The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 per unit, the quantity demanded is 64 units. The initial cost is $150 and the cost per unit is $2. What price will yield a maximum profit?

Answers

Answer 1

q(p) = k/p^3 . . . . . . . . we want to find k
q(10) = k/10^3 = 64
k = 64,000

Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3

Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150

Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3

A price of $3 per unit will yield a maximum profit.

The Quantity Demanded X For A Product Is Inversely Proportional To The Cube Of The Price P For P >

Related Questions

suppose you spina spinner numbered 1 through 6, and you sa 3 five times in a row.What is the theoretical possibility of spinning a 3 on the next spin

Answers

it would still be a 1/6th chance that you will gey the number three. i would say that just because you got 3 5 times in a row will not increase or decrease your chances of another 3.

A provider order has been received for a dobutamine (dobutrex®) drip at 7 mcg/kg/min. the patient's weight is 220 lbs. how many milligrams per hour should be given?

Answers

To figure this out you first need to determine how many kg there are in 220 lbs. 1 lb equals 0.454 kg, so 220 lbs= 99.88 kg.

It states that a patient receives 7mcg per kg per minute, so the patient will receive 7 x 99.88=699.16 mcg per minute.

You need to convert this to a number of mcg per hour, so multiply the amount by 60 to get 41949.6 mcg per hour.

Final answer:

The patient's weight is first converted from lbs to kg, resulting in 100 kg. The dosage in micrograms per hour is then found to be 42000 mcg/hour. Lastly, this is converted to milligrams to give a final dosage of 42 mg/hour.

Explanation:

This is a question pertaining to medical dosage calculations. First, we need to convert the patient's weight from pounds to kilograms since our dosage is based on that unit. We know that 1 kg equates to approximately 2.2 lbs. So, the patient's weight in kilograms would be 220 lbs/2.2 = 100 kg.

Now, we can use the patient's weight to find the dosage per minute: 7 mcg/kg/min * 100 kg = 700 mcg/min. But the question asks for the dosage per hour, so we must convert minutes to hours: 700 mcg/min * 60 min/hour = 42000 mcg/hour. Finally, we need convert from mcg to mg as the question asked for the amount in milligrams. Since there are 1000 mcg in 1 mg, the dosage becomes: 42000 mcg/hour / 1000 = 42 mg/hour.

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Harry's Health club costs $20 per month plus a $75 membership fee. Fiona's fitness costs $35 per month. What is the dollar amount at the break even point?

Answers

Answer: The break even point is after 5 months.

First, we need to set up an equation for each plan.

Harry's Health Club can be y = 20x + 75 because it starts at 75 and increase 20 per month.

Fiona's Fitness can be just y = 35x because it is just 35 per month.

Set the equation equal to each other and solve.

20x + 75 = 35x
75 = 15x
5 = x

PLEASE HELP RIGHT NOW! 15pts Square RSTU is constructed with line PQ drawn through its center. If the square is dilated using a scale factor of one over two(1/2) and a line is drawn through the center of the new dilated figure, what relationship will the new line have with line PQ? Explain your reasoning using complete sentences.

Answers

The line would lie on the same line as original but it will be 1/2 the length.

The line PQ will also dilate using a scale factor of 1/2 and length becomes PQ/2.

What is dilation?

Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.

Given that,

A square is RSTU.

Also, a line PQ drawn through the center.

When the square is dilated using a scale factor of 1/2,

The line that is drawn through the center will also be dilated.

Hence, the line PQ will be dilated by 1/2,

And the length of line will be PQ/2.

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Find two ratios equal to the given ratio : 1/5:1 3/5

Answers

Hi there!

To find two ratios equal to the given ratio, all we need to do is multiply both sides of the ratio by the same number.

1:3 is an equal ratio because we multiply both sides of it by 5.

2:6 is also an equal ratio because we multiply both sides by 10.

Hope this helps!

The sum of Emil’s and Rosa’s ages is 27 years. Nine years ago Emil was twice as old
as Rosa was then. How old is each person?

Answers

e + r = 27;
e - 9 = 2 x ( r - 9 );
So, e = 27 - r;
Then, 27 -r - 9 = 2r - 18;
18 - r = 2r - 18;
18 + 18 = 2r + r;
36 = 3r
Finally, r = 12 years (Rosa);
e = 27 - 12;
e = 15 years (Emil);

Match each prism with its volume. Ignore units.

