Find the number of units x that produces the minimum average cost per unit C in the given equation. C = 0.001x3 + 5x + 250

Answers

Answer 1

Answer:

50 units

Step-by-step explanation:

Find the number of units x that produces the minimum average cost per unit C in the given equation.

C = 0.001x³ + 5x + 250

unit cost f(x) = C/x

= 0.001x³/x + 5x/x+ 250/x

f(x) = 0.001x² + 5 + 250/x

f'(x) = 0.002x - 250/x²

We equate the first derivative to zero

0.002x - 250/x² = 0

0.002x = 250/x²

Cross Multiply

0.002x × x² = 250

0.002x³ = 250

x³ = 250/0.002

x³ = 125000

x = 3√(125000)

x = 50 units

Therefore, the number of units x that produces the minimum average cost per unit C is 50 units.


Related Questions

what is two and three hundreds seventy thousandths in decimal form

Answers

Answer:

2.370

Step-by-step explanation:

In this, the word "and" means the decimal point so:

two and 3

=

2.3

so the tenths place would be the first number after the decimal point, you can think of it as counting backwards. 1000  100  10  "0"  0.1  0.01  0.001

                                                thousnd hundrd tn zro tnths hundrds thousndths

so the 3 hundred would be 0.3 and the sevenTY thousandths would be 0.070

so add that all up and you get:

2.370

or

two and three hundreds seventy thousandths

Hope this helped! Pls Brainliest! It would help and mean a lot! ; )

A probability experiment is conducted in which the sample space of the experiment is S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event E={2, 3, 4, 5, 6, 7}, event F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}. Assume that each outcome is equally likely. List the outcome s in For G. Now find P( For G) by counting the numb er of outcomes in For G. Determine P (For G ) using the General Addition Rule.

Answers

Answer:

The answer is " [tex]\bold{\frac{2}{3}}[/tex]"

Step-by-step explanation:

Given set:

[tex]\to F \ or\ G = \{ 5,6,7,8,9,10,11,12\}[/tex]

In the above-given set, there are 8 elements and 12 possible outcomes so, the equation is:

[tex]\to P( F\ or \ G) = \frac{8}{12}[/tex]

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

by using the general addition Rule:

[tex]\to P(F \cup G) = P(F) +P(G)- P(F \cap G)[/tex]

                    [tex]=\frac{5}{12}+\frac{4}{12}- P(E \cap H)\\\\=\frac{6}{12}+\frac{3}{12}- \frac{1}{12}\\\\=\frac{6+3-1}{12}\\\\=\frac{8}{12}\\\\=\frac{2}{3}\\\\[/tex]

Which is cd = pq – a solved for q?

Answers

Step-by-step explanation:

The answer is

[tex]q = \frac{cd}{p} [/tex]

170% of what is 166?

Answers

Answer:

97.65

Step-by-step explanation:

97.65

Step-by-step explanation

In Mario kart the special blocks are programmed to deliver 3 green shells for every 11 bananas.if in the last game characters received 104 more bananas than green shells, how many green shells were received?

Answers

Answer:

look im putting this here bc i have to answer 50 questionsfor a quest sdo dont report me ;-;

Step-by-step explanation:

The length of a rectangle is 2 times the width. If the perimeter is to be less than 96 meters. What are the possible

values for the width? (Use w as the width)

Preview

TIP

Enter your answer using inequality notation. Example: 3 <=w<4

Use or to combine intervals. Example: w< 2 or w >= 3

Enter all real numbers for solutions of that type

Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 243,

5+4)

Enter DNE for an empty set. Use oo to enter Infinity.

Answers

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

A right triangle has one 40° angle. Find the other two angles.
° (smaller value)
° (larger value)

Answers

a triangle = 180°

one angle = 90°
second angle = 40°
third angle = 50°

I need help ASAP!! Please

Answers

Answer:

26.31

Step-by-step explanation:

You just have to count up the shapes in each place.

You just got off the Haunted Mansion ride and the next ride you want to go
on is Splash Mountain. You have a fast pass that requires you to arrive at
Splash Mountain in 7 3⁄4 minutes. Splash Mountain is 1 3/5 miles away. You are able to cover 2/7 of a mile every minute. Can you make it to Splash Mountain?

