Revenue, profit and expenses are all integral parts of a company's balance sheet
The expense in terms of q is [tex]\mathbf{E = 8q + 12000}[/tex]The expense in terms of p is [tex]\mathbf{E = -80p + 172000}[/tex]The revenue in terms of p is [tex]\mathbf{R = -10p^2 + 20000p}[/tex]The profit in terms of p [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]The price that yields the maximum profit is $1004The maximum profit is $9908160The expense function is given as:
[tex]\mathbf{E = 8q + 12000}[/tex]
The demand function is given as:
[tex]\mathbf{p = -10p + 20000}[/tex]
(a) The expense in terms of q
This is already given as: [tex]\mathbf{E = 8q + 12000}[/tex]
(b) The expense in terms of p
Substitute -10p + 20000 for p in [tex]\mathbf{E = 8q + 12000}[/tex]
[tex]\mathbf{E = 8(-10p + 20000) + 12000}[/tex]
Expand
[tex]\mathbf{E = -80p + 160000 + 12000}[/tex]
[tex]\mathbf{E = -80p + 172000}[/tex]
(c) The revenue in terms of P
This is calculated as:
[tex]\mathbf{R = p \times q}[/tex]
So, we have:
[tex]\mathbf{R = p \times (-10p + 20000)}[/tex]
Expand
[tex]\mathbf{R = -10p^2 + 20000p}[/tex]
(d) The profit in terms of p
We have:
[tex]\mathbf{R = -10p^2 + 20000p}[/tex] and [tex]\mathbf{E = -80p + 172000}[/tex]
So, the profit P is calculated as:
[tex]\mathbf{P =R - E}[/tex]
This gives
[tex]\mathbf{P =-10p^2 + 20000p +80p - 172000}[/tex]
[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
(e) The price that yields maximum profit
In (d), we have:
[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
The maximum price is calculated using:
[tex]\mathbf{p = -\frac{b}{2a}}[/tex]
Where:
[tex]\mathbf{b =20080}[/tex]
[tex]\mathbf{a = -10}[/tex]
So, the equation becomes
[tex]\mathbf{p = -\frac{20080}{2 \times -10}}[/tex]
[tex]\mathbf{p = 1004}[/tex]
Hence, the price that yields the maximum profit is $1004
(f) The maximum profit
In (e), we have: [tex]\mathbf{p = 1004}[/tex]
Substitute 1004 for p in [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
[tex]\mathbf{P =-10(1004)^2 + 20080(1004) - 172000}[/tex]
[tex]\mathbf{P =9908160}[/tex]
Hence, the maximum profit is $9908160
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Select the correct answer.
What is the vertex of the function f(x) = |x + 7| − 3?
BRAINLIEST
can you help me out :)
Answer:
DC = 30.47 units
KL = 5.34 units
Step-by-step explanation:
Cos 54 * 20 = AD
Sin 54 = BD/20
Sin 54*20 = BD
BD = 0.809*20 = 16.2
Tang 28 = BD/DC
DC = BD/tang 28
DC = 16.2/0.5317
Tan 51 = JL/14
JL = 1.2349 * 14 = 17.29 units
Cos 72 = KL/JL
Cos 72 * 17.29 = KL
cos 72 = 0.309
KL = 0.309 * 17.29 = 5.34 units
Choose the graph that matches the inequality –x + y ≥ 2
Answer:
D
Step-by-step explanation:
-x + y >= 2
first of all, it means it includes the line (the "=" part).
that eliminates B and C.
then just look at the line function itself :
-x + y = 2
y = x + 2
and now
y >= x + 2
so, everything above the line (and again including the line), as every y value greater than or equal to the result of the line function is valid.
The required graph has been attached below which represents the given inequality –x + y ≥ 2. which is the correct answer that would be an option (D).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question below as
–x + y ≥ 2
First and foremost, it signifies that it includes the line (the "=" element).
This rules out B and C.
Then evaluate the line function itself:
-x + y = 2
y = x + 2
and now
y ≥ x + 2
As a consequence, anything above the line (and including the line) is legitimate, as is any y value larger than or equal to the result of the line function.
Thus, the required graph has been attached below which represents the given inequality –x + y ≥ 2.
