A general linear demand function has the form q = mp + b (m and b constants, m ‡ 0).
(a) Obtain a formula for the price elasticity E of demand at a unit price of p.
E =
(b) Obtain a formula for the price p that maximizes revenue.
p =
Answers
The price elasticity of demand at a unit price of p is E = mp/(mp+b) and the price that maximizes revenue is p = -b/(2m).
(a) The price elasticity of demand is given by the formula:
E = (dQ/dP) x (P/Q)
where Q is the quantity demanded, P is the price, and dQ/dP is the derivative of the demand function with respect to price.
In this case, the demand function is:
Q = mP + b
Taking the derivative with respect to P, we get:
dQ/dP = m
So the price elasticity of demand at a unit price of p is:
E = (dQ/dP) x (P/Q)
= m x (p/(mp+b))
= mp/(mp+b)
(b) The revenue R is given by:
R = P x Q
= P(mP+b)
= mP² + bP
To find the price that maximizes revenue, we need to take the derivative of the revenue function with respect to P and set it equal to zero:
dR/dP = 2mP + b = 0
Solving for P, we get:
P = -b/(2m)
So the price that maximizes revenue is:
p = -b/(2m)
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Related Questions
Answer these 4 questions for brainliest! :)
For questions 1 - 4, simplify the variable expression as much as possible.
1. x + 4 - 3 + 1
2. x - 5 + 5x + 2
3. 2x + 7 - 4x - 8
4. (4 + 3)x + 2x - 5
thank you for your help and have a blessed day!
Answers
Answer: 1. X+2
2. 6x-3
3. -2x-1
4. 9x5
Step-by-step explanation:
1. X+4-3+1 There is only one variable, so you don’t need to worry about that. Just do all of the numerical operations. 4-3+1= 2. So it would be x+2
2. X-5+5x+2. Again, do the numerical operations first. -5+2=-3. X+5x=6x. So it would be 6x-3.
3. 2x+7-4x-8. 7-8=-1. 2x-4x=-2x. So it would be -2x-1.
4. (4+3)x+2x-5. Do the operation in the parenthesis first. Then it would be (7)x or just 7x+2x-5. Simplify to 9x-5.
In a double-blind, placebo-controlled experiment:
a. subjects are assigned to different treatment groups, one of which receives an inactive substance that appears to be a treatment, through random selection.
b. a subject does not know whether he or she received a treatment or an inactive substance.
c. subjects with similar characteristics are assigned to the same group.
d. neither the subjects nor the people administering the treatments know who received a treatment and who received an inactive substance.
e. a subject who received an inactive substance reports an improvement in health or behavior.
Answers
The correct statement among the options (a)-(e) is d. neither the subjects nor the people administering the treatments know who received a treatment and who received an inactive substance.
In a double-blind, placebo-controlled experiment, both the subjects and the people administering the treatments are unaware of which participants received the active treatment and which received the placebo (inactive substance).
This is done to minimize bias and ensure the validity of the results. By keeping both the subjects and the administrators blinded to the treatment assignments, the study can effectively evaluate the true effects of the treatment without any potential influence from expectations or biases.
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what is 0.46 as a fraction?
Answers
Answer: 46/100 or in its simplest form it would be 23/50
Step-by-step explanation:
Answer:
46/100
Step-by-step explanation:
It's just how you say the number. forty six hundredths right,
Pls mark Brainliest
Which line has a slope of 1/2 and a y-intercept of 2?
