Answer:
[tex](a)[/tex] [tex]P(x) = 0.02x^2 +50x - 100[/tex]
[tex](b)[/tex] [tex]Average = 0.02x + 50 - \frac{100}{x}[/tex] and [tex]Marginal = 0.04x + 50[/tex]
[tex](c)[/tex] [tex]Average = 59.8[/tex] and [tex]Marginal = 70[/tex]
(d) See Explanation
Step-by-step explanation:
Given
[tex]p(x) = 100[/tex]
[tex]C(x) = -0.02x^2 +50x +100[/tex]
Solving (a) Profit function; P(x)
[tex]P(x) = xp(x) - C(x)[/tex]
This gives:
[tex]P(x) = x*100 - (-0.02x^2 + 50x + 100)[/tex]
[tex]P(x) = 100x + 0.02x^2 - 50x - 100[/tex]
Collect like terms
[tex]P(x) = 0.02x^2 - 50x +100x - 100[/tex]
[tex]P(x) = 0.02x^2 +50x - 100[/tex]
Solving (b): Average profit function and Marginal profit function
[tex]Average = \frac{P(x)}{x}[/tex]
This gives:
[tex]Average = \frac{0.02x^2 + 50x - 100}{x}[/tex]
Break down the fraction
[tex]Average = \frac{0.02x^2}{x} + \frac{50x}{x} - \frac{100}{x}[/tex]
[tex]Average = 0.02x + 50 - \frac{100}{x}[/tex]
[tex]Marginal = \frac{dP}{dx}[/tex]
[tex]P(x) = 0.02x^2 +50x - 100[/tex]
Differentiate
[tex]\frac{dP}{dx} = 2 * 0.02x + 50 - 0[/tex]
[tex]\frac{dP}{dx} = 0.04x + 50[/tex]
Hence:
[tex]Marginal = 0.04x + 50[/tex]
Solving (c): Average profit and Marginal profit if x = a
[tex]a = 500[/tex]
So:
[tex]x =500[/tex]
Substitute 500 for x
[tex]Average = 0.02x + 50 - \frac{100}{x}[/tex]
[tex]Average = 0.02 * 500 + 50 - \frac{100}{500}[/tex]
[tex]Average = 59.8[/tex]
[tex]Marginal = 0.04x + 50[/tex]
[tex]Marginal = 0.04*500 + 50[/tex]
[tex]Marginal = 70[/tex]
Solving (d): Interpret the values in (c)
[tex]Average = 59.8[/tex]
They make a profit of 59.8 for the first 500 items
[tex]Marginal = 70[/tex]
From the 501st item, the profit is 70
Please help!
Alex knows 18% of the students surveyed at his school are dropped off by car, while 22% walk or ride bikes, and the rest ride the bus. Which table could represent this information?
Please hurry, im on a unit test!
Answer:
Option a doesn't equal 100.
option b equals 100
c doesnt equal 100
d doesnt equal 100
the answer is b
What is the complete factorization of x^2+4x-45
In NTUV, the measure of N=90) UV = 8.7 feet, and VT = 3.6 feet. Find the measure of to the nearest degree.
Answer:
5
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
find the value of each variable or indicated measures
Answer:
Step-by-step explanation:
To find the angle measure of an angle inside an arc then you multiply 1/2 by the sum of the 2 intercepted arcs.
x=1/2(42+56)
x=1/2(98)
x=49
5 - 3(7x + 8)
It tells me to simply each expression and then this is the expression.
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{5 - 3(7x + 8)}\\\\\large\text{DISTRIBUTE -3 WITHIN the PARENTHESES}\\\large\textsf{5 - 3(7x) + (-3)(8)}\\\large\textsf{-3(7x) = -21x}\\\large\textsf{-3(8) = -24}\\\large\textsf{= \underline{5 - 21x - 24}}\\\\\large\text{COMBINE the LIKE TERMS}\\\large\textsf{(-21x) + (5 - 24)}\\\large\textsf{-21 does NOT have any LIKE TERMS so we could leave it the same}\\\large\textsf{5 - 24 is the only LIKE TERM pair}\\\large\textsf{5 - 24 = -19}\\\large\textsf{-21x = -21x}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge\textsf{\bf -21x - 19}}}}\huge\checkmark[/tex]
[tex]\bf{Good\ luck\ on\ your\ assignment\ and\ enjoy\ your\ day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
can anyone help me? :)
Answer:
7\11
Step-by-step explanation:
you just multiply to get an integer then convert that
What is the volume of this regular prism?