Hence, the correct answer would be an option (D).
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Which is a solution for 7 (x plus 2) equals 35?
what is the solution to this system of equations?
5x-y=40
y=2x-4
A) 20, 12
B) -20, 12
C) 12, -20
D) 12, 20
u=xk , for x
please help me
Answer:
x=u/k
Step-by-step explanation:
To get x, you would divide by k. Because its x times k. The oppisite is division. This gets you u/k=x
x is equal to u divided by k.
x=u/k
Which angle is the smallest?
12
10
D
Answer:
Step-by-step explanation:
Find m<1. Please help quick!
Answer:
17°
Step-by-step explanation:
Look everything you have above the horizontal line.
It's a 73° angle, plus the one you need, plus 90°. They add up to 180.
m+73+90=180, or m=17.
Simplify this expression:
[tex]7xy - x^{2}t+4xy+5x^{2}t[/tex]
Answer:
[tex]11xy+4x^{2} t[/tex]
Step-by-step explanation:
1. Collect Like Terms
[tex](7xy+4xy)+(-x^{2} t+5x^{2} t)\\[/tex]
2. Simplify.
[tex]11xy+4x^{2} t[/tex]
he directions for Grow Better fertilizer say that the 25-pound bag covers a 1,000-foot row of vegetables Which brand would Cala need more of to fertilize her vegetables? Explain
Using the principle of proportional relationship, the amount in pounds of Grow better Fertilizer exceeds the required amount of Feed all Fertilizer. Hence, more of Grow better Fertilizer would be needed.
Feed - All Fertilizer :
2 pounds = 100 foot row
x pounds = 450 foot row
Cross multiply
100x = 900
Divide both sides by 100
x = 900 / 100
x = 9 pounds
Grow better Fertilizer :
25 pounds = 1000 foot rows
x pounds = 450 foot rows
Cross multiply
1000x = 450 × 25
1000x = 11250
Divide both sides by 1000
x = 11250 / 1000
x = 11.25 pounds
Hence, Cala will need more of Grow better Fertilizer.
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered 7,160 kilograms of sugar. This time, the bakery is ordering 40% less sugar. How much sugar is that?
Answer:
4296 kg
Step-by-step explanation:
40/100 = x/7160
716 times 6 is 4296
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
12 * 3 * 5 * 5 = 900
900
I would appreciate if you answered!
Answer:
None of those options
Step-by-step explanation:
I just did the work myself and even ran it through a calculator but the correct answer isn't one of those options. Here's my work:
[tex]-\frac{5}{6} =z+\frac{1}{8}\\-\frac{5}{8}-\frac{1}{8}=z\\-\frac{40}{48}-\frac{6}{48}=z\\-\frac{46}{48}=z\\-\frac{23}{24}[/tex]
I'd contact you teacher about that...it might be an error in their system (it's happened to me a few times before where the correct answer is marked as incorrect or isn't even an option)
please this is half my grade!!!
Benjamin has a ladder that is 15 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 13.8 ft above the ground. What is the angle, rounded to the nearest tenth, that the ladder makes with the ground? Show your work
2. What is the length of side YZ to the nearest tenth? Show your work.
side XY is 11 feet, and angle Z is 35 degrees(this is a right triangle)
3. What are the exact measures of the other two sides of the triangle? Use special right triangles ratios and show your work.
Side AC is 14 feet, this is a right triangle, and angle A is 30 degrees
The special right triangle is the right triangle that have acute angle values
that simplify the process of finding its dimensions.
The correct values are;
1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
Reasons:
1. The length of the ladder = 15 ft.
Height of the ladder above the ground, h = 13.8 ft.
Required:
The angle the ladder makes with the ground.
Solution:
The angle the ladder makes with the ground is given by the equation;
[tex]sin(\theta) = \dfrac{Length \ of \ the \ ladder}{Height\ of \ the \ ladder \ above the \ ground} = \dfrac{13.8}{15} = 0.92[/tex]
[tex]\theta = arcsin\left(0.92 \right) \approx 66.93^{\circ}[/tex]
2. The given parameters are;
XY = 11
∠Z = 35°
YZ = Required
In a right triangle, the side facing the acute angle is a leg of the triangle.
