An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function below, where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars.
m(x) = 20x - 5x^3/4 + 0.01x^2
The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell x(p) = 320 - 7.7p planes.
(a) Find the cost, demand (or price), and revenue functions.
C(x) =
p(x) =
R(x) =
(b) Find the production level that maximizes profit.
Planes =
(c) Find the associated selling price of the aircraft that maximizes profit.
= $_______ million
(d) Find the maximum profit.
= $ _______ million
Answer:
[tex](a)[/tex] [tex]C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2[/tex]
[tex]p(x)=320-7.7p[/tex]
[tex]R(x)=(320-7.7p)p=320p-7.7p^2[/tex]
[tex](b)[/tex] [tex]x=82 \text{planes}[/tex]
[tex](c)[/tex] [tex]p=\$30.91 M\;\; \text{per plane}[/tex]
[tex](d)[/tex] maximum profit [tex]=\$ 15.90M[/tex]
Step-by-step explanation:
Given that,
The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.
The additional cost of manufacturing each plane can be modelled by the function.
[tex]m(x)=20x-5x^{\frac{3}{4}}+0.01x^2[/tex]
[tex](a)[/tex] Find the cost, demand (or price), and revenue functions.
[tex]C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2[/tex]
[tex]p(x)=320-7.7p[/tex]
[tex]R(x)=(320-7.7p)p=320p-7.7p^2[/tex]
[tex](b)[/tex] Find the production level that maximizes profit.
[tex]f=R(x)-C(x)[/tex]
[tex]\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)[/tex]
[tex]\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx[/tex]
[tex]x=320-7.7p[/tex]
[tex]p=\frac{320-x}{7.7}[/tex]
[tex]\frac{dp}{dx} = \frac{-1}{7.7}[/tex]
[tex]\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0[/tex]
[tex]\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0[/tex]
[tex]\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0[/tex]
[tex]\Rightarrow x=82 \text{planes}[/tex]
[tex](c)[/tex] Find the associated selling price of the aircraft that maximizes profit.
[tex]p=\frac{320-82}{7.7}[/tex]
[tex]\Rightarrow p=\$30.91 M\;\; \text{per plane}[/tex]
[tex](d)[/tex] Find the maximum profit.
Manufacturing cost of one plane is:
[tex]m(1)=20-5+0.01[/tex]
[tex]=\$15.01 M[/tex]
maximum profit [tex]=\$(30.91-15.01)M[/tex]
[tex]=\$15.90M[/tex]
A family wants to rent a car to go on vacation. Company A charges $60.50 and 12 cents per mile. Company B charges $45.40 and 10 cents per mile. How much more does charge for x miles than Company B?
Answer:
$15.02
Step-by-step explanation:
Let's write out some equations.
Company A:
60.50+0.12x=A
Company b:
45.50+0.10x=B
Now let's compare. If x=1, Company A charges
60.50+0.12=60.62=A
On the other hand, Company B charges
45.50+0.10=45.60=B
A-B=60.62-45.60=15.02
Since these are linear we can safely assume that this is constant :)
Make A the subject of the formula
R=square root of a/3
Answer:
R=√a/3
now put square on both side to remove square root
(√A/3)²=R²
A/3=R²
so we get
A=3(R²)
plz mark me brainest
A researcher observes the level of aggression of six 5-year-old boys over the course of a school day. The number of incidents for the group of boys was 2, 4, 6, 12, 8, 10. What is the mean number of aggressive acts for this group of children?
a) 9
b) 5
c) 7
d) 4
Answer:
[tex]Mean = 7[/tex]
Step-by-step explanation:
Given
[tex]Data: 2, 4, 6, 12, 8, 10.[/tex]
Required
Determine the mean
The mean of a data is calculated as thus:
[tex]Mean = \frac{\sum x}{n}[/tex]
In this case:
[tex]n = 6[/tex]
So, the formula becomes:
[tex]Mean = \frac{2+4+6+12+8+10}{6}[/tex]
[tex]Mean = \frac{42}{6}[/tex]
[tex]Mean = 7[/tex]
I need the answers to this
Answer:
i can't not understand sorry
- 5x2 + 2x + 9= 0
factorize
Answer:
Please check the explanation.