9.70 cubic inches
Step-by-step explanation:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Answer:
9.70 cubic inches
Step-by-step explanation:
Surface Area (SA) = √(25 + 10 * √5) * a² + 5 * l * h
2
Volume (V) = √(25 + 10 * √5) * a² * h
4
In a 400 meter race, 4 runners pass a baton as each of them runs 100 meters of the race. The table shows the split times for the first 3 runners of a relay team. Suppose the team has set a goal of running the race in 210 seconds. Solve the equation
(53,715 + 51.3 + 52.62) + n = 210 to find the number of seconds, n, within which the 4th runner must finish for the team to meet its goal.
Will send image
Answer:
Since the equation is addition, reverse it into subtraction. 210-53.715-51.3-52.62= 52.365. You can add 53.715 by 51.3 by 52.62 by 52.365 to check your answer, and it will be 210 so the 4th runner ran 52.365 seconds.
i also got this question but i figured it out lol
3. Blackberry is also in the business of selling phones. The data for the profit that Blackberry makes on selling tablets is represented by the following equation with profit being P(b) and b being number of blackberry phones sold (both variables in millions):
P(b) = -x2 + 8x – 8
a. Use the quadratic formula to solve the equation. What do these points tell us about the graph?
b. Complete the following table. Based on the table, estimate the vertex for the function. Is the vertex a max. or a min. point?
Blackberry: Profit from Smart Phones Sold
Smart Phones sold (in millions) b Profit (in millions of dollars) P(b)
-1
0
2 4
3
4
5 7
6
c. Sketch a graph for Blackberry. Label the x and y axis (for b and P(b))
Here is my answer. I left the latter question in a. as I don't actually know the answer. Anyway, I hope this is helpful although not complete.
please please help me
solve 4x+9y= 61 and 7x+6y=58 by substitution
Answer:
what?
Step-by-step explanation:
The measure of ∠CBD is 45% of the measure of ∠ABC. Find the value of x. due today
Answer:
45°
Step-by-step explanation:
I assume you meant 45°, not 45%.
90-45=45
If it is actually 45%, then the answer would be:
90x.55=49.5°
find an equivalent ratio in simplest terms 18:99
Answer:
2:11
Step-by-step explanation:
divide both sides by 9
PLEASE HELP ME I LITERALLY HAVE NO IDEA HOW TO DO THIS!!!!!!!!!!!!!!!!!!
Answer:
24
Step-by-step explanation:
First, find the total volume of the shape by multiplying all side lengths:
1 * 2 * (3/2) = 3 cubic cm
A cube with side length of 1/2 has a volume of (1/2)(1/2)(1/2) = 1/8 cubic cm
If the total volume is 3 cubic cm, how many 1/8 cm cubes would fit?
3 / (1/8) = 24 cubes
can anyone tell me time it's 11:24PM for me
Answer:
It's 11:55
Step-by-step explanation:
what is 8 with an exponent of 2 equal to ?
Answer:
64
The Exponent 2 is like multiplying 8 by itself.
Ex: 8 x 8
HOPE THIS HELPED :)
Which of the following statements is NOT true about the graph of a system of equations with no solutions?
A. The lines will have the different slopes.
B. The lines will have different y-intercepts.
C. The lines will share none of the same points.
D. The lines will have the same slope.
Answer:
A
Step-by-step explanation:
A would be the best answer here because equations with no solutions would be parallel. That means they would have the same slope but with different y-intercepts. Since where the equations share points would be the solution, they cannot share points either.
Solve these equations. Show solutions on a number line. |x - 14| = 14
Answer:
how are we supposed to get a number line if you didn't provide it i would answer it/
Step-by-step explanation:
Answer:
x=0 or x=28
im not sure
find equation for the line with slope -10/7 and goes through point (-35, -1)
Answer:
y = -10/7x - 51
Step-by-step explanation:
y - y1 = m(x - x1)
y + 1 = -10/7(x + 35)
y + 1 = -10/7x - 50
y = -10/7x - 51
Pleaseeeeeeeeeeeeeeeee help nowwwwwwwwwwwwwww
Find 10.8% of 405. Round to the nearest tenth.
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
it would increase
Step-by-step explanation:
2. Next Christmas, I'm buying my Valentine a brand new car. I estimate that it will cost me about
$32,000 so I'm planning on putting down a 20% down payment. Chase Bank is offering to give me a
car loan with 4.5% annual interest compounded monthly for 5 years. What will my monthly payment
be?
A =R2-(1+1)
1
L
bungee sgch rkaos cus xuie. how d uurneciif enc uksnw elzowncuejicnf u
What is the approximate distance from one corner of the soccer field to the opposite comer?