Answers
Answer:
it would be the bottom left graph
Step-by-step explanation:
Rise over Run
Solve each system of the new equations by adding or subtracting
Answers
Given the equations
x + y = 5----------------------(1)
x - 3y = 3-----------------------(2)
Subtract equation (2) from (1)
x - x -3y - y = 3 - 5
-4y = -2
Divide both -4
\(\begin{gathered} \frac{-4y}{-4}\text{ = }\frac{-2}{-4} \\ y\text{ = }\frac{1}{2}\text{ = 0.5} \\ \end{gathered}\)Substitute y = 1/2 into equation (1)
x + y = 5
\(\begin{gathered} x\text{ + }\frac{1}{2}\text{ =5} \\ x\text{ = 5 -}\frac{1}{2} \\ x\text{ = }\frac{10-1}{2} \\ x=\frac{9}{2}\text{ = 4.5} \\ \end{gathered}\)Hence, the solution to the equations is
\(\begin{gathered} x\text{ = }4.5,\text{ y = 0.5} \\ Or\text{ in coordinate form, (4.5, 0.5)} \end{gathered}\)Find the H.C.F of the following numbers by the prime factorization method
a)18 and 27
b)35and 75
c)144and 360
d)30,40and45
e)144,384and432
Answers
Answer:
Step-by-step explanation:
is a 18 and 27 yes to the following question
a) 18 = 2 x 3^2
27 = 3^3
-> HCF = 3^2 = 9
b) 35 = 5 x 7
75 = 3 x 5^2
-> HCF = 5
c) 144 = 2^4 x 3^2
360 = 2^3 x 3^2 x 5
-> HCF = 2^3 x 3^2 = 72.
d) 30 = 2 x 3 x 5
40 = 2^3 x 5
45 = 3^2 x 5
-> HCF = 5
e) 144 = 2^4 x 3^2
384 = 2^7 x 3
432 = 2^4 x 3^3
-> HCF = 2^4 x 3 = 48.
If a figure has a length and width that are the measured in meters, what would be the units for the area of the figure
Answers
Answer:
metre squared (m²)
Step-by-step explanation:
metre×metre=metre squared (m²)
Ann and Betty shared a sum of money in the ratio 2:3 respectively. Ann Received $120. What was Betty’s share?
Answers
Answer:
A:B::2:3
123:x
set up as fractions:
\(\frac{2}{3}\) \(\frac{120}{x}\) 120*3=360
360/2=180
Betty Received $180
Write a polynomial that represents the area of the shaded region.
Answers
Answer:
10x-22
Step-by-step explanation:
((x+2)(x-1))-((x-4)(x-5))
(x^2-x-2)-(x^2-9x+20)
x^2 + x - 2
+ (-x^2+9x-20)
_______________
10x-22
The boss told the management team some sad news too. “I’m cutting your hourly pay. You now get paid per project you finish. I will give you $10 for each finished schedule you create and $20 for each meeting you complete! You cannot make more than $100 per day! Also you must make more than twice as many schedules as meetings!”
Create a system of linear inequalities to model the situation above, where x is the number of schedules made and y is the number of meetings completed.
Answers
The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x
How to create a system of linear inequalities to model the situationFrom the question, we have the following parameters that can be used in our computation:
Each finished schedule = $10Each meeting = $20Amount to make = Not more than $100You must make more than twice as many schedules as meetingsUsing the following representations:
x = the number of schedules madey = the number of meetings completedWe have the following system of inequalities from the given statements
10x + 20y ≤ 100
y > 2x
Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x
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PLEASE HELP ME 15 POINTS
1- Which vehicle has the better gas mileage? Explain your reasoning using a line graph comparing the number of gallons to the number of miles covered.
2- Describe the graph:
Answers
You have to add the background info for us to answer this
SONGS
CUT
Match each question you might ask yourself on the left with how you might respond on the right
Why don't like spinach?
I left my coat in the car
Why am I so cold?
It tastes bitter to me
DOO
Why was I late for school?
I forgot to set my alarm
Answers
Answer:
Step-by-step explanation:
why dont you like spinach? it tastes bitter to me
why am is so cold? i left my coat in the car
Why was i late for school? i forgot to set my alarm
Solve the problem. Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average
Answers
The additional amount of $7,000 must be invested in the account that pays 13% simple interest to achieve an average return of 11%.
To calculate amount of additional money to be invested that pays 13% interest on average:
Let additional amount to be invested in the account paying 13% simple interest be x dollars.
