The total revenue for Dante's Villas is given as the function R(x) = 500x -0.5x², where x is the number of rooms booked. What number of rooms booked produces
the maximum revenue?
Answers
Answer:
500 rooms booked will produce the maximum revenue
Step-by-step explanation:
Revenue function
\(R(x) = -0.5x^2 + 500x\)
where x = number of rooms booked
The maximum revenue is determined by setting the marginal revenue to 0 and solving for x
The marginal revenue is the first derivative of R(x) = R'(x)
\(MR = R'(x) =\) \(\dfrac{d}{dx}\left(-0.5x^2+\:500x\right)\)
\(=-\dfrac{d}{dx}\left(0.5x^2\right)+\dfrac{d}{dx}\left(500x\right)\)
\(\dfrac{d}{dx}\left(0.5x^2\right)= = 2(0.5x) = x\\\\\dfrac{d}{dx}\left(500x\right)=500\)
\(MR = -x + 500\)
Set this equal to zero and solve for x
\(-x + 500 = 0\\\\x = 500\\\\\)
So revenue is maximized at 500 rooms booked
The maximum revenue is found by substituting 500 in the original equation for revenue
\(R\left(500\right)=-0.5\left(500\right)^2+\:500\left(500\right)\\\\= 375,000\)
Related Questions
On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, 0), B (0, 2), C (3, 2), and D (4, 0). The second trapezoid has points A prime (negative 1, 0), B prime (0, negative 2), C prime (3, negative 2), and D prime (4, 0). What is the rule for the reflection? ry-axis(x, y) → (–x, y) ry-axis(x, y) → (x, –y) rx-axis(x, y) → (–x, y) rx-axis(x, y) → (x, –y)
Answers
Answer:
The answer is D
Step-by-step explanation:
I just took the test
The rule of reflection is rx-axis (x , y) → (x, –y)
What is rigid transformation?A rigid transformation (also called an isometry is ais transformation of the plan that preserves length. In a rigid transformation the preimage and image are congruent (have the same e shape and sizes).
If pint (x, y) is reflected across than e x-axis, then its image will be (x, -y), and the rule of reflection is; rx-axis (x , y) → (x , -y)
If point (x , y) reflected across the y-axis , then its image will be (-x, y) , the rule of reflection is; ry-axis (x , y) → (-x , y)
The first trapezoid has vertices
A (-1, 0) B (0and, 2), C (3, 2), and D (4, 0).
The second trapezoid has vertices
A' (-1, , B' (0, - , C' (3, - , D' (4, 0)
The x-coordinates of point A' , B' , C' , D' have the same values and opposite signs of the x-coordinates of points B and C.
Hence, The rule of reflection is rx-axis (x , y) → (x, –y)
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Which statement is correctly written as a conditional statement?
The number 10 is an even number, or it is a composite number.
If the number 10 is an even number, then it is a composite number.
The number 10 is an even number when it is a composite number.
A number, such as 10, is a composite number because it is even.
Answers
The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.
What are natural numbers, rational numbers, integers and irrational numbers?Natural numbers are: 1, 2, 3, ....
Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Rational numbers are numbers which can be written in the form of a/b
where a and b are integers.
Irrational numbers are those real numbers which are not rational numbers.
Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
A composite number is a number divisible by another number than 1 and the number itself.
To find example, a sum of two composite numbers, which is not a composite number, is needed.
The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.
Hence so the correct option is D.
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Explain what the diameter of a circle is. If you had the diameter of a circle, how could you solve for the circumference?
Answers
Answer:
The diameter cannot solve for the circumference, you need the Radius to do it.
Step-by-step explanation:
If you want to use the Diameter divide the Diameter by 2. Diameter=D Radius=R
So to find the circumference of a Circle, 2÷D=R. Now we do 2\(\pi\)R. So now to find the answer we have to do 2x\(\pi\)xR
Use the graph to determine :) thank you so much
Answers
a. The open intervals on which the function is increasing is: B. There is no interval on which the function is increasing.
b. The function is decreasing on the interval: [-2, -∞].
c. The function is constant on the interval: [-∞, -2].
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the following open intervals:
increasing = None.
decreasing = [-2, -∞].
constant = [-∞, -2].
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Aleks topic please help
Answers
Answer:
Item price now= 3.95
Step-by-step explanation:
To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answers
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
Peter rolls a fair dice 114 times. How many times would Peter expect to roll a number greater than 1?
Answers
Answer:
A dice of six faces has 5 numbers bigger than 1 (from 2 to 6).
Then, the number Peter is expecting is : 114 x (5/6) = 95 (times)
Hope this helps!
:)
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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in the diagram below of triangle MNP, Q is a midpoint of MN and R is a midpoint of NP . if QR = 11-x, and MP=57-7x, what is the measure of MP?
Answers
Answer:
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Given:
Given that MNP is a triangle. Q is the midpoint of MN and R is the midpoint of NP.
The length of QR is 4x -11 and the length of MP is 9x - 29.
We need to determine the measure of MP.
Value of x:
The value of x can be determined using the triangle midsegment theorem.
