A company has found that its supply function is equal to the square of the price of their product, all divided by three. The market for its products is also related to price. demand is a basic 920 units minus thirty times price, minus a quarter of the square of the price. What is the ideal price of their product, to make sure that there is neither a surplus nor a shortage? How many units will they sell at this price?

Answers

Answer 1

Given that the supply function for the company is equal to the square of the price of their product, all divided by three,

i.e. [tex]Q_s=\frac{p^2}{3}[/tex]

and the demand is a basic 920 units minus thirty times price, minus a quarter of the square of the price,

i.e. [tex]Q_d=920-30p- \frac{1}{4} p^2[/tex]

The ideal price of their product, to make sure that there is neither a surplus nor a shortage is the equilibrium price which is the price when supply equals demand.

i.e.
[tex]Q_s=Q_d \\ \\ \Rightarrow\frac{p^2}{3}=920-30p- \frac{1}{4} p^2 \\ \\ \Rightarrow \frac{7}{12} p^2+30p-920=0 \\ \\ \Rightarrow p= \frac{-30\pm\sqrt{30^2-4(\frac{7}{12})(-920)}}{2(\frac{7}{12})} \\ \\ =\frac{-30\pm\sqrt{900+\frac{6440}{3}}}{\frac{7}{6}}=\frac{-30\pm\sqrt{\frac{9140}{3}}}{1.1667} \\ \\ =\frac{-30\pm55.1966}{1.1667}= \frac{25.1966}{1.1667} =21.60[/tex]

Therefore, the ideal price of their product, to make sure that there is neither a surplus nor a shortage is $21.60

The number of units they will sell at this price is given by

[tex]Q= \frac{(21.60)^2}{3} \\ \\ = \frac{466.43}{3} \approx155\ units[/tex]

Related Questions

How to find the distance between two lines in 3d?

Answers

use graph paper, draw the 3d shape and count the squares as one unit each

Answer:

Step-by-step explanation:

On a tour of an old gold mine, you find a nugget containing 0.82 ounce of gold. gold is worth $1566.80 per ounce. how much is your nugget worth?

Answers

Given:
Value of a gold nugget = $1566.80 per ounce.

For a nugget containing 0.82 oz of gold, the value is
(0.82 oz)*(1566.80 $/oz) = $1284.78

Answer: $1,284.78

Since the gold is worth $1566.80 per ounce, then the nugget is worth $1284.776.

Worth of gold per ounce = $1566.80 per ounceAmount of gold that the nugget contains = 0.82 ounces of gold

This is a question relating to multiplication. Therefore, in order to know the worth of the nugget, we've to multiply 0.82 by $1566.80. This will be:

= 0.82 × $1566.80

= $1284.776

Therefore, the value of the nuggets is $1284.776.

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Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign

Answers

sqrt (x-6) + 2 = 6

sqrt(x-6) = 4

sqrt(x-6) squared = 4 squared

x-6 = 16

x = 10

Assume the ball passes through the points (3,8), (5,20/3), and (6,5) . Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola. Write the system in the space provided.

Answers

A parabola is the shape of the graph of a quadratic function. Quadratic functions have the general form:

[tex]y=ax^2+bx+c[/tex]

Here, you've been given the x and y values for three points on the parabola, and you've been asked to set up a system of equations that include those three points. All this problem is really asking is to plug each of those values into the general equation.

The system should look like:

[tex]\begin{array}{lcl} 3^2a+3b+c & = & 8 \\ 5^2a+5b+c & = & 20/3 \\ 6^2a+6b+c & = & 5 \end{array}[/tex]

Which, when simplified, looks like:

[tex]\begin{array}{lcl} 9a+3b+c & = & 8 \\ 25a+5b+c & = & 20/3 \\ 36a+6b+c & = & 5 \end{array}[/tex]

To solve this question:

First, we need to know the standard equation of a parabola.Then, with the three points given, we can build a system of three equations.

Doing this, we get that the system is, with the 3 equations:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

Equation of a parabola:

A parabola is a second degree polynomial, having an standard equation of:

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

Point (3,8)

This means that when [tex]x = 3, y = 8[/tex]. So

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]8 = a\times3^2 + 3b + c[/tex]

[tex]9a^2 + 3b + c = 8[/tex]

Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.

(5,20/3)

This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]

[tex]25a + 5b + c = \frac{20}{3}[/tex]

[tex]75a + 15b + 3c = 20[/tex]

Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.

(6,5)

This means that when [tex]x = 6, y = 5[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]5 = a\times6^2 + 6b + c[/tex]

[tex]36a + 6b + c = 5[/tex]

Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.

After all, the system of equations is:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

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Which graph can be used to find the solution(s) to x2 – 1 = x + 1?