Step-by-step explanation:
Given the quadratic equation
5x²−2x−9 = 0
To factor the quadratic function 5x²−2x−9, we should solve the corresponding quadratic equation 5x²−2x−9 = 0.
Indeed, if x₁ and x₂ are the roots of the quadratic equation ax²+bx+c=0, then
ax²+bx+c = a(x-x₁)(x-x₂)
Now,
solving the quadratic function 5x²−2x−9 = 0
[tex]-5x^2+2x+9=0[/tex]
subtract 9 from both sides
[tex]-5x^2+2x+9-9=0-9[/tex]
Simplify
[tex]-5x^2+2x=-9[/tex]
Divide both sides by -5
[tex]\frac{-5x^2+2x}{-5}=\frac{-9}{-5}[/tex]
[tex]x^2-\frac{2x}{5}=\frac{9}{5}[/tex]
Add (-1/5)² to both sides
[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{9}{5}+\left(-\frac{1}{5}\right)^2[/tex]
[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{46}{25}[/tex]
[tex]\left(x-\frac{1}{5}\right)^2=\frac{46}{25} \\[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
so solving
[tex]x-\frac{1}{5}=\sqrt{\frac{46}{25}}[/tex]
[tex]x-\frac{1}{5}=\frac{\sqrt{46}}{\sqrt{25}}[/tex]
Add 1/5 to both sides
[tex]x-\frac{1}{5}+\frac{1}{5}=\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]
[tex]x=\frac{\sqrt{46}+1}{5}[/tex]
similarly solving
[tex]x-\frac{1}{5}=-\sqrt{\frac{46}{25}}[/tex]
[tex]x-\frac{1}{5}=-\frac{\sqrt{46}}{5}[/tex]
Add 1/5 to both sides
[tex]x-\frac{1}{5}+\frac{1}{5}=-\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]
[tex]x=\frac{-\sqrt{46}+1}{5}[/tex]
Thus, the roots are:
[tex]x_{1} =\frac{\sqrt{46}+1}{5},\:x_{2}=\frac{-\sqrt{46}+1}{5}[/tex]
Conclusion:
Since the roots are irrational, we do not factor further.
Therefore, we leave 5x²−2x−9 as it is.
7. The unlabeled graph shows the relationship
between two customary units of measure.
Only two pairs of units can be represented
Mini-Task
by the graph.
10
8
6
2
0 24
6
8 10
a. Determine the possible pairs of units.
b. Describe the relationship for each pair.
Answer:
I am not sure about that
Last year, a college's tuition was $. 42,000This year, the tuition increased by 4%. Find this year's tuition by using a percent greater than 100.
Answer:
$43680
Step-by-step explanation:
Given data
Tuition was $. 42,000 last year
The tuition increased by 4%
Hence the current year tuition is given as
Current tuition= 42,000 + 4/100*42,000
Current tuition= 42,000 + 0.04*42,000
Current tuition= 42,000 +1680
Current tuition= $43680
Hence the current tuition is $43680
At the start of a trip, a car’s gas tank contains gallons of gasoline. During the trip, the car consumes 1⁄8 gallons of gasoline. How much gasoline is left in the tank? Please explain thoroughly.
Please solve the question below 3
Answer:
17》6
18》12
19》8
20》3
21》2
the bar with age 18 this is because as you minus from both sides the middle number will be in age 18
What is the probability that a point would be in the blue region? Triangle area=bh/2
Answer:
okay so look
Step-by-step explanation:
you calculate the area of the whole square then the area of the triangle , then you subtract the area of the square with the area of the triangle so you'll get the area of the blue region
Solve 3[-x + (2x+ 1)] =X- 1.
x= ?
Answer:
x= -2
Step-by-step explanation:
9
Select the correct answer.
Which statement is true about this equation?
-9(x + 3) + 12 = -3(2x + 5) - 3x
OA
The equation has one solution, x= 1.
OB. The equation has one solution, x = 0.
OC. The equation has no solution.
OD
The equation has infinitely many solutions.
Reset
Next
Answer: D. The equation has infinitely many solutions.