Answers

Answer:

You can make it to Splash Mountain

Step-by-step explanation:

From the question,

The distance you need to cover to Splash Mountain is 1 3/5 miles, and the time you have to arrive there is in 7 3/4 minutes.

Also, from the question,

You are able to cover 2/7 of a mile every minute, that is

Your speed is 2/7 mile per minute

To determine if you can make it to Splash Mountain, we will determine the distance you can cover, traveling at this speed of 2/7 mile per minute for 7 3/4 minutes. If the distance you can cover is more than 1 3/5 miles, then you can make it; but if the distance you can cover is less than 1 3/5 miles, then you cannot make it.

From

Speed = Distance / Time

Distance = Speed × Time

Speed = 2/7 mile/minute

Time = 7 3/4 minutes = 31/4 minutes

∴Distance = 2/7 × 31/4

Distance = 31/14 miles = 2 3/14 miles

The distance you can cover traveling 2/7 of a mile every minute for 7 3/4 minutes is 2 3/14 miles, since this is more than 1 3/5 miles, then you can make it to Splash Mountain.

Hence, you can make it to Splash Mountain.

Help I will award brainliest help asap! Uwu: If a man can run p miles in x minutes, how long will it take him to run q miles at the same rate?

Answers

Answer:

Speed= Dist/time= p/x miles per minute

Time to run q miles=q divided by p/x= qx/p minutes

Step-by-step explanation:

I don’t know exactly what you’re asking here but a relative equation that can be used if you have either p or q is p/x=q/x.

Suppose that minor errors occur on a computer in a space station, which will require re-calculation. Assume the occurrence of errors follows a Poisson process with a rate of 1/2 per hour. (a) Find the probability that no errors occur during a day. (b) Suppose that the system cannot correct more than 25 minor errors in a day, in which case a critical error will arise. What is the probability that a critical error occurs since the start of a day? Keep up to the 6th decimal place in your answer. (c) Suppose the error correction protocols reset themselves so long as there are no more than five minor errors occurring within a 2 hour window. The system just started up and an error occurred. What is the probability the next reset will occur within 2 hours?

Answers

Answer:

a

  [tex] P(X = 0) =  0.6065 [/tex]

b

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

c

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Step-by-step explanation:

From the question we are told that

  The rate  is [tex]\lambda =  \frac{1}{2}\   hr^{-1}[/tex]    =  0.5 / hr

  Generally  Poisson distribution formula is mathematically represented as

       [tex]P(X = x) =  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

Generally the probability that no error occurred during a day is mathematically represented as  

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

   [tex][tex]P(X = 0) =  \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}[/tex]

=>  [tex] P(X = 0) =  0.6065 [/tex]

Generally the probability that  a critical error occurs since the start of a day is mathematically represented as

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

      [tex]P(x \ge 25 ) =  1 - P(x <  25 )[/tex]

Here

     [tex]P(x <  25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}[/tex]

=>   [tex]P(x <  25 ) =  \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + 6.0*10^{-32}[/tex]

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

Considering question c

Here  t =  2  

Gnerally given that the  system just started up and an error occurred  the probability the next reset will occur within 2 hours

[tex]P(x \le 5 ) =  \sum_{n=0}^{5}  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{(0.5 *  2) ^ 0 e^{- 0.5  * 2 }}{0!} + \cdots  +   \frac{(0.5 *  2) ^ 5  e^{- 0.5  * 2 }}{5!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{1* 2.7183 }{1 } + \cdots  +   \frac{1  *2.7183 }{120}[/tex]

=>  [tex]P(x \le 5 ) =   2.7183 + \cdots  +   0.0226525[/tex]

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Working simultaneously, eight pumps fill in a pool in 32 hours. All pumps work at the same pace. If only half of the pumps are working, in how many hours will the pool be filled in?

Answers

Answer:

64 hours

Step-by-step explanation:

Since there are only half of the pumps that are working the time will double. 32x2 is 64

Answer: 16 hours

Step-by-step explanation

Step 1: Split 8 in half because we are using half the amount of pumps which is 4. Now we know the amount of pumps being used.

Step 2: Next we find the unit rate by dividing 32 and 8 to get 4

Step 3: Lastly we multiply 4x4 because 4 is the amount of pumps being used and the other 4 is the unit rate. Once we multiply we get 16 which is the answer: 16 hours

result when the number 90 is decreased by 7.1%? Round your answer to the nearest tenth.