Answers

Let

[tex]f(x)=x^{2}-1[/tex]

[tex]g(x)=x+1[/tex]

we know that

The function f(x) is a vertical parabola open upward

the vertex is the point [tex](0,-1)[/tex] ------> is a minimum

The function g(x) is a linear equation

The y-intercept is the point [tex](0,1)[/tex] -----> for [tex]x=0[/tex] find the value of g(x)

therefore

the answer in the attached figure

The graph that can be used to find the solution of the given polynomial is given by option C) and this can be determined by using the given data.

Given :

Equation --- [tex]x^2 -1 = x+1[/tex]

The following steps can be used in order to determine the graph that can be used to find the solution of the given polynomial:

Step 1 - Separate LHS and RHS of the given polynomial.

[tex]\rm y = x^2-1[/tex] --- (1)

y = x + 1 --- (2)

Step 2 - Draw the graph of a line (y = x + 1) that passes through the points (-1,0) and (0,1).

Step 3 - Now, draw the graph of the equation (1). The shape of this graph is the upward parabola.

Step 4 - The two graphs intersect each other at (-1,0) and (2,3).

From the above steps, it can be concluded that the correct option is C).

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Match the inequality to the graph of its solution.
a. c + 7 ≤ 3
b. c - 3 > 1
c. c - 7 < 3

Answers

case a) [tex]c+7 \leq 3[/tex]

[tex]c+7 \leq 3\\ c\leq3-7\\c\leq -4[/tex]

the solution is the interval-------> (-∞,-4]

the answer case a) in the attached figure

case b) [tex]c-3 > 1[/tex]

[tex]c-3 > 1\\c > 1+3\\c> 4[/tex]

the solution is the interval-------> (4,∞)

the answer case b) in the attached figure

case c) [tex]c-7< 3[/tex]

[tex]c-7< 3\\ c<3+7\\ c< 10[/tex]

the solution is the interval-------> (-∞,10)

the answer case c) in the attached figure

Inequalities are used to represent unequal expressions.

Graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]Graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]Graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex]

[tex]\mathbf{(a)\ c + 7 \le 3}[/tex]

Subtract 7 from both sides

[tex]\mathbf{c \le -4}[/tex]

The above means that:

The graph points leftThe graph starts at -4, with a closed circle

Hence, graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]

[tex]\mathbf{(b)\ c - 3 > 1}[/tex]

Add 1 to both sides

[tex]\mathbf{c > 4}[/tex]

The above means that:

The graph points rightThe graph starts at 4, with an open circle

Hence, graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]

[tex]\mathbf{(c)\ c - 7 < 3}[/tex]

Add 7 to both sides

[tex]\mathbf{c < 10}[/tex]

The above means that:

The graph points leftThe graph starts at 10, with an opened circle

Hence, graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex]

Answers

set two fractions on is 4/30 since you need 4 drivers every 30. Then set one as X/75 since you don't know how many drivers but you know 75 is the area. Use cross multiplication, you will get that X = 10

Answer:10 hahhahaahaahahaahahahhhahahaahahahhahahahahhahahahahahahahahahahahahahahhahahahahahhaahhaahahahhahahaahhahaaaaahahahahahahahahahahahahahahahaahahahahahaahahhaahahahaaaahahhahaahahaahahahahaaaahhahhahhahahahahhahahahahahhahahahahhahahahahahahhahhahahahahahahahhaahhaahhahahahahahhaahaahahahahahahahaaahhahahahahahahahahhahahahahahahahahahahahahahaha

Please help me asap
It's due tomorrow

Answers

You have 3n. You want n, so divide all three sides by 3.

-15 < 3n <= 6

-5 < n <= 2

n is an integers and must be greater than -5 and can be as great as 2.
n can be -4, -3, -2, -1, 0, 1, 2

im pretty sure somone answered this but

Rosemary left a 15% tip for a meal that cost $39.

What was the amount of the tip?

Answers

For that you must calculate:
$39 * 15%
Maybe you know it, but as a normal number 15% are 0,15:
$39*0,15 = $5,85

ANSWER: The amount of the tip was $5,85.

Which inequality represents this sentence? Ten minus three is greater than one plus two.

Answers

Ten minus three ⇒ 10 - 3
One plus two ⇒ 1 + 2

Greater than use the symbol >

Ten minus three greater than one plus two
10 - 3 > 1 + 2
7 > 3

According to question we have: (10-3) which is equal to 7 i.e (10-3) = 7 ......eq.(1) also (1+2) is equal to 3 i.e (1+2) = 3 ......eq.(2) now from eq(1) and (2) we have 7>3 ..........(applying greater than symbol) so (10-3) > (1+2) hence, Ten minus three is greater(>) than one plus two.