The interest earned from the $14,000 invested at 10% interest can be calculated as:
Interest 10% = 14,000 * 10% = 1,400
The interest earned from the additional amount invested at 13% interest can be calculated as:
Interest 13% = x * 13% = 0.13x
The total interest earned from both investments is the sum of the interest earned at 10% and 13%:
Total Interest = Interest 10% + Interest 13%
= 1,400 + 0.13x
To achieve an average return of 11%, the total interest earned must be 11% of the total investment amount:
Total Interest = 11% * (14,000 + x)
The equation will become:
1,400 + 0.13x = 0.11 * (14,000 + x)
1,400 + 0.13x = 1,540 + 0.11x
Subtracting 0.11x from both sides:
0.02x = 140
x = 7,000
Therefore, an additional amount of $7,000 must be invested in the account that pays 13% simple interest to achieve an average return of 11%.
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The complete question is:
Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11% ?
Three people become infected with a virus that spreads quickly. Each day that passes, the number of infected people doubles. How can the number of infected people be determined from the number of days that have passed?
Answers
Answer: raise 2 to the number of days, and then multiply this value by 3.
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Find the area of a triangle with the vertices (8, 1), (10,0), and (6,0)
Answers
PLEASE GIVE BRAINLIEST :)
Answer:
2 square units
Step-by-step explanation:
To find the area of a triangle with given vertices, we can use the formula:
A = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.
Plugging in the given values, we get:
A = 1/2 * |(8*(0-0) + 10*(1-0) + 6*(0-1))|
= 1/2 * |(0 + 10 - 6)|
= 1/2 * 4
= 2
Therefore, the area of the triangle is 2 square units.
Solve for x please. :)
Answers
Answer:
x=105
Step-by-step explanation:
75+75+x+x=360
150+2x=360
2x=210
x=105
I hope this is correct and helps you!
Answer:
x = 105°
Step-by-step explanation:
Because x° and 75° are supplementary angles (sum equals 180°), we cand do 180° - 75° to find x.
180° - 75° = x
x = 105°
What does it mean to have 2 equal roots?
Answers
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
What is square root ?A number's root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as or as 3 x 3.
Here,
If an equation have 2 roots , it means it is a quadratic function
If D=0, a quadratic function has two roots that are equal.
D (discriminant) = 0
=>b24ac=0 is required for a polynomial function to have equal roots.
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
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25
A classrom contain children, out of which bare
girls, what percentage of the class are
boy
Answers
Answer:
76%
Step-by-step explanation:
number of girls is 6
number of boys is 25-6=19
percentage of boys = number of boys ÷ total no of students * 100
so... (19÷25)*100=76%
A translation is applied to the square formed by the points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6) . Select the phrase from the drop-down menu to correctly describe the translation. The square was translated Choose... .
Answers
The square was translated 2 units downwards.
Describing the transformationFrom the question, we have the following parameters that can be used in our computation:
Points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6)The square was translated 2 units downward since all the y-coordinates of the vertices of the image square are 2 units less than the corresponding y-coordinates of the vertices of the pre-image square.
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n a school of 600, a survey was conducted with 10% of the population. The survey was conducted to narrow the choices for the new mascot. What was the frequency of Bears, if the following was the result of the survey?
Bears=22
Panthers=15
Beavers=2
Jaguars=21
Answers
Answer:
37%
Step-by-step explanation:
10% of 600 students is 60 students surveyed and 22 people chose bears. So to find the percent out of 60 just divide 22 by 60
22/60=.36666
move the decimal to get about 37%
hope this helps
kim orders catering from midtown diner for $35. she spends $5 on a large order of potato salad and the rest on turkey sandwiches. each sandwich is $2.50. How many sandwiches did kim buy ?
Answers
Answer:
12
Step-by-step explanation:
35-5=30
After that you dived 30 by 2.5 which gets you 12
what should be t-value to indicate that curve is not over flattening in smoothening of time series data
Answers
When smoothing time series data, it's important to ensure that the curve is not over-flattened, as this can lead to important information being lost.