Applying the theorem, we have;
Substituting the lengths, we get;
Subtracting both sides by 8x, we have;
Adding both sides of the equation by 29, we get;
Thus, the value of x is 7.
Measure of MP:
The measure of MP can be determined by substituting x = 7 in the length of MP.
Thus, we have;
Thus, the measure of MP is 34.
Step-by-step explanation:
write an equation in point slope form of the line through point J(4,1) with slope -4
Answers
Answer:
y - 1 = - 4(x - 4)Step-by-step explanation:
Point- slope form:
y - y₁ = m(x - x₁), where m- the slope, (x₁, y₁) - the point on the lineGiven:
m = - 4,Point J(4, 1)Substitute into equation to get the line:
y - 1 = - 4(x - 4)What should you substitute for x in the second equation (bottom equation) in order to solve the system by the substitution method?
Answers
We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
The given system of equations are 2x-1/3y = -2...(1)
3x+y=1...(2)
We solve this system of equations by using substitution method.
Let us solve for x in equation to substitute it in equation (2).
2x=-2+1/3y
Divide both sides of equation by 2.
x=-1+1/6y
Now plug in the value of x in equation 2.
Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
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y=c+bx2, find y where c = 14/5, B = 4/5,x=2
Answers
Answer:
ASAP................Research the use in the military of magnetic anomaly detectors, MADs. Write a brief 300-word essay answer the following questions on MADs. What is the main idea behind MADs? What can be detected by using MADs? A brief history of the MAD development.
Step-by-step explanation:
A number increased by a% and decreased by 80% is 400. What is the number?
Answers
Answer:
\(x = \frac{2000 }{(\frac{a+100}{100})}\)
updated response , given that you confirmed the question....
if the percent is the variable a% then ....
\(x*(\frac{a+100}{100}) = 2000\)
\(x = \frac{2000 }{(\frac{a+100}{100})}\)
I think that there is missing information here ....
you can make any number work here the result of the number being increased by the percent has to be 2000...
so if if the number is 1000 then the percent would be 100%
if you make the number 1500 then the percent would be 33 1/3 %
Step-by-step explanation:
The number is \(\frac{2000}{(1+\frac{a}{100})}\)
What will be the new number when the original number is increased by a% and decreased by 80%?Let us assume that the number be x.
When the number x is increased by a% the new number will be,
\(x(1+\frac{a}{100})\)
Now, this number is decreased by 80%. So, the new number will be,
\(x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20\)
By the given condition,
When x increased by a% and decreased by 80% it becomes 400
Therefore, we can write
\(x(1+\frac{a}{100})*0.20=400\)
\(x(1+\frac{a}{100})=\frac{400}{0.20}\)
\(x(1+\frac{a}{100})=2000\)
\(x=\frac{2000}{(1+\frac{a}{100})}\)
So, the number will be \(\frac{2000}{(1+\frac{a}{100})}\).
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Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
Answers
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
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Magan went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium. Magan purchased a total of 11 cans of soup and frozen dinners which collectively contain 4750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Answers
Magan bought 8 cans of soup and 3 cans of frozen dinners.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x represent the number of cans of soup purchased and y the number of frozen dinners purchased.
Magan purchased a total of 11 cans of soup and frozen dinners.
As per the given information, we can write the equations would be as
x + y = 11 ....(i)
Also:
350x + 650y = 4750
7x +13y =95 ....(ii)
Solving equations (i) and (ii) simultaneously gives the values are:
x = 8, and y = 3
Thus, Magan bought 8 cans of soup and 3 cans of frozen dinners.
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Express your answer in scientific notation.
Answers
Answer:
43.6*10⁴
Step-by-step explanation:
4.9 * 10⁵ = 49*10⁴
then:
4.9*10⁵ - 5.9*10⁴ = 49*10⁴ - 5.9*10⁴ = (49-5.4)*10⁴ = 43.6*10⁴
Answer:
4.32 × 10^5
Step-by-step explanation:
First, multiply 4.9 by 10^5=490000 and 5.8 by 10^4=58000. Subtract 58000 from 490000=432000. Then, scientific notation is a number between 1 and 10 being multiplied by a power of ten, so get 432000 down to a number between 1 and 10, which is 4.32 and 4.32 multiplied by 10^5 is 432000.
(hope this helps :P)
PLEASE HELP IF POSSIBLE, ASAP!!!!!!!! :)
Answers
The Sum of all 3 needs to equal 1
A. 1/9 + 1/2 + 1/3 = 17/18
B. 1/9 + 2/9 + 1/3 = 6/9 = 2/3
C. 1/6 + 3/9 + 1/3 = 3/18 + 6/18 + 6/18 = 15/18
D. 2/9 + 8/18 + 1/3 = 4/18 + 8/18 + 6/18 = 18/18 = 1
The answer is D
plz answer the rest..... will mark as brainlist
Answers
Answer:
I answered it using pictures because I dont know how else to put the answers down.
Writing
Tammy bought some books. She spent a total of $45 after a discount of S6 off of her total purchase. Each book cost $3. How many books did she buy?
(a) Write an equation that could be used to answer the question above.