A game shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2 cm. What is the area of the plastic that is needed to make one cylinder?

Answers

To start, you know that this question is asking for the surface area of one of the cylinders, and the formula to finding the surface area of a cylinder is A=2πrh+2πr^2.

Now, to find the surface area, you first need to figure out the height of the plastic cylinder and its radius.
Since you know that the diameter (twice the radius) of the cylinder is equivalent to 4 marbles, and each marble has a diameter of 2 cm, the diameter of the cylinder would be 8 cm. Then, to find its radius, you divide by 2, so its radius is 4.
Now, since you know that the height of the cylinder is 10 marbles, you multiply 10 by 2 to get that the height is 20 cm tall.
Since you now have the values of the height and the radius, plug the values into the surface area of a cylinder formula (r is radius and h is height).
A=2π(4)(20)+2π(4)^2.
Assuming that pi is 3.14, when you simplify this using PEMDAS, you get
502.4+100.48 which then simplifies to 602.88, the area of the plastic to make one cylinder.

Astronauts use a tool in space that weigh 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.

Answers

First you need to find how many grams is 1 ounce. 1o z.is 28.35 g, then you need to multiply 28.35 g by 5 which is 141.75. you need to round it to the nearest hundred so it is about 142 grams.
the key here would be
1 oz. = 28.35g or 1 oz. = 28 g

Answer: 141.75

Step-by-step explanation: Yw future edge users

How do you find a literal equation for d=rt,
solve for t.

Answers

d = rt

d/r = t divide both sides by r

t = d/r <<< the equation

hope this helped, God bless!

Answer: [tex]\frac{d}{r} = t[/tex]

Step-by-step explanation: To solve for t in the equation d = rt, all we have to do is get t by itself on the right side of the equation.

Since t is being multiplied by r, we simply divide both sides of the equation by r. On the right, the r's cancel and we are left with r.

On the left side of the equation we have [tex]\frac{d}{r}[/tex].

Therefore, our answer is [tex]\frac{d}{r} = t[/tex].

You deposit $1,000 in a savings account that earns 0.5% each month. Assuming you do not deposit or withdraw any money from the account, how much will you have in the account after 3 years?

Answers

0.5% is 5$ so 5$ x 12 = 60 60 x 3 is 180 180 is your answer

The equation for that is:

x(dollar amount) · y(time in years it was in the bank) · z(percent of interest as a decimal)

Lets fill in the numbers:

1000 x 3 x .005 = 15

Add the 15 to the total and the final answer is:

$1015

Hope this helps!

A company donates 935 pencils to a shcool the pencil are divided evenly amog 9classroom the rest goes to the library how many pencil were donated to the schooland the library

Answers

935\9=103.8 now you subtract 103.8-935 you get the answer.

Answer:

103.8

Step-by-step explanation:

calculator

Simplify. 4^3 x 4^4/ 4^9

A. 4^16

B. 4^2

C. 1/4^2

D 1/4

Answers

the answer is A. 4^16

C as 256x64 = 16384/262144 = 0.0625 1/4^2 would equal to 1/16 which would equal 0.0625

Find the total area of the solid figure with the length, 3 width 5, and height 6

Answers

To find the area of a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

Good Luck

A = w x l x h
A = 3 x 5 x 6
A = 90

The ratio of computers to desk is 2 to 3. If there are 15 desk, how many computers are there?

Answers

15/5 = 3

The ratio of computers to desk is 2 to 3
2 x 3 = 6 (computers)
3 x 3 = 9 (desks)

answer
6 computers

Final answer:

To find the number of computers given the ratio of computers to desks and the number of desks, set up a proportion and solve for the unknown value.

Explanation:

In this question, we are given the ratio of computers to desks, which is 2 to 3. We are also given the number of desks, which is 15. To find the number of computers, we can set up a proportion:

2 computers / 3 desks = x computers / 15 desks

By cross-multiplying and solving for x, we find that there are 10 computers.

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Ohhhhhhh! I have a Brainliest

Answers

In week 2 it took 25 minutes also the mode is 75.

If correct brainliest please

Thank you

:)

Can someone clearly explain and workout Q19? Much appreciated

Answers

The x coefficient is 2
Take half of 2 to get 2/2 = 1
Square 1 to get 1^2 = 1

Add and subtract 1 to the expression. This is the same as adding 0.

x^2 + 2x + 2
x^2 + 2x + 2 + 0
x^2 + 2x + 2 + (1-1)
(x^2 + 2x + 1) + 2 - 1
(x+1)^2 + 1

Answer: (x+1)^2 + 1

factor the trinomial x^2 - 16x +63

Answers

Factor the following:
x^2 - 16 x + 63
The factors of 63 that sum to -16 are -7 and -9. So, x^2 - 16 x + 63 = (x - 7) (x - 9):
Answer: (x - 7) (x - 9)

A college student borrows $3,000 for 3 months to pay for a semester of school. If the interest is $61.88 find the monthly payment

Answers

Given:
Amount borrowed = $3,000
Interest = $61.88
Duration = 3 months

Obligation = 3000 + 61.88 = 3061.88
Monthly payment = 3061.88/3 = $1,020.63

Answer: $1,020.63

The student must make monthly payments of $1,020.63 to repay the $3,000 loan with $61.88 in interest over 3 months.

The student has borrowed $3,000 for 3 months and the interest incurred on this loan is $61.88. To find the monthly payment, we need to add the total interest to the principal borrowed and then divide it by the number of payments (which is 3 in this case).

The total repayment amount is calculated as $3,000 principal + $61.88 interest = $3,061.88.

Now, we divide the total repayment amount by the number of monthly payments:

Monthly Payment = Total Repayment Amount / Number of Payments

Monthly Payment = $3,061.88 / 3

Monthly Payment = $1,020.63

Therefore, the student will need to make monthly payments of $1,020.63 to repay the $3,000 loan over 3 months.

How to find slope when there is the y intercept and x-intercept?

Answers

First graph your x and y intercept then pick any two points on the line.
[tex] \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
that's the equation used to find your slope

Example:

(4,2) (8,6) let's say those are the points you pick from the line

so then you subtract 6-2=4 (6 is your y2 and 2 is your y1)

then subtracts 8-4=4 (8is your x2 and 4 is your x1)

then your left with
[tex] \frac{2}{4} [/tex]
if you can reduce the reduce in this case you can which leaves you with
[tex] \frac{1}{2} [/tex]
and that's how you find the slope

Maddie plays 16 Games of tennis. Her went to loss ratio is 10 to 6. She is expected to play 12 more games during the season. How many do you expect her to win

Answers

6:10 would be her winning ratio so 6/10 gives you .6 so .6*12(number of games) give you 6 so Maddie will win about 6 more games

A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 72 mph. how long before the two trains are 330 miles apart?

Answers

Final answer:

The two trains will be 330 miles apart after 2.5 hours.

Explanation:

To find how long it takes for the two trains to be 330 miles apart, we can apply the formula for relative velocity:

Relative velocity = sum of their speeds

The first train is moving east at 60 mph, and the second train is moving west at 72 mph. So their relative velocity is 60 mph + 72 mph = 132 mph.

To find the time it takes for the trains to be 330 miles apart, we can use the formula:

Distance = speed × time

330 miles = 132 mph × time

Solving for time, we have:

Time = 330 miles / 132 mph = 2.5 hours

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How many times larger is 2 x 10-6 than 2 x 10-11?

Answers

[tex]\mathsf{\dfrac{2\cdot10^{-6}}{2\cdot10^{-11}}}\\ \\ \\ \mathsf{1\cdot10^{-6+11}}\\ \\ \boxed{\mathsf{10^5~or~100000~times~larger}}[/tex]

If y varies directly with x in the following table problem, find the constant of variation (k) and write the equation x 6,9,12,15 Y 10,15,20,25

Answers

We are told that y varies directly with x.
Therefore
y = k*x
where
k = the constant of variation

The given table and the ratio of k=y/x is shown below.

x y k
--- ------ --------
6 10 1.667
9 15 1.667
12 20 1.667
15 25 1.667

Answer:
k = 1.667
y = 1.667x

What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ?

Answers

The line y = x/3 - 1, or y = (x/3) - 1, is the same as y = (1/3)x - 1
The slope here is 1/3 as this equation is in y = mx+b form (m = slope, b = y intercept)

Using the starting point of 1/3, we will...
Flip the fraction: 1/3 ----> 3/1 = 3
Then flip the sign from positive to negative: 3 ----> -3

The original slope is 1/3
The perpendicular slope is -3
The two slopes multiply to -1
We'll use m = -3 along with x = 4 and y = 2
We generate those x,y values from (x,y) = (4,2) as the given point

Plug m = -3, x = 4, y = 2 into the equation below. Solve for b
y = mx+b
2 = -3*4 + b
2 = -12 + b
2+12 = -12+b+12
14 = b
b = 14

So because m = -3 and b = 14, we go from y = mx+b to y = -3x+14

--------------------------------------------------------------------------------

Final Answer: y = -3x+14

Visual proof can be found using software like GeoGebra as shown in the attached image.

How many different primes are in the prime factorization of 20! or 20 factorial?

Answers

3. 20's prime factorization is 2,2,5

BRAINLIEST TO BEST ANSWER

What are the domain and range of the function

Answers

the arrows on the end of the line means it continues

both the domain and the range for this graph is negative infinity to infinity

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