Answer:
a) x = 798 is the quantity that maximizes the profit
b)po(x) = 401 $/unit
c)P(max ) = 636105 $
Step-by-step explanation:
The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:
R(x) = p(x) * x
R(x) = ( 800 - 0,5*x ) * x
R(x) = 800*x - 0,5*x²
The equation for the profit is:
P(x) = R(x) - C(x)
P(x) = 800*x - 0,5*x² - ( 300 + 2*x)
P(x) = 798*x - 0,5*x² - 300
a) P(x) = 798*x - 0,5*x² - 300
Taking derivatives on both sides of the equation:
P´(x) = 798 - x
If P´(x) = 0 then 798 - x = 0
x = 798 is the quantity that maximizes the profit
b) Selling price for the optimal quantity is:
p(x) = 800 - 0,5*x
p(x) = 800 - 0,5* 798
po (x) = 800 - 399
po(x) = 401 $/unit
c) Pmax = ?
P(x) = 798*x - 0,5*x² - 300 by subtitution of x = 798
P(max) = 636804 - 399 - 300
P(max ) = 636105 $
a) The quantity that will maximize profit is [tex]100 \ units[/tex].
b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.
c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].
Demand Function:A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.
The given demand function,
[tex]P=800-\frac{1}{2}x[/tex]
So, the revenue function is,
[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]
[tex]\Rightarrow[/tex]Average cost is
[tex]\bar{C}=300+2x[/tex]
So, the total cost function is,
[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]
a) Profit function:
[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]
For maximum,
[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]
b) Selling Price:
[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]
c) Maximum Profit:
[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]
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Given the equation 5(-2x -10) = 25(x + 1), solve for the value of x that will make the equation true.
Answer:
Step-by-step explanation:
5(-2x -10) = 25(x + 1)
-10x - 50 = 25x + 25
by transposing
-10x - 25x = 25 + 50
-35x = 75
x = -75/35
x = 15/7
or 2.142857..... in decimal
Hope this helps
plz mark as brainliest!!!!!!!
78.540 round to the nearest hundred
Answer:
78.5
Step-by-step explanation:
Answer ASAP: What is the smallest positive number that can be added to 55 so that the resulting number and 45 have 9 as their greatest common factor?
Answer:
55 + 45 = 90
90 divided by 45 = 2
90 divided by 9 = 10
Step-by-step explanation:
- 8n - 8 = -72
I don’t know how to do this
Answer:
n=8
Step-by-step explanation:
Add 8 to both sides of the equals sign, then bring down -8n, add -72+8, You'll get -64, lastly you divide -64 and -8, and you'll get your answer
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......................;-;
|3d-3n|-4 if n=2 and d=3
Answer:
-1
Step-by-step explanation:
[tex]|3d-3n|-4[/tex]
Once we have an absolute value, we know that
[tex]|3d-3n| \geq 0[/tex]
[tex]\text{For }n=2 \text{ and } d=3[/tex]
[tex]|3(3)-3(2)|-4[/tex]
[tex]|9-6|-4[/tex]
[tex]|3|-4[/tex]
[tex]3-4[/tex]
[tex]-1[/tex]
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. When each data class has the same frequency, the distribution is symmetric. Choose the correct answer below.
a. The statement is true.
b. The statement is false. When each data class has the same frequency, the distribution is bimodal.
c. The statement is false. When each data class has the same frequency, the distribution is skewed left.
d. The statement is false. When each data class has the same frequency, the distribution is skewed right.
Answer:
A; the statement is true
Step-by-step explanation:
In this question, we are to select which of the options is correct according to the initial statement.
The statement is true.
If the data classes have same frequency, then the distribution is said to be symmetrical in nature.
What is meant by being symmetrical in this case is that the data classes are skewed left as far as they are skewed right from a given center point.
Evaluate the function at the specified value and simplify
f(x)=|x|+8;f(-3)?
Step-by-step explanation:
f(x)=|x|+8
f(-3)=|-3|+8 =3+8 =11
by which smallest number can 275 be multiplied to get perfect square
Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true?
The percent error for this year was lower. Raul estimated better last year.
The percent error for this year was higher. Raul estimated better last year.
The percent error for this year was lower. Raul estimated better this year.
The percent error for this year was higher. Raul estimated better this year.
Answer:
3
Step-by-step explanation:
Answer:
C. The percent error for this year was lower. Raul estimated better this year.
Edge2021 <33 Please mark brainliest luv
On a drive from your home to town, you
wish to average 60 mph. The distance from
your home to town is 78 miles. However,
at 39 miles (half way), you find you have
averaged only 45 mph.
What average speed must you maintain in
the remaining distance in order to have an
overall average speed of 60 mph?
Answer in units of mph.