ITEMBANK: Move to Top
36
45
216
250
546
60

Answers

1. 5x5x10= 250in 3. 3x3x5=45ft 4. 8x8x8=216 I can't see the numbers for the 2nd rectangular prism, you would simply just multiply those 3 numbers together to get the volume.

Prism 1) 4×5×3 = 60
Prism 2) 5×5×10 = 250
Prism 3) I can't see the numbers but I'm guessing the answer would be 546, as it's the only one left.
Prism 4) 5×3×3 = 45
Prism 5) 6×6×6 = 216
Hope this helps, although, if you don't understand something, ask me!

i really need help. thanks

Answers

Break the parking lot into different polygons that you can easily find the area of. Then find the add all the areas of the diagram and multiply by 75 to get the amount of money needed.

PLEASE, PLEASE HELP ME

Answers

Ok 12356. Hope this helps

if you use the distributive property the 3(a+b) will equal to 3a +3b

Five years ago the population of Australia was 23.13 million. It has grown by 870 000. What is the population of Australia now?

Answers

23,130,000 + 870,000 = 24,000,000

The current population of Australia is 24 million.

It is given to us that the initial population was 23.13 million and the population 5 year later has grown by 870000 or 0.87 million. Thus to find the current population we simply need to add the initial population and the growth that has happened in 5 years. This gives us:

[tex]Current\ population = 23.13\ million + 0.87\ million = 24\ million[/tex]

Thus, the current population of Australia is 24 million.

PLEASE HELP QUICK
Which question can best be answered by finding the volume of a figure?

A)How much gas is needed to fill a gas tank?

B)How much wrapping paper is needed to cover a prism?

C)How much wood is needed to frame a window?

D)How much material is needed to line a garden with a sheet of weed-blocking material?

Answers

A should be the correct answer

The correct answer is A

Hope this helps

~ Jordan ~

An airplane takes 5 hours to travel a distance of 3300 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind.

Answers

The speed with the wind is (3300 mi)/(5 h) = 660 mi/h.
The speed against the wind is (3300 mi)/(6 h) = 550 mi/h.

The speed of the plane in still air is the average of these speeds, 605 mi/h.
The speed of the wind is the difference between the plane's speed in still air and its speed in moving air, 55 mph.

Final answer:

The speed of the plane in still air is 605 miles per hour and the wind speed is 55 miles per hour. This is found through solving simultaneous equations derived from the given distance, and time taken both with and against the wind.

Explanation:

In this problem, the plane's speed in still air can be denoted as 'p' and the wind speed as 'w'. Given the total distance of the trip as 3300 miles, the total time with the wind as 5 hours, and the total time against the wind as 6 hours, we can create two equations: p + w = 3300/5 = 660 miles/hour (with the wind) and p - w = 3300/6 = 550 miles/hour (against the wind).

These equations can be solved simultaneously to get the values of 'p' and 'w'. By adding the two equations, we get 2p = 660 + 550 = 1210. Dividing by 2 gives p = 605 miles/hour. With the value of 'p' we can find 'w' by substituting p = 605 into either of the original equations (let's use p - w = 550): 605 - w = 550, which leads to w = 55 miles/hour.

So, the speed of the plane in still air is 605 miles per hour and the speed of the wind is 55 miles per hour.

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Please help me 4and 5

Answers

what grade are you in

all books in a store are being discounted by 30 percent

part a: let x represent the regular price of any book in the store.write an equation that can be used to find the sale price of any book in the store.

Jerome bought a book on sale at the store. the sale price of the book was $ 8.96.

part b: solve the equation to find the regular price of the book to the nearest cent.

Answers

okay, I'm not sure if I'm understanding this right but I think the equation to find the sale price would be x-30%.

The regular price of $8.96 should be 11.65.

Roger served 5/8 pound of cracker wich was 2/3 of the entire box what was the weight of the crackers originally in the box

Answers

Answer:
original weight of the box = 15 / 16 pounds

Explanation:
Assume that the original amount in the box is x.
We are given that:
5/8 pounds represent 2/3 of the total amount (x).
This can be translated into the following equation:
(2/3) x = 5 / 8

Now, we will solve for x as follows:
(2/3) x = 5 / 8
Multiply both sides by 24 to get rid of the denominators as follows:
(2/3) x * 24 = (5 / 8) * 24
16 x = 15
Divide both sides by 16 to isolate the x as follows:
x = 15 / 16 pounds

Hope this helps :)

The original weight of the crackers in the box is 15/16 pound.

The question asks us to determine the original weight of a box of crackers, given that 5/8 pound of crackers was served, which was 2/3 of the entire box.