BRAINLIEST! HELP! Please help me! I NEED PART D AND E! I’m so lost :(
If you can show your work so I understand that would be awesome! Thanks so much!!
Part A-The pyramids have always fascinated Kristina, so she wants to build to model pyramids to put on her mantle. She wants her model of Khufu’s pyramid to have a volume of 73.5 inches and a height of 4.5 inches. What would the side length of the base of the pyramid be is this a rational or irrational? Why?
Part B- The volume of Khafre’s pyramid is about 9/10 the volume of Khufu‘s pyramid. If Kristina wants to make the second model pyramid so it’s volume is 9/10 of the volume of the first model pyramid, what volume should she make the second model pyramid?
Part C- if the height is 4.41 inches and the volume is the volume found in Part B, what will the side length of the pyramids base be? Is the number rational or irrational? Why?
Part D- for the model to be scale, the ratio of the height to the side length should be the same for both the actual pyramid and the model. Is the model of Khufu‘s pyramid to scale? If not, is it close?
Part E- Is the model of Khafre’s pyramid to scale? If not, is it close?
Part A
Given:
Volume of square pyramid = 73.5 cubic inches
height of square pyramid = 4.5 inches
To find:
1)Side length of square pyramid.
2)if side length of square pyramid is rational or irrational
Steps:
1) Side length = [tex]\sqrt{\frac{3v}{h} }[/tex]
Side length = [tex]\sqrt{\frac{3*73.5}{4.5} }[/tex]
Side length = [tex]\sqrt{\frac{3*73.5*10}{4.5*10} }[/tex] (multiplying both sides to make it a whole number)
Side length = [tex]\sqrt{\frac{3*735}{45} }[/tex]
Side length = [tex]\sqrt{\frac{735}{15} }[/tex] (3 gets canceled out)
Side length = [tex]\sqrt{49}[/tex]
Side length = 7 inches
Therefore, the side length of the square pyramid is 7 inches long
2) 7 is a rational number, so the side length of the square pyramid is a rational number.
It is a rational number because,
it can be written in the form p/q, where
1) q [tex]\neq[/tex]0
2) p and q are co-prime
3) p and q are integers
Part B
Given:
Volume of Khafre's pyramid = 9/10 of Khufu's pyramid's volume
Volume of Kristina's first pyramid = 73.5 cubic inches
To find:
Volume of Kristina's second pyramid
Steps:
Volume of Kristina's second pyramid = 9/10 the volume of Kristina first pyramid
Volume of second pyramid = [tex]\frac{9}{10}*73.5[/tex]
Volume of second pyramid = 9 [tex]*[/tex] 7.35
Volume of second pyramid = 66.15 cubic inches
The volume of the second pyramid should be 66.15 cubic inches
Part C
Given:
Height of pyramid = 4.41 inches
Volume of pyramid = 66.15 cubic inches
To find:
1) Side length of pyramid
2) if the side length is rational or irrational
Steps:
1) Side length = [tex]\sqrt{\frac{3v}{h} }[/tex]
Side length = [tex]\sqrt{\frac{3*66.15}{4.41} }[/tex]
Side length = [tex]\sqrt{\frac{3*66.15*100}{4.41*100} }[/tex] (multiplying both sides to make it a whole number)
Side length = [tex]\sqrt{\frac{3*6615}{441} }[/tex]
Side length = [tex]\sqrt{\frac{6615}{147} }[/tex] (3 gets canceled)
Side length = [tex]\sqrt{45}[/tex]
Side length of pyramid is [tex]\sqrt{45}[/tex] inches
2) [tex]\sqrt{45}[/tex] cant be written in the form of a fraction, so it is an irrational number
(if u want i can explain this more)
Part D
Given
Height of model pyramid = 4.5 inches
Height of Khufu's pyramid = 755.75 feet (had to search the internet for the answer, so I am not sure if it is correct)
Side length of model pyramid = 7 inches
Side length of Khufu's pyramid = 481.4 feet (had to search the internet for the answer)
To find:
1)If the model is to scale with Khufu's pyramid
2) If the model is close to scale with Khufu's pyramid
Steps:
1) First lets find the ratio of the height to the side length of the model
Ratio = 4.5 in : 7 in
= 45 : 70
= 9 : 14
= 0.6428
Now lets find the ratio of the height to the side length of Khufu's pyramid
Ratio = 481.4 feet : 755.75 feet
= 5776.8 in : 9069 in
= 0.6369
Therefore the model is not to scale with Khufu's pyramid
2) Yes the scale is close
Part E
Given:
Height of model pyramid = 4.41 inches
Height of Khafre's pyramid = 448 feet
Side length of model pyramid = [tex]\sqrt{45}[/tex] inches