Answer:
Your average speed must be 90 mph in the remaining distance in order to have overall average speed of 60 mph
Step-by-step explanation:
The rule of distance is d = v × t, where
v is the average speedt is the time∵ You wish to average 60 mph on a drive from your home to town
∵ The distance from your home to town is 78 miles
→ Find the time of your journey using the rule above
∴ 78 = 60 × t
→ Divide both sides by 60
∴ [tex]\frac{78}{60}[/tex] = t
∴ t = [tex]\frac{13}{10}[/tex] hours
∵ You have averaged only 45 mph in the first 39 miles (half way)
∴ v1 = 45 mph
∴ d1 = 39 miles
→ Find the time of this part
∴ 39 = 45 × t1
→ Divide both sides by 45
∴ [tex]\frac{39}{45}[/tex] = t1
∴ t1 = [tex]\frac{13}{15}[/tex] hour
→ Subtract the time of the first part from the time of the journey to
find the time for the second part
∵ t2 = t - t1
∴ t2 = [tex]\frac{13}{10}[/tex] - [tex]\frac{13}{15}[/tex]
∴ t2 = [tex]\frac{13}{30}[/tex] hour
→ Now let us find the average speed of the second part of his journey
∵ d2 = 39 miles ⇒ (78 - 39)
∵ t2 = [tex]\frac{13}{30}[/tex] hour
∴ 39 = v2 × [tex]\frac{13}{30}[/tex]
→ Divide both sides by [tex]\frac{13}{30}[/tex]
∴ 39 ÷ [tex]\frac{13}{30}[/tex] = v2
∴ 90 = v2
∴ v2 = 90 mph
∴ Your average speed must be 90 mph in the remaining distance in
order to have overall average speed of 60 mph
- You invest $1,000 in a stock market index fund that earns 8% compounded annually overa
10-year period (a simplified example since stock market returns vary year to year). How
much would your investment be worth after this 10-year period?
A. $1,080
B. $1,800
C. $2,000
D. More than $2,000
Answer:
I believe c
Step-by-step explanation:
I believe this because if you invest in stock for ten years as on this paragraph the answer is C
Option D is correct. we worth more than $2000 after 10 year period.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that You invest $1,000 in a stock market index fund that earns 8% compounded annually over a 10-year period.
We have to find the investment be worth after this 10-year period.
A=P(1+r)ⁿ
P is the initial amount
r is rate of interest
n is the time
A=1000(1+0.08)¹⁰
A=1000(1.08)¹⁰
A=1000×2.1589
A=2158.9
Hence, option D is correct. we worth more than $2000 after 10 year period.
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what is the measure of CAB?
∠CAB and the angle above it whose measure is 84° are vertically opposite angles , which means their measure will be equal .
∴ The measure of angle CAB = 84°By the definition of vertically opposite angle, Measure of an angle CAB is, 84°.
What are Parallel lines?Parallel lines are those lines that are equidistance from each other and never intersect each other.
We know that;
The vertically opposite angles are equal to each other.
Here, ∠CAB and the angle above it whose measure is 84° are vertically opposite angles.
Hence, Measure of ∠CAB = 84°
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Edgar has 20 dimes and nickels,all together sum up to $1.40.what does each one of them cost?
Answer:Edgar has 12 nickles and 8 dimes.
Step-by-step explanation:
I need somw help on this pls ^^
Answer:
100=9s+10
there are 10 students on each bus
According to modern science. Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose you represent the entire history of Earth by 12 hours on a clock, with the birth of Earth at the stroke of midnight and today at the stroke of noon. How long before noon does written human history begin?
Answer:
11:59:59. Human history can be represented as only less than one second in a 12 hour clock.
Measures of the missing numbered angles
Answer:
23
Step-by-step explanation:
PLZ HELP FAST
A cruise ship is currently 15 kilometers away from its port and is traveling away from the port at 15
kilometers per hour. The function y = 15x + 15 relates the number of kilometers y the ship will be from
its port x hours from now. How far will the cruise ship be from its port 3 hours from now?
The cruise ship will be______ kilometers away from port in 3 hours.
Answer:
45
Step-by-step explanation:
Answer: 60 kilometers
Step-by-step explanation:
Plug in your hours:
y = 15(3) + 15
y = 45 + 15
y = 60 kilometers
Hope this helps!
The following table shows the annual profits for two small florist shops what shop had the greater total profit? How much greater was its profit?
Plz answer ASAP I will mark u brainlyest this is my 5th time asking please answer
Answer:
Shop A & $400
Step-by-step explanation:
-4.7 + 27.5 + 122.3 = $145.1 (Shop A)
-0. 2 + 14.5 + 130.4 = $144.7 (Shop B)
Difference = 145.1 - 144.7 = $0.4
0.4 × 1000 = $400
Lindy owes her friend Amanda$3. If she borrows another $6, how much will she owe altogether?