We can set up the proportion by stating that 5/8 pound represents 2/3 of the whole, so let's represent the total weight of the crackers with the variable 'w'. The equation to represent this situation is (5/8) pound = (2/3) * w.

To solve for 'w', we'll multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

(5/8) * (3/2) = w

Simplifying this equation gives us the total weight:

(5 * 3) / (8 * 2) = w

15 / 16 = w

w = 15/16 pound, which is the original weight of the crackers in the box.

A square pyramid and a cube have the same volume if the length of each side of the base of the square pyramid is 2 cm in the height of the cube is 4 cm what is the height of the pyramid

a 8cm
b 16cm
c 24cm
d 48 cm

Answers

Vol sq. pyramid = 1/3×s^2×h
Vol cube = s^3
since height of cube is 4, that height = s
V = (4)^3 = 64 cubic cm
now since their Vs are the same,
1/3×s^2×h = 64
they said length of side in square pyramid
was 2, then:
1/3×(2)^2×h = 64
1/3×4×h = 64
4/3 h = 64
h = 64×3/4 = 16×3 = 48 cm

D) is the correct answer

15 POINT QUESTION Which polynomial is a quintic trinomial?
A) −x^4−5x^2+1
B) x^3+2x^2−8x+16
C) 3x^5+7x^2−9x^4
D) x^2 + 4

Answers

A quintic polynomial means a polynomials who's highest exponent value is 5. And a trinomial is a polynomial that has exactly three terms. So the answer is C

The quintic polynomial is [tex]3x^5+7x^2-9x^4[/tex]. Therefore, option C is the correct answer.

What is a quintic trinomial?

A quintic function is defined by a polynomial having highest degree five. A trinomial is defined as a polynomial having three terms. Therefore, a quintic trinomial refers to a polynomial having three terms with a highest power five.

Here, the polynomial [tex]3x^5+7x^2-9x^4[/tex] has the highest power 5.

So, the polynomial [tex]3x^5+7x^2-9x^4[/tex] is a quintic polynomial.

The quintic polynomial is [tex]3x^5+7x^2-9x^4[/tex]. Therefore, option C is the correct answer.

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the bottom of a circular swimming pool with a diameter of 30 feet is painted blue. How many square feet are blue?

Answers

The blue area covers 225π square feet.

The area of the circular pool:

Radius (r) = Diameter/2 = 30 feet / 2 = 15 feet

Area = πr^2 = π(15 ft)^2 = 225π square feet

Thus, the total area painted blue is:

225π square feet

Aiden needs 15 liters of cleaning solution. He can buy a 2-gallon jug ($4.28) a 3 gallon jug ($5.92) a 4 gallon jug ($6.56) a 7 gallon jug ($12.98). Which jug should he purchase to get at least 15 liters of cleaning solution and spend the least amount of money?

Answers

We need 15 liters
2 gallon jug 4.28*2=8.56 1 gallon=3.78, 2 gallons=7.57 liters

3 gallon jug 5.92*3=17.76 3 gallons=11.35 liters

4 gallon jug 6.56*4=26.24 4 gallons=15.14 liters

the best solution is to buy 2 times the 2 gallon jug because he will spent
8.56*2=17.12 for 4 gallons(aprox 15 liters)
instead of the 4 gallon jug which costs 26.24

7 gallon this is more expensive and he does not that much solution

Aiden should purchase a 4-gallon jug ($6.56) to get at least 15 liters of cleaning solution and spend the least amount of money.

What is unit conversion?

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

Aiden needs 15 liters of cleaning solution.

He can buy a 2-gallon jug ($4.28) a 3-gallon jug ($5.92) a 4-gallon jug ($6.56) a 7-gallon jug ($12.98).

As we know,

1 gallon = 4.54 liters

2 gallon = 9.09 liters

3 gallon = 13.63 liters

4 gallon = 18.18 liters

7 gallon = 31.82 liters

Thus, Aiden should purchase a 4-gallon jug ($6.56) to get at least 15 liters of cleaning solution and spend the least amount of money.

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Pre-Algrebra help neededdd!!!!

Answers

Your answer would be D.

if this answer is incorrect, then i am sorry..

Answer:

it is d

Step-by-step explanation:

The area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 miles. What is the width of the park?

Answers

Hi

We know that Area= length * width right?

So this is what we do.