Answers

Answer:

83

Step-by-step explanation:

you need to think about the equation and think of the number closest to each number and decide which fits

Answer:

83.6

Step-by-step explanation:

You need to subtract 7.1 from 100, because it's a percentage, to get the resulting percent. Then multiply 90 with the answer you got in percent.

The probability of getting a white marble from the bag is 1/6. If there are eight white marbles in the bag, what is the total number of marbles in the bag?
A. 36
B. 24
C. 48
D. 14

Answers

Answer:

C: 48

Step-by-step explanation:

1/6 chance so multiply by 6, 8 marbles so multiply by 8, 8(6)=48

Answer:

48 marbles, it's C

Step-by-step explanation:

why?

Because 1/6 of the marbles are white. and there are 8 white marbles. so that means, 1/6=8 marbles.

So you just get 1/6 to 6/6

so you do, 8*6 which equals to 48

Does anyone have the answer?

Answers

Answer:

hi to what. good bye???????


Order from least to greatest:
-5/6,0.567,-0.11,-1/4

Answers

Answer:

-5/6,-1/4,-0.11,0.567

Step-by-step explanation:

A scaled drawing of a rectangle park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area of the actual park in square units?

Answers

Area of the actual park is 56000 square yards.

Step-by-step explanation:

A scale drawing of a rectangular park has dimensions as 5 inches width and 7 inches length.

Actual length of the park has been given as 280 yards.

So scale factor used in the drawing is 7 inches

= 280 yards

Or 1 inch = 40 yards

Since width of the rectangular park is = 5 inch

So actual width of the park will be = 5×40 = 200 yards

Now we can calculate the area of the park.

Actual area of the park = Length × Width

= 280×200

= 56000 yards²

Therefore, area of the actual park is 56000 square yards.

PLEASE HELP WILL GIVE CROWN



A submarine is 50 feet below sea level. It rises toward the surface for 12 seconds at a rate of 3 feet per second.
How many feet below sea level is the submarine when it is finished rising?

Answers

3x12 is 36. 50-36 is 14. so the submarine will be at 14 feet below sea level

Answer:

14

Step-by-step explanation:

umm I don't know if im dumb but isn't it just 3 times 12 giving you 36 and than 50 minus 36 with an answer of 14

A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend.

Which expression uses the distributive property to show equivalent expressions for this situation?

54 + 42 = (3)(18) + (6)(7)
54 + 42 = (9)(10) + 6
54 + 42 = 90 + 6
54 + 42 = 6(9 + 7)

Answers

Answer:

54 + 42 = 6(9 + 7)

Step-by-step explanation:

Using distributive property on the right side of the equality, you multiply 6 and nine and 6 and 7 to get rid of the parenthesis.

Answer:

its the last one

Step-by-step explanation:

For a school project, the school bought 36 hamsters for $5.90 each and 40 cages for $30.25 each.
How much did the school spend in all?

Answers

1,422.4 is the answer please give brainliest

PLEASE HELP ME ANSWER BOTH QUESTIONS WILL MARK BRAINLIEST!!!

Answers

Answer:

2034

Step-by-step explanation:

Help it’s for algebra 1

Answers

f(2) = -5(2) + 7
f(2) = -10 + 7
f(2) = -3

Which of these is a biomorphic shape? Choose the answer.
O a capital letter W
O a microphone
an outline of a pine tree
O a pyramid

Answers

Answer:

Option C: an outline of a pine tree

Step-by-step explanation:

Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.

A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.

Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".

Thus, it is a bimorphic shape.

Answer:

C. an outline of a pine tree

Step-by-step explanation:

I just took the test!

PLZ HELP I WILL MARK BRAINLEST!

Answers

Answer: 16.4cm

Step-by-step explanation: 4cm=20km

82/20 is 4.1. 20 multiplied by 4.1 and you get 16.4cm

Please help answer this I will make you brainlst

Answers

Answer:

Read the comments that is where i put the answer at + my work.