Answer:
9
Step-by-step explanation:
add 3 and 6
what value of x will make the equation f(x)=6 true ?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = 6[/tex]
Required
Solve for x
The question is incomplete as the function f(x) is not given.
However, the following explanation will guide you
As a point of reference, we assume that f(x) is:
[tex]f(x) = 2x + 4[/tex]
To solve further, we substitute 6 for f(x)
[tex]6 = 2x + 4[/tex]
Then, we solve for x
[tex]2x = 6 - 4[/tex]
[tex]2x = 2[/tex]
Divide through by 2
[tex]x = 1[/tex]
So, in your case.
All you need to do is substitute 6 for f(x) then solve for x
The Jackson family went to eat at Applebees. Their bill came to $32.89. They gave the waiter a 15% tip. What was the total amount they paid for their bill?
$32.89
15% tip
Is $4.94
Making the total of the bill
$37.83
if $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in 3 years ?
Answer:
154.44
Step-by-step explanation:
What is 13% of 396?
Y is 13% of 396
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 13% * 396
Converting percent to decimal:
p = 13%/100 = 0.13
Y = 0.13 * 396
Y = 51.48
Now multiply by 3 (amount of continuous years)
51.48 * 3
=154.44
Hope it helps!
Hey now please just anser if itnus a try i will still give 5 stars. THE Question is what is the most easy way to SOLVE THE NINES TABLE IK THIS BUT I WANT to see who else knows sorry fir the big ketters i did not means to put that
Answer:
Tbh, I think the easiest way is to count on your fingers. I still do it, however I can now do my chart tables to 17x17 by using fingers. People may tease, however, it is a good way to make sure you do not mess up as much as memorizing. You should memorize, and count on your fingers at the same time to solve extremely fast.
Step-by-step explanation:
9x4
You can pretend that your thumb equals nine, and count 9 plus 9 plus 9 plus 9, with each other finger, such as your ring finger, pointer, middle, and pinky , which equals 36. 5x9, you have five fingers on each hand, so each finger can equal nine (I don't care if people say that your thumb isn't a finger, just take it and move on lol).
Pls help. .................................
A is the correct answer
The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic typically are:
Answer:
The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic typically are different.
Step-by-step explanation:
An F statistic is a value derived by running an ANOVA test or a regression analysis to find out if the means between two populations are significantly different.
The homoskedasticity-only” F-statistic is derived by running two regressions, one under the null hypothesis and one under the alternative hypothesis. If the “unrestricted” model fits sufficiently better, reject the null.
In the first regression, the restricted regression (the null hypothesis) is forced to be true. This is the regression in which all the coefficients are set to zero; the relevant regressors are excluded from the regression. In the second regression, the unrestricted regression, the alternative hypothesis is allowed to be true. If the sum of squared residuals is sufficiently smaller in the unrestricted than the restricted regression, then the test rejects the null hypothesis
The heteroskedasticity-robust F-statistic is built in to STATA (“test” command); this tests all q restrictions at once.
The homoskedasticity-only F-statistic is important historically (and also in practice), and can help intuition, but isn’t valid when there is heteroskedasticity
PLEASE HELP! DUE TODAY!
Answer:
D. y=x-10
Step-by-step explanation:
Answer: C
Step-by-step explanation: Subtract X from both sides, you will have
Y= -x+10
Use the remainder theorem to verify this statement. (x+5) is a factor of the function f(x)= x^3+3x^2-25x-75. Find the (blank) of f(x) and x+5. The (blank) of this operation is 0. Therefore, (x+5) is (blank) of function f. So f(blank) =0.
Blank choices:
1. product, sum, difference, or quotient
2. sum, discriminant, quotient, or remainder
3. the opposite, the simplified form, not a factor, a factor
4. -5, -75, 75, 5
Answer: I got this answer wrong but I go two right look at the step by step explanation
Hopefully that helped a little
Step-by-step explanation:
The expression (x + 5) is a factor of given function f(x) So the remainder of the function will be zero.
Remainder theorem:
The given function,
[tex]f(x) = x^3+3x^2-25x-75[/tex]
Equate (x + 5) is equal to 0.
x + 5 = 0
x = -5
Substitute x = -5 in given equation.
[tex]f(x) = x^3+3x^2-25x-75\\\\f(-5) = -5^3+3(-5)^2-25(-5)-75\\\\f(-5) = 0[/tex]
Since f(-5) = 0. thus, (x + 5) is a factor of given function f(x).
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Please help multiple choice
Step-by-step explanation:
Hope this helps, good night
The angle measures of triangle QRS are given:
The measure of angle Q is (5x−15)°.
The measure of angle R is 75°.
The measure of angle S is (3x)°.
What is the value of x?
Answer:
x = 15°
Step-by-step explanation:
(5x-15) + 75 + 3x = 180
8x + 60 = 180
8x = 120
x = 15°