Step-by-step explanation:
Given equation: [tex]-9(x + 3) + 12 = -3(2x + 5) - 3x[/tex]
[tex]\Rightarrow -9(x)+(-9)(3)+12=(-3)(2x)+(-3)(5)-3x\\\\\Rightarrow\ -9x-27+12=-6x-15-3x\\\\\Rightarrow\ -9x-15=-9x-15\\\\\Rightarrow\ -9x+9x=-15+15\\\\\Rightarrow\ 0=0[/tex]
which is true.
This happens when all numbers are solutions.
i.e. The equation has infinitely many solutions.
Correct option : D.
what is the equation of the line passing through the point (2,-1) with a slope of -3
Note: this answer assumes that the equation of the line must be in slope-intercept form.
Answer:
[tex]y= -3x + 5[/tex]
Explanation:
When you need to write an equation and know its slope and a point it intersects, you can use the point slope formula [tex]y-y_1 = m (x-x_1)[/tex] first. In order to write an equation using this formula, the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] must be substituted in for real values.
The [tex]m[/tex] represents the slope, so write the slope of this equation, -3, in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects. We know that the line must intersect the point (2, -1). Write 2 in the place of
[tex]y-(-1) = -3(x-(2))[/tex]
[tex]y+1 = -3(x-2)[/tex]
Now, to put it in slope-intercept or [tex]y = mx + b[/tex] form, just expand the right side and isolate [tex]y[/tex]:
[tex]y+1 = -3(x-2)\\y + 1 = -3x + 6 \\y = -3x + 5[/tex]
Therefore, [tex]y= -3x + 5[/tex] is the answer.
You can use a number line to help you order rational numbers.
True or False
True.
Hope this helped!
Answer:
I would say true
Step-by-step explanation:
Megan has a bowl containing $1.95 in pennies and dimes. If she has 3 times as many pennies as she has dimes, how many pennies and how many dimes does she have?
Answer: she has 15 dimes and 45 pennies.
Step-by-step explanation:
01p+1d=1.95
p=3d
01(3d)+.1d=1.95
p=3.15
03d+.1d=1.95
p=45
.13d=1.95
d=15
brainly solve 100 points
Answer:
1.9059 x 10 -12
Step-by-step explanation:
A rectangular garden has a walkway around it. The area of the garden is 6(4.5x +3.5). The combined area of the garden and the walkway is 6.5(6x + 6). Find the area of the walkway around the garden as the sum of two terms. The area of the walkway around the garden is (Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answer:
13x+23.5
Step-by-step explanation: I dont know how to explain
ALRIGHT I NEED HELP AGAIN HELP ME STRANGERS
A body has a weight of 10Kg and volume
of 952 cm ^ 3. find out the density body
O 10,5 g/cm^3
O 952 Kg/cm^3
O 1050 g/cm^3
O 10500 kg/cm^3
if x+y = 1, and x^2 + y^2 = -1, what is x^7 + y^13?
1) 0
2) 1
3) -2
4) 2
5) -1
Solve for x and y :
x + y = 1 → y = 1 - x
x ² + y ² = -1
x ² + (1 - x)² = -1
x ² + (1 - 2x + x ²) = -1
2x ² - 2x + 1 = -1
2x ² - 2x + 2 = 0
x ² - x + 1 = 0
x ² - x + 1/4 = -3/4
(x - 1/2)² = -3/4
x - 1/2 = ±√(-3/4)
x - 1/2 = ±√3/2 i
x = 1/2 ± √3/2 i → x = exp(± iπ/3)
y = 1 - (1/2 ± √3/2 i ) → y = -1/2 ± √3/2 i → y = exp(± 2iπ/3)
Then
x ⁷ + y ¹³ = exp(± 7iπ/3) + exp(± 26iπ/3)
… = exp(± iπ/3) + exp(± 2iπ/3)
since 7π/3 is equivalent to π/3, and 26π/3 is equivalent to 2π/3 (both modulo 2π).
In either case, we get
x ⁷ + y ¹³ = x + y = 1
so the answer is (2) 1.
Find the missing term.
(Blank) + 7 - 3i) + (5 + 91) + 131 = 10 - 5i.
