Answer:
To recoup the cost of buying 200 canned drinks, Jack needs to make a profit of zero, meaning that the revenue from selling the drinks needs to equal the cost of buying them.
Let's start by setting the profit equation equal to zero and solving for x:
0 = 1.25x - 100
1.25x = 100
x = 80
Therefore, Jack needs to sell 80 cans of drinks to recoup the cost of buying 200 canned drinks.
Step-by-step explanation:
Alexis is on her senior soccoer team. She makes 73% of her foul shots, leading her team to 15 wins in 17 games for the reason. If Alexis took 86 foul shots during the season, how many shots did she make
Alexis made 63 foul shots during the season.
If Alexis made 73% of her foul shots, then she made 0.73 * 86 = 62.78 foul shots during the season.
However, since foul shots must be whole numbers, Alexis would have made either 62 or 63 shots.
We know that Alexis and her team won 15 out of 17 games during the season. This means that Alexis made foul shots in each of these 15 games, for a total of 15 * 2 = 30 foul shots.
If Alexis made a total of 62 foul shots during the season, she would have had to make an additional 32 foul shots in the two games they lost (17 games - 15 games they won = 2 games they lost). That would mean she made 16 foul shots in each of the two games they lost, which is unlikely.
Therefore, Alexis must have made 63 foul shots during the season, leaving only 23 foul shots missed (86 total foul shots - 63 made foul shots).
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For the following Graph, select the answer for the
following questions.
What is the Domain?
What is the Range?
Is it a Function?
-6 -5 -4 -8 -2
O [-2,2]
O(-5,5)
O (-∞0,00)
O(-00, 4]
[-4,3)
No
[0,00)
Yes
20 40 D N +
5+
4+
3
+ N O 40 60
-2
-3
-4--
-5
-61
Domain: [-6,-2], Range: [-4,3) and Function: Yes, this graph can be expressed as a function as it passes the vertical line test.
What is Function?A function is a set of instructions used to perform a specific task. It is a fundamental building block of computer programming, and it is used to create programs that can perform specific tasks. A function is a named block of code that performs a specific task. It can take one or more arguments as input and return a value as output. Functions can be used to divide a large program into smaller, more manageable pieces. Functions are also useful for code reuse, since the same code can be used multiple times within a program. In addition, functions can help improve program efficiency since code does not need to be written multiple times.
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The domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).
What is function?Function is an operation that takes one or more input values and produces one or more output values. It is a mathematical concept that is used in programming to create programs that can be used to solve problems. Functions can be used to organize code blocks into reusable pieces, making it easier to debug and maintain the code. A good example of a function is the mathematical function f(x) = x2, which takes an input value x and produces an output value of x2.
The domain of the inverse of a function is the range of the original function, and the range of the inverse is the domain of the original function. Therefore, since the domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).
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Complete Question is attached below:
A project has 4,416 apartments, each apartment has an average of 4 persons what is the total number of residents in the project
The total number of residents in the project is 17,664.
The total number of residents in the project can be calculated by using the following formula:
Number of residents = Number of apartments x Average number of persons per apartment
In this case, the calculation would be:
Number of residents = 4,416 x 4
Number of residents = 17,664
Therefore, the total number of residents in the project is 17,664.
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simplify: -√72
5-6√/2
0 -36√/2
6√√/2
06√/12
Answer: 6√√/2
Step-by-step explanation: just did it
Answer:
Step-by-step explanation:
[tex]-\sqrt{72}=-\sqrt{2*6*6}=-6\sqrt{2}[/tex]
Determine whether given the coordinates of the vertices. Explain.
P(0,3), Q(0,-1), R(-2,-1), S(1,2), T(1,-2) U(-1,-2)
Question 10 options:
No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU.
Yes; Both triangles have an obtuse angle.
No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU
The correct option is No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
What is Side-Angle-Side (SAS) criterion?
The Side-Angle-Side (SAS) criterion is a rule used in geometry to determine whether two triangles are congruent, which means they have the same size and shape. The SAS criterion states that if two sides and the angle between them in one triangle are equal to two corresponding sides and the angle between them in another triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the two triangles are equal in length and measure.
To determine whether the two triangles are congruent, we can use the side-angle-side (SAS) congruence criterion. We can see that triangle PQR has sides PQ, QR, and RP, and angle QPR, while triangle STU has sides ST, TU, and US, and angle TSU. We can compare the corresponding sides and angles:
PQ is of length 4, and ST is of length 4.
QR is of length 1, and TU is of length 4.
RP is of length 2, and US is of length 2.
Angle QPR is a right angle, while angle TSU is an acute angle.
Therefore, the two triangles do not have the same corresponding sides and angles, and we cannot conclude that they are congruent.
The correct option is:
No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.
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As of 2018 we have an excess of natural resources and are able to support a population of about 9 billion people. However, natural resources are being depleted at about 1% per year. When will we no longer have enough natural resources to support the growing population?
After 71 years we will no longer have enough natural resources to support the growing population.
What is a population?
The population of a given place is the total number of people who typically reside there as of January 1 of a given year.
Total population supported by resources = 9 billion = 9 x [tex]10^9[/tex]
Because resources are being depleted 1% per year = 90000000000 x 1%
= 9 x [tex]10^7[/tex]
Total world population = 6.4 x [tex]10^9[/tex]
Now, for to find time of resource depletion,
Resource problem = 6.4 x [tex]10^9[/tex] ÷ 9 x [tex]10^7[/tex]
On solving we get 71 years
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Write your answer using decimals.Use 3.14 for pi.
The area of the composite figure is the sum of the whole area of each shape. Therefore, the area of the figure is 151.585 ft².
How to find the area of a composite figure?The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.
Therefore, the composite figure can be divided into two rectangles and a quarter circle.
Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.
Hence, the area of the composite figure is the sum of the area of the two rectangle and area of the quarter circle.
area of the composite figure = area of rectangle + area of rectangle + area of quarter circle
area of the composite figure = 5 × 8 + 8 × 6 + 1 / 4 × π × 9²
area of the composite figure = 40 + 48 + 81π / 4
area of the composite figure = 88 + 254.34 / 4
area of the composite figure = 88 + 63.585
area of the composite figure = 151.585 ft²
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−4 × 4 × 4 × 4×4 × 4 × 4 in exponential
Answer: -4 to the 7th power.
Step-by-step explanation:
Answer:
-45,000
Step-by-step explanation:
Show that ABCD is a parallelogram.
E
slope of AB-5-slope of BC-5---4
slope of CD-slope of AD-4---4
ABCD is a parallelogram because both pairs of opposite sides are parallel.
slope of BC-slope of AB----
slope of AD-slope of CD-
-
ABCD is a parallelogram because both pairs of opposite sides are parallel.
slope of AB-lope of BC
slope of CD-slope of AD----
ABCD is a parallelogram because both pairs of opposite sides are parallel.
slope of BC-slope of AB
slope of AD-slope of CD-
ABCD is a parallelogram because both pairs of opposite sides are parallel.
The evidence which supports the fact that the shape ABCD is a parallelogram is; ABCD is a parallelogram because both pairs of opposite sides are parallel.
Which piece of evidence implies ABCD is a parallelogram?From the features of parallelograms, it can be inferred that the opposite sides of a parallelogram are parallel.
Also, parallel lines are lines whose slopes are equal.
On this note;
slope of AB-2/5 slope of BC = -4
slope of CD-2/5 slope of AD = -4
Hence, it can be inferred that opposite sides AB and CD as well as BC and AD are parallel.
Ultimately, ABCD is a parallelogram because both pairs of opposite sides are parallel.
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Consider the random variable X such that X ∼ B(7, p), p < 0. 5, and P(X = 4) = 0. 9724. Find P(X = 2)
The probability of X = 2 can be found using the binomial probability formula, with p ≈ 0.119 obtained by solving for p using the equation P(X = 4) = 0.9724. The resulting probability is approximately 0.193.
We can use the binomial probability formula to find P(X = 2):
P(X = 2) = (7 choose 2) * p² * (1-p)⁽⁷⁻²⁾
We know that P(X = 4) = (7 choose 4) * p⁴ * (1-p)⁽⁷⁻⁴⁾ = 0.9724
Solving for p in this equation, we get p ≈ 0.119
Substituting this value of p in the formula for P(X = 2), we get:
P(X = 2) = (7 choose 2) * 0.119² * 0.881⁽⁷⁻²⁾ ≈ 0.193
Therefore, the probability that X = 2 is approximately 0.193.
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Find the area of the parallelogram.
The area for the parallelogram is equal to 255 square centimeters and the correct option is A = 255 cm²
Area of parallelogramIn calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.
we shall calculate for the height h using Pythagoras rule for the triangle as follows:
h² + 9² = 15²
h² + 81 = 225
h² = 225 - 81 {subtract 81 from both sides}
h² = 144
h = √144 {take square root of both sides}
h = 12
area of parallelogram = 21 cm × 12 cm
area of parallelogram = 254 cm²
Therefore, the area for the parallelogram is equal to 255 square centimetres.
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Solve the system of equations
-2x + y = 10 and 8x + 3y = 32 by
combining the equations.
try
2x
8x
-2x
-8x
O
-
+y
+3y
=
= 10)
=
=32)
=
+y
10
+3y = 32
x+ 0] ² y=
To solve the system using the elimination method (AKA combining the equations), you want to first set up the system so that one variable will be eliminated when you add the equations together.
The first equation has -2x, while the second one has -8x. If we multiply the entire first equation by -4, we'd turn that -2x into 8x, which would cancel out when you add that with the -8x in the second equation:
-4 ( -2x + y = 10 ) –> 8x - 4y = -40
-8x + 3y = 32 –> -8x + 3y = 32
And if you add the new equations on the right, you'll end up with
0x - y = -8
which means y = 8.
We could do the something similar to eliminate the y's. The first equation has y, while the second one has 3y. If we multiply the entire first equation by -3, we'd turn that y into -3y, which would cancel out when you add that with the 3y in the second equation:
-3 ( -2x + y = 10 ) –> 6x - 3y = -30
-8x + 3y = 32 –> -8x + 3y = 32
And if you add the new equations on the right, you'll end up with
-2x + 0y = 2
which means x = -1.
Putting those together, we have a solution of (-1, 8), which checks in both equations.
Select all the expressions that equal 6^{-10}6 −10.
a. 6^{-5} \times 6^{2}6 −5 ×6 2
b. (\frac{1}{6^{2}})^{5}( 6 21 ) 5
c. (6^{-5})^{2}(6 −5 )2
d. \frac{6^{-3}}{6^7}676−3
e. \frac{6^{5} \times 6^{-3}}{6^{-8}}6−865 ×6 −3
Any given expressions in the οptions that simplifies tο -9.9999 are equal tο [tex]6^{-10}\times6 -10[/tex] ( since the expressiοns in the οptiοns are nοt clear, mentiοning the value)
What is