Confused on this please help

Answers

Answer: it would be half the size

Step-by-step explanation:

Suppose that Smartphone A has 256 MB RAM and 32 GB R OM, and the resolution of its camera is 8 MP; Smart- phone B has 288 MB RAM and 64 GB R OM, and the resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB R OM, and the resolution of its camera is 5 M P . Determine the truth v alue of each of these propositions. a) Smartphone B has the most RAM of these three smart- phones. b) Smartphone C has more R O M o r a higher resolution camera than Smartphone B. c) Smartphone B has more RAM, more R OM, and a higher resolution camera than Smartphone A. d) If Smartphone B has more RAM and more R O M than Smartphone C, then it also has a higher resolution camera. e) Smartphone A has more RAM than Smartphone B i f and only if Smartphone B has more RAM than Smart- phone A.

Answers

Answer:

A.) TRUE

B.) TRUE

C.) FALSE

D.) FALSE

E.) FALSE

Step-by-step explanation:

Given that :

SMARTPHONE A:

RAM : 256 MB

ROM : 32 GB

CAMERA RESOLUTION : 8 MP

SMARTPHONE B:

RAM : 288 MB

ROM : 64 GB

CAMERA RESOLUTION : 4 MP

SMARTPHONE C:

RAM : 128 MB

ROM : 32 GB

CAMERA RESOLUTION : 5 MP

Determine the truth value of each of these propositions.

A) Smartphone B has the most RAM of these three smart- phones.

TRUE ; 288 > (256 and 128)

B) Smartphone C has more R O M o r a higher resolution camera than Smartphone B.

C ROM > B ROM = FALSE

C CAMERA RESOLUTION > B camera resolution = TRUE

FALSE or TRUE = TRUE

C.) Smartphone B has more RAM, more R OM, and a higher resolution camera than Smartphone A.

RAM = TRUE ; ROM = TRUE ; CAMERA RESOLUTION = FALSE

TRUE and TRUE and FALSE = FALSE

d) If Smartphone B has more RAM and more R O M than Smartphone C, then it also has a higher resolution camera.

CAMERA RESOLUTION ON SMARTPHONE B IS LESS, HENCE, STATEMENT = FALSE

e) Smartphone A has more RAM than Smartphone B i f and only if Smartphone B has more RAM than Smart- phone A.

1st statement = FALSE

2nd condition = TRUE

FALSE and TRUE

= FALSE

.
***
9. The game of euchre uses only the 9s, 10s, it is
jacks, queens, kings, and aces from a standard
deck of cards. How many five-card hands have
a) all red cards?
b) at least two red cards?
c) at most two red cards?
Answer
a) From those information we know that have 24 card
In those cards it have 12 red.
12C5=792
B)
at least 2 red card=No restriction- without red card- at least one red card
= 24C5-(12C0*12C5)-(12C1*12C4)
=35772
C) at most 2 red card

24C5-(12C0*12C5)-(12C1*12C4)-(12C2*12C3)
=21252

Answers

I’m pretty sure it’s c

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of at most 2 red cards is 0.5.

What is Binomial distribution?

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Using the given information the number of cards is 24 out of which 12 are red. Therefore, the probability of getting a red card is 0.5.

A) All red cards.

P(X=5) = ⁵C₅ (0.5⁵) (0.5⁰)

            = 0.03125

B.) at least two red cards.

P(X≥2) = 1 - ⁵C₀ (0.5⁰) (0.5⁵) - ⁵C₁ (0.5¹) (0.5⁴)

= 0.8125

C.)  At most 2 red cards.

P(X≤2) = ⁵C₀ (0.5⁰) (0.5⁵) + ⁵C₁ (0.5¹) (0.5⁴) + ⁵C₂ (0.5²) (0.5³)

           = 0.5

Learn more about Binomial Distribution:

https://brainly.com/question/14565246

#SPJ2

Ten less than 5 times the value of a number is equal to 10 times the quantity of
12 more than one-fourth of the number. If a is the number, what is the value of a?