First, choose the appropriate form. Then, fill in the blanks with the
numbers 45, 6, and 3. Let b represent the number of books.
X
5
o 16+ = 0
(b) Solve the equation in part (a) to find the number of books.
b = 0
Answers
Answer:
b=17
Step-by-step explanation:
b=(45+6)/3
b=51/3
b=17
she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.
derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answers
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)
Hosting a dinner party for 38 people, you plan to serve peach pie for desert.
Each pie has 8 slices.
How many slices are in each pie?
Answers
Answer:
40 slices
Step-by-step explanation:
I rounded 38 to 40 and divided by 8
A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answers
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
Evaluate and match each expression on the left to its value on the right, when x=6 and y=5
12 + x
3x + y
4y -10
(1)/(2)xy
Answers
Answer:
12 + x --> 18
3x + y --> 23
4y - 10 --> 10
(1)/(2)xy --> (1)/(60)
Step-by-step explanation:
Let's evaluate each expression with the given values of x=6 and y=5:
Expression: 12 + x
Substituting x=6 into the expression, we get: 12 + 6 = 18
Expression: 3x + y
Substituting x=6 and y=5 into the expression, we get: 3(6) + 5 = 18 + 5 = 23
Expression: 4y - 10
Substituting y=5 into the expression, we get: 4(5) - 10 = 20 - 10 = 10
Expression: (1)/(2)xy
Substituting x=6 and y=5 into the expression, we get: (1)/(2)(6)(5) = (1)/(2)(30) = (1)/(60)
For questions 3-4, use the graph of the polynomial function to find the factorization of the polynomial. Assume there is no constant term. 3
Answers
3. The factored polynomial is p(x) = (x - 1)(x - 5)
4. The factored polynomial is p(x) = (x + 3)²
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.
This implies that its factors are (x - 1) and (x - 5)
So, the factored polynomial is p(x) = (x - 1)(x - 5)
4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots
This implies that its factors are (x - (-3)) = (x + 3) twice
So, the factored polynomial is p(x) = (x + 3)²
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Someone help me please and thank you
Answers
Answer: 2a < 2b
Step-by-step explanation:
We are given a statement:
a < b and b < c, then 2a ____ 2b
We can use simple numbers that make the statement true.
Where,
a = 2
b = 3
c = 4
Now lets plug it in.
2 < 3 and 3 < 4, then 2(2) ____ 2(3)
and lets simplify:
2 < 3 and 3 < 4, then 4 ____ 6
We can see that 4 is less than 6,
so as a is less than b, 2a is less than 2b.
The only thing changing is the coefficient being multiplied by the variables a and b.
what are the 2 violins to all the instruments
2 violins, 1 viola, and 1 cello
Answers
Analyzing a Graphical Relationship
Speed of Bus
Use the drop-down menus to complete each sentence,
In section A, speed is
as time is
increasing
In section B. speed is
as time is
increasing
In section C. speed is
as time is
increasing
In section D, speed is
as time is
increasing
Speed (mph)
D
С
B
Time (minutes)
« Previous Activity
Type here to search
A
.
1447 PM
9/21/2020
Answers
Answer: A : decreasing B : constant C: increasing D: Constant
Step-by-step explanation:
What is the difference of the polynomials?
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
Answers:
A.) -x^3 + 6x^2 + 9
B.) -x^3 + 2x^2 - 9
C.) 5x^3 - 2x^2 - 2x - 9
D.) 5x^3 - 2x^2 + 2x + 9
Answers
Answer:
D
Step-by-step explanation:
We want to find the difference between the two polynomials:
\((5x^3+4x^2)-(6x^2-2x-9)\)
Distribute the negative:
\(=(5x^3+4x^2)+(-6x^2+2x+9)\)
Rearrange the terms:
\(=(5x^3)+(4x^2-6x^2)+(2x)+(9)\)
Combine like terms. Hence:
\(=5x^3-2x^2+2x+9\)
Our answer is D.
32. Determine the ratio in which the line 3x + y - 9 = O divides the segment join the
points (1, 3) and (2,7).
linn whose inclination is
Answers
Answer:
This might help u......
Assume that Hogan Surgical Instruments Co. has $2,500,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 18 percent, but with a high-liquidity plan, the return will be 14 percent. If the firm goes with a short-term financing plan, the financing costs on the $2,500,000 will be 10 percent, and with a long-term financing plan, the financing costs on the $2,500,000 will be 12 percent.
Answers
The the anticipated return after financing cost with the most aggressive asset financing mix is $200000.
Most aggressive
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $450,000 + (-$250,000)
Anticipated return = $200,000
Most conservative
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Long-term financing = –$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $350,000 + (-$300,000)
Anticipated return = $50,000
Moderate approach
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Long-term financing =–$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $450,000 + (-$300,000)
Anticipated return = $150,000
Moderate approach
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $350,000 + (-$250,000)
Anticipated return = $100,000
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Complete question:
a. Compute the anticipated return after financing cost with the most aggressive asset financing mix.
b. Compute the anticipated return after financing cost with the most conservative asset financing mix.
c. Compute the anticipated return after financing cost with the two moderate approaches to the asset financing mix.