Therefore;
XY is the opposite side to ∠Z
[tex]sin(\angle Z) = \dfrac{XY}{YZ}[/tex]
Which gives;
[tex]sin(35^{\circ}) = \dfrac{11}{YZ}[/tex]
[tex]YZ= \dfrac{11}{sin(35^{\circ}) } \approx 19.18[/tex]
YZ ≈ 19.18 ft.
3. AC = 14 ft.
∠A = 30
Required:
The length of the other two sides
Solution:
Where by AC is the hypotenuse side, we have;
CB = AC × sin(∠A)
Therefore;
CB = 14 × sin(30°) = 7
CB = 7 ft.
AB = AC × cos(∠A) = 14 × cos(30°) = 7·√3
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1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
A particular plant root grows 3.5 inches per month.How many centimeters is the plant growing each month?
Answer:1 inch = 2.54 centimeters so the answer is 3.76
Step-by-step explanation:
(1 inch = 2.54 centimeters). 0.73 centimeters 1.38 centimeters 6.04 centimeters 8.89 centimeters unsubscribe · report · tue mathematics
The value of a new car in 2015 was 40,000 dollar. It depreciates each year by 7%. How much will the car be worth in 2026?
Answer: $30,800
Step-by-step explanation: First you have to subtract 2026 - 2015, which is 11 years. Since it depreciates by 7% each year, you would multiply 7 by 11, which is 77. 77 is the percent of depreciation of the car. After that, you would divide 40000 by 100, which is 400. Then you multiply 400 by 77 to get you final answer.
c) 2 x x 3 x y
Please help
would love it if someone helped with this question please...
Answer:
$40.00
Step-by-step explanation:
to find the cost multiply the cost per unit by the number of units: 10/6 x 24 = 40
Can somebody show me how to do this with answers? I don’t understand how my teacher shows me
If you mean adding text above the underscore press the text button on the left and it will allow you to click above the underscore and add text as an answer to said problem.
4x+8=3
help asap
step by step please
[tex]4x +8 =3\\\\\implies 4x = - 5 \\\\\implies x = - \dfrac 54[/tex]
Answer:
x= -5/4
Step-by-step explanation:
4x+8=3
4x=3-8
4x=-5
x= -5/4
Factories often add filler when making meatballs sold by the bag. One factory obtained 72 kg of beef from overseas. They want to add 1.2 oz of filler for each
pound of beef, How many ounces of filler will the factory need in order to make meatbälls out of this shipment of beef? Help
Answer:
158.732829
rounded up: 159
Step-by-step explanation:
trust the calculator
Write the transformed equation for g(x)+4 calling it h(x)
Answer:
h(x) = (1/3)x + 6
Step-by-step explanation:
yeah-ya ....... right?
multiples of 7 between 30 and 50
Answer:
It is 35, 42, 49
7x5=35
7×6=42
7²=49
3x^2x4x^5 p please helppppppppppppppppppppppppppppppppppppp
Answer:
i think it is 120
Step-by-step explanation:
What is considered an exponential monthly growth rate.
The Answer equals 1.9%
Susan made $117 for hours 9 of work.
At the same rate, how much would she make for 7 hours of work?
(21x)-(-16+7x) Subtract.
Answer:
=14x+16
Step-by-step explanation:
21x−(−16+7x)
=21x+−1(−16+7x)
=21x+(−1)(−16)+−1(7x)
=21x+16+−7x
=21x+16+−7x
=(21x+−7x)+(16)
=14x+16
Answer:
14x+16
Step-by-step explanation:
(21x)-(-16+7x)
Distribute the minus sign
21x+16-7x
Combine like terms
14x+16
Hurry please
Answer ASAP
Solve for r.
-70 +1 > 22
OR
102 +41 81
WILL MARK BRAINLIEST
Solve 39.2 ÷ 7 = ________.
5.2
5.3
5.5
5.6
Answer:
5.6
Step-by-step explanation:
Answer:
5.6
Step-by-step explanation:
I just take each answer and multiply it by 7 until the answer matches 39.2.
5.6 * 7 = 39.2