Options:
-2 - 24i
2 - 12i
-12-24
-2 + 141
Answer:
-2 - 24i
Step-by-step explanation:
a + bi + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i
a + bi + 7 + 5 - 3i + 9i + 13i = 10 - 5i
a + bi + 12 + 19i = 10 - 5i
a + bi = 10 - 5i - 12 - 9i
a + bi = 10 - 12 - 5i - 9i
a + bi = -2 - 24i
Fourteen out of the twenty people in your class have black hair.
Please help quickly, if someone answers quickly I'll give them Brainly.
Simonne predicted that she would sell 99 picture frames. She actually sold 88 picture frames. What are the values of 'a' and 'b'? Round round to the nearest tenth if necessary.
Item-
Picture frames
Approximate value-
99
Exact value-
88
Error-
Blank
Absolute error-
Blank
Ratio-
a
percent error-
b
Possible answers:
1. a= 11/99; b= 11.1%
2. a= 11/88; b= 12.5%
3. a= 88/99; b= 88/99%
4. a= 11/11; b= 100%
Step-by-step explanation:
Ratio
= Difference between Prediction and Actual / Prediction
= (99 - 88)/99 = 11/99.
Percentage Error
= Difference between Prediction and Actual * 100%
= (99 - 88) * 100% = 11.1%. (1)
The ratio (a) & percent error (b) will be option A which is a=11/99 and b= 11.11% respectively
Ratio and Percent errorRatio can be defined as difference between approximate value and exact value divided by approximate value.Percent error is ratio multiplied by 100How to solve this problem?Given
Approximate value = 99 frames
Exact value = 88 frames
Ratio (a) = (Approximate value - Exact value) / Approximate value∴ Ratio (a) = (99-88)/99
∴ a = 11/99
Ratio (a) x 100∴ Percent error (b) = (11/99) x 100
∴ b = 11.11%
So, the answer of ratio (a) & percent error (b) will be 11/99 and 11.11% respectively
Learn more about Ratio and percent error here:
https://brainly.com/question/5493941
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Use Euler’s Formula to find the missing number.
Faces: _____
Edges: 15
Vertices: 9
Use Euler’s Formula to find the missing number.
Answer:18
#CARRYONLEARNING #STUDYWELLAnswer:
Use Euler’s Formula to find the missing number.
Faces: __8__
Edges: 15
Vertices: 9
Answer is 8
Step-by-step explanation:
please help asap!!!!
Answer:
z = 25
Step-by-step explanation:
adjacent angles in a rhombus are supplementary
3z - 15 + 7z - 55 = 180
10z - 70 = 180
10z = 250
z = 25
which graph beat represents this system of linear equations and it’s solution
Help me with this please worth 40 points!!!
Rewrite the following without an exponent. 6^-2
Please answer ASAP!
Answer:
Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]
Step-by-step explanation:
We need to rewrite the following without an exponent. [tex]6^{-2}[/tex]
We need to solve the exponent to find the result.
We know the exponent rule: [tex]a^{-b}=\frac{1}{a^b}[/tex]
Now using this rule to solve the equation:
[tex]6^{-2}\\=\frac{1}{6^2}\\We \:know \:that\:6^2 = 6\times 6=36\\=\frac{1}{36}[/tex]
So, Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]
I will give Brainiest to whoever answers correctly !!!
Hey there!
I believe the answer to your question is 47.21 ml of oxygen are in the 55 ml sample of sea water.
To get this, you can do 0.8584 x 55 = 47.212, because you want to find 85.84% of 55, to know how much oxygen is in the sample. Then, you round it to the nearest hundreth.
Hope it helps! Have a great day! Do tell me if I'm mistaken.
At the movie theatre, child admission is $5.70 and adult admission is $9.80. On Wednesday, 149 tickets were sold for a total sales of $1222.40. How many child tickets were sold that day?
Answer:
I am not sure but sold of the say 2,334
Answer:
58 child tickets
Step-by-step explanation:
5.7(x)+9.8(149-x)=1222.40
5.7x+1460.2-9.8x=1222.40
1460.2-4.1x=1222.40
-4.1x=-237.8
x=58