Side length of Khafre's pyramid = 706 feet
To find:
1) If the model is to scale with Khafre's pyramid
2) If the model is close to scale with Khafre's pyramid
Steps:
1) First lets find the ratio of the height to the side length of the model pyramid,
Ratio = 4.41 in : [tex]\sqrt{45}[/tex] in
= 4.41 : 6.7082
= 0.6574
Now lets find the ratio of the height to the side length of Khafre's pyramid
Ratio = 448 ft : 706 ft
= 5376 in : 8472 in
= 0.6345
Therefore the model is not to scale with Khafre's pyramid
2) No, the model is not close to scale, (it depends by what is meant by close, for me its 0.01)
Happy to help, and I hope you learnt something from this answer that will help you in the future
If you didn't understand any topic pls ask
Manipulate the radius and height of the cone, setting different values for each. Record the radius, height, and exact volume of the cone in terms
of m). The first one has been done for you. Also calculate the decimal value of the volume, and verify that it matches the volume displayed by the
tool (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= 2000π unit³
Volume= 6284 unit³
Step-by-step explanation:
The decimal value of the volume already given= 600π
The decimal value of the volume already given= 600*3.142
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= πr²h/3
Volume= 11²*12/3 *π
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume = πr²h/3
Volume= 4²*6/3(π)
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= πr²h/3
Volume= 20²*15/3(π)
Volume= 2000π unit³
Volume= 6284 unit³
Hope this helps, best of look to all who needed help!!
Suppose a white dwarf star has a diameter of approximately 1.8083 to the power of 4 km. Use the formula 4n to the power of 2 to find the approximate surface area of the star.
ANSWER:
The surface area of the star is 3.2700 x [tex]10^{8}[/tex] square kilometres.
EXPLANATIONS:
Diameter of the star = 1.8083 x [tex]10^{4}[/tex] Km.
Surface area of the star = 4[tex]n^{2}[/tex]
Where n is the radius of the star.
So that;
n = [tex]\frac{ 1.8083 * 10^{4} }{2}[/tex]
= 0.90415 x [tex]10^{4}[/tex]
n = 0.90415 x [tex]10^{4}[/tex] Km
Thus,
Surface area = 4 x [tex](0.90415*10^{4} )^{2}[/tex]
= 326994889
Surface area = 3.2700 x [tex]10^{8}[/tex] [tex]km^{2}[/tex]
Therefore, the surface area of the star is 3.2700 x [tex]10^{8}[/tex] square kilometres.
The area of a rectangular sheet of metal is 135 square inches. The perimeter is 48 inches. What are the dimensions of the sheet?
Answer: The length is 15 inches and breadth is 9 inches
Step-by-step explanation:
Given : Area of rectangular sheet = 135 square inches
Perimeter of rectangular sheet = 48 square inches
Now Area of rectangular sheet = [tex]Length\times Breadth[/tex] = 135 square inches
perimeter of rectangular sheet = [tex]2\times (Length+Breadth)[/tex] = 48 square inches
Thus [tex](Length+Breadth)[/tex] = 24 square inches
Thus Length = 15 inches
Breadth = 9 inches
23.
If A, B, C are distinct digits, which of the following numbers cannot be the largest possible 6-digit number
written using three digits A, two digits B, and one digit C?
(A) AAABBC (B) CAAABB (C) BBAAAC (D) AAABCB (E) AAACBB
Answer:
The number that cannot be the largest possible 6-digit number is;
(D) AAABCB
Step-by-step explanation:
From the question, we have;
A, B, and C = Distinct digits, therefore, A ≠ B ≠ C
The number of digits in the number to be formed = 6 digits
The number of 'A' in the number to be formed = 3
The number of 'B' in the number to be formed = 2
The number of 'C' in the number to be formed = 1
We have;
When A > B > C
The largest possible number = AAABBC
When C > A > B
The largest possible number = CAAABB
When B > A > C
The largest possible number = BBAAAC
When A > C > B
The largest possible number = AAACBB
Therefore, given that when A > B > C, the largest possible number = AAABBC, we have;
AAABBC > AAABCB, because B > C, therefore, within the tens and unit of the two 6 digit numbers, we have, BC > CB
∴ AAABBC > AAABCB and AAABCB, cannot be the largest possible 6-digit number
PLEASE HELP ME........
Answer:
the answer is A!!!
i think it right not sure
Quick answer please
Answer:
D) 20m³
Step-by-step explanation:
1/2x4x2x5=20