Total area/length

25/54 / 5/9

You get the width to be 5/6

CHECK:
5/6*5/9=25/54

Hope this helps :)

Lucy has a strawberry lace that is 36cm long. She needs pieces 18mm long to decorate a cake. How long is the 36cm one in mm

Answers

The strawberry lace is 36 cms long.
36 cms = 360 mm
(Because we multiply by 10, when we convert from cm to mm).

Given Lucy has a strawberry lace that is 36cm long.

The question is asking to convert 36 cm to mm.

1 centimeter is equal to 10 millimeters: 1 cm = 10 mm.

The distance 36 in millimeters (mm) is equal to the distance 36 in centimeters (cm) times 10

36 cm = 36x 10=360 mm

36 cm converted to mm is 360 mm.

The strawberry lace that is 36cm long in mm is equal to 360 mm.

A table has 16 glasses on it. 7of the glasses are large. The rest are small. How many glasses are small?

Answers

9? Unless it’s a trick question

There are 9 small glasses on the table

Find the missing length for a right triangle with hypotenuse of 18 and a leg length of 6. Round to the nearest whole number if necessary. (1 point) a) 17 b) 324 c) 19 d) 36

Answers

[tex] a^2 + b^2 = c^2 [/tex]

[tex] a^2 + 6^2 = 18^2 [/tex]

[tex] a^2 + 36 = 324 [/tex]

[tex] a^2 = 288 [/tex]

[tex] a = \sqrt{288} [/tex]

[tex] a = \sqrt{144 \times 2} [/tex]

[tex] a = 12\sqrt{2} [/tex]

[tex] a \approx 17 [/tex]

if you want it rounded its 16.97 or 16.9

write the rule for the pattern 1,5,9,13,17

Answers

An increase by four.

The rule is of this problem here is +4

The line plots show the number of hours two groups of teens spent online last week. How does the data compare for the two groups of teens? The 16- to 18-year olds spent about the same hours online, on average, as the 13- to 15-year olds. The mode for the hours spent online for the 13- to 15-year olds is greater than the mode for the hours last week for the 16- to 18-year olds. The median value for the hours spent online for the 13- to 15-year olds is greater than the median value for the hours spent online for the 16- to 18- year olds. The range of hours spent online for the 13- to 15-year olds is greater than the range of hours spent online for the 16- to 18-year olds.

Answers

From your choices above, the answer is C. The median value for the hours spent online for the 13- to 15-year olds is greater than the median value for the hours spent online for the 16- to 18- year olds.

Answer:

The 16- to 18-year olds spent about the same hours online, on average, as the 13- to 15-year olds.

Step-by-step explanation:

Just took the test and this was the answer, view the image below to see if its the right chart.

Helppp!!!! I’m not sure what this is...

Answers

The near and far faces appear to be trapezoids, with bases 12 in and 8 in and height 8 in. Hence each of them has an area
.. Atrapezoid = (1/2)(b1 +b2)h
.. = (1/2)(12 in + 8 in)*(8 in)
.. = 80 in^2

The remaining faces unroll into a rectangle 8 in wide and (12 +8 +8+9) in long. The area of a rectangle is the product of its length and width.
.. Arectangle = length*width
.. = (37 in)*(8 in) = 296 in^2

The total surface area is the sum of the rectangle area and the two trapezoidal faces.
.. Atotal = Arectangle + 2*Atrapezoid
.. = 296 in^2 +2*80 in^2
.. = 456 in^2

The 1st selection is appropriate.

Madeline sold $167 worth of items at a garage sale and then received her $232 paycheck. Estimate how much money she now has by rounding to the nearest ten first and then adding the rounded numbers.

Answers

the answer is 60 dollars

Madeline has approximately $400 after rounding her garage sale earnings and paycheck to the nearest ten and adding them together.

The question involves estimating the total amount of money Madeline has after selling items at a garage sale and receiving her paycheck. To estimate the total amount, we need to round each amount to the nearest ten and then add the rounded numbers together.

First, round $167 to the nearest ten, which is $170.

Next, round $232 to the nearest ten, which is $230.

Finally, add the rounded numbers: $170 + $230 = $400.

Help asap pleaseeeeeeeeeeeeeeeeee

Answers

Hey there :)

A radius is a straight line from the centre of a circle to its circumference

So in this example, Line A F is the radius of circle F (your second option)

-22< m-57 solve this please
thankyouu

Answers

Isolate the m, add 57 to both sides

-22 (+57) < m - 57 (+57)

simplify

-22 + 57 < m

answer: 35 < m

hope this helps

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