Answers

Answer:

52

Step-by-step explanation:

given that the number is a

The expression for Ten less than 5 times the value of a number is given by

5a - 10

10 times the quantity of  12 more than one-fourth of the number.

a/4 is one-fourth  of number

12 more than one-fourth of the number

a/4 + 12

expression for  10 times the quantity of  12 more than one-fourth of the number. is given by

10(a/4 + 12) = 10a/4 + 12*10 = 2.5a + 120

Given that the above two expression are equal

equating them we have

5a - 10 = 2.5a + 120

adding 10 both sides

=>5a - 10+ 10  = 2.5a + 120 + 10

=> 5a = 2.5a + 130

subtracting 2.5a from both sides

=> 5a - 2.5a = 2.5a + 130 - 2.5a

=> 2.5a = 130

dividing both side by 2.5

=> a = 130/2.5 = 52

Thus, value of a is 52

Consider the following cost function.
A. Find the average cost and marginal cost functions.
B. Determine the average and marginal cost when x = a.
C. Interpret the values obtained in part​ (b).
C(x) = 1000 + 0.1x, 0 ≤ x ≤ 50000 ≤ x ≤ 5000, a = 2000

Answers

Answer:

a)Average cost function =[tex]\bar{C(x)}=\frac{1000+0.1x}{x}[/tex]

Marginal cost function =[tex]C'x=0.1[/tex]

b) [tex]\bar{C(2000)}=0.6[/tex]

[tex]C'(2000)=0.1[/tex]

c)[tex]\bar{C(2000)}=0.6[/tex] is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item

Step-by-step explanation:

Cost function: [tex]C(x) = 1000 + 0.1x[/tex]

a)Find the average cost and marginal cost functions.

Average cost function =[tex]\bar{C(x)}=\frac{C(x)}{x}[/tex]

Average cost function =[tex]\bar{C(x)}=\frac{1000+0.1x}{x}[/tex]

Marginal cost function =[tex]C'x=0.1[/tex]

b) Determine the average and marginal cost when x = a.

a = 2000

Average cost function =[tex]\bar{C(x)}=\frac{1000+0.1x}{x}=\frac{1000+0.1a}{a}=\frac{1000+0.1(2000)}{2000}=0.6[/tex]

So, [tex]\bar{C(2000)}=0.6[/tex]

Marginal cost function =[tex]C'(2000)=0.1[/tex]

c)Interpret the values obtained in part​ (b).

[tex]\bar{C(2000)}=0.6[/tex] is the average cost to produce first 2000 items

C'(2000)=0.1 is the marginal cost to produce 2001 th item

Other Questions
Math help please! - ( 4/5 ) song of the open road by Walt Whitman afoot and light-hearted, i take to the open road, healthy, free, the world before me, the long brown path before me, leading wherever I choose. Henceforth I ask not good-fortunei myself am good-fortune; henceforth I whimper no more, postpone no more, need nothing, strong and content, I travel the open road. . . .from this hour, freedom! From this hour I ordain myself loosd of limits and imaginary lines, going where I list, my own master, total and absolute, listening to others, and considering well what they say, pausing, searching, receiving, contemplating, gently, but with undeniable will, divesting myself of the holds that would hold me. I inhale great draughts of space; the east and the west are mine, and the north and the south are mine. I am larger, better than I thought; I did not know I held so much goodness. all seems beautiful to me; I can repeat over to men and women, you have done such good to me, i would do the same to you. I will recruit for myself and you as I go; I will scatter myself among men and women as I go; I will toss the new gladness and roughness among them; whoever denies me, it shall not trouble me; whoever accepts me, he or she shall be blessed, and shall bless me. Part a) what is a theme of "song of the open road"? taking a vacation allows someone to spend meaningful time with friends and family. traveling is a freeing experience that allows for independence and self-reflection. being rooted in one place doing everyday activities is better than wandering alone on the open road.only when people are traveling can they truly prioritize the needs of others over their own needs. Part b) which two quotes from the poem best help Whitman develop the theme identified in part a?"from this hour, freedom! / from this hour I ordain myself loosd of limits and imaginary lines,""I can repeat over to men and women, you have done such good to me, I would do the same to you.""pausing, searching, receiving, contemplating, / gently, but with undeniable will, divesting myself of the holds that would hold me.""I will recruit for myself and you as i go; / i will scatter myself among men and women as I go;" Match this weakness of the articles of confideration to the outcome it caused:Congress had no power to enforce laws...A)the federal government could print money B) the federal government controlled all tradeC) the federal government had no control over state lawD) the federal government controlled state affairs The witchcraft trials that took place in Salem, Massachusetts in 1692 and 1693 have raised many questions. 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Explain how residents of a community are affected by violent activism.