)

Volume of the cuboid = 4(x^2+11x+x+11)

Volume of the cuboid = 4(x^2+12x+11)

Volume of the cuboid = 4x*2+48x+44

925 = 4x*2+48x+44

4x*2+48x+44-925 = 0

4x*2+48x-881 = 0

Divide through by 4

x^2 + 12x - 220.25 = 0

Factorize using the general formula;

x = -12±√12²-4(-220.25)/2

x = -12±√144+881/2

x = -12±√1025/2

x = -12±32/2

x = 12+32/2

x = 20/2

x = 10

Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm

Dimension is 4cm by 11cm by 21cm

If using the method of completing the square to solve the quadratic equation x squared -20x+24=0, which number would have to be added to “complete the square”

Answers

Oksuru   k diyaf         ramincok ani kasilm asiyla olusan bir refle kstir.

what is the measure of <x​

Answers

Answer:

X=17

Step-by-step explanation:

73+x=90 90-73=17

2. Convert 25.2625° from decimal degrees to degrees-minutes-seconds.

Answers

Answer:15

Step-by-step explanation:

A carpenter use 65 shelves to make 13 bookcases. She uses the same number of shelves for each bookcase. Are 32 shelves enough to build 6 more bookcases?

Answers

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

will give brainliest!!! hurry up and solve it plzz​

Answers

Answer:

8

Step-by-step explanation:

we can say that AD is congruent to DC

so your equation for x is: 4x - 1 = 2x

solve this to get x = 0.5

plug x into and equation and multiply you answer by 2 to find the hypotenuse of triangle ABC and DEF

4(0.5) - 1 = 1

hypotenuse: 1 x 2 = 2

since we know x is 0.5, plug this into 4x + 1 to find the length of the leg FE,

4(0.5) + 1 = 3

In the diagram, it shows that the legs of triangle are congruent

this means that FE, ED, BA, and BC are all congruent

since we know FE is 3, we know that all the other sides are 3 as well

this means that the perimeter of the triangle is: leg + leg + hypotenuse

so 3 + 3 + 2

the perimeter is 8

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