What should be t-value to indicate that curve is not over flattening?To avoid over-flattening, one approach is to use a threshold value, or "t-value", to determine the maximum amount of smoothing that can be applied.Here are some steps to consider when choosing a t-value:Plot the original time series data and the smoothed curve to visualize the smoothing effect.Compare the slope of the smoothed curve to the slope of the original data.Choose a t-value that preserves the important features of the original data, such as trends, seasonality, and outliers.Ensure that the smoothed curve still accurately represents the underlying pattern in the data, while reducing noise and variability.Re-evaluate the t-value if necessary, based on the visual comparison of the original data and the smoothed curve.The t-value should be chosen such that the smoothed curve captures the underlying pattern in the data, while retaining important features such as trends and seasonality. If the t-value is set too high, the curve may become over-flattened and important information may be lost. On the other hand, if the t-value is set too low, the curve may not effectively reduce noise and variability in the data.To learn more about T-value refer:
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A restaurant recorded what items from the kids menu were ordered on Friday night. Twenty-eight of the 76 kids at the restaurant Friday night ordered chicken nuggets. What is the ratio of kids who did not order chicken nuggets to the number of kids who did? Write your ratio in simplest form.
Answers
Answer:
12:7
Step-by-step explanation:
Total number of kids = 76
Total number of kids that ordered chicken nuggets = 28
Total number of kids that did not order chicken nuggets = 76 - 28
= 48
The ratio of kids who did not order chicken nuggets to the number of kids who did is:
= 48 : 28
In simplest form :
= 12:7
1. True or False: The slope of this line is 1/3. if false what is the slope of the line
Answers
Which ordered pair is the solution of the linear system 3x+4y= -10 and 2x-4y= 0?
Answers
Answer:
-2,-1
Step-by-step explanation:
Use Desmos Graphing For futher explanation.
:)
hey! Solving linear equations with integers! i don’t think it should be that hard since it’s practice, I just need some help with a bit more problems! :’)
1) -3 ( 3 - x ) = 2x + 5
2) -6 - 9p = + 3p
3) -5 (-4 - a ) = 3a + 8
4) s - 6 = -5s
that should be it! Ty
Answers
Solution 1 :-
>> -3 (3 - x) = 2x + 5
>> -3 × (3 - x) = 2x + 5
>> -9 + 3x = 2x + 5
>> 3x - 2x = 9 + 5
>> x = 14
Solution 2 :-
>> -6 - 9p = 3p
>> -9p - 3p = 6
>> -12p = 6
>> p = -1/2
Solution 3 :-
>> -5 (-4 - a) = 3a + 8
>> -5 × (-4 - a) = 3a + 8
>> 20 + 5a = 3a + 8
>> 5a - 3a = 8 - 20
>> 2a = -12
>> a = -12 / 2
>> a = -6
Solution 4 :-
>> s - 6 = -5s
>> s + 5s = 6
>> 6s = 6
>> s = 6 / 6
>> s = 1
Answer:
1) x = 14
2) p = - \(\frac{1}{2}\) (- 1/2)
3) a = -6
4) s = 1
work shown in image :)
hope this helps!!
What is 213 divided? Also how do you break 23 into tens and ones?
Answers
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
Write an equation for the line that passes through E(4, -3) and is parallel to the line
0 = 5x - 7y - 27 Write the equation in general form.
Answers
Answer:
y= 5x/7 -27/7
if they are parallel there gradient is the same
m1=m2
y-y1=m(x-x1)
plug in the gradient and points E
y-(-3)=5/7( x-4)
y= 5/7(x) -20/7 +3
final answer
y= 5/7(x) +1/7
A cube-shaped box has a volume of 64 cubic inches.
If the box is packed full of cubes with edge lengths of 1 inch, how many cubes can fit along one side of the box?
2 cubes
4 cubes
8 cubes
16 cubes
Answers
4x4x4= 64 cubic inches
So the answer is 4 cubes
PLEASE HELPPPPP BRAINLIEST PLUS POINTS
Answers
MN = TS
5x -2 = 3x + 1
Add 2 to both sides:
5x = 3x + 3
Subtract 3x from both sides:
2x = 3
Divide both sides by 2
X = 3/2
Now you have x solve for TS
TS = 3x + 1 = 3(3/2) + 1 = 4 1/2 + 1 = 5 and 1/2
The smaller triangle is 2/3 the size ( 26/39 = 2/3)
5 1/2 x 2/3 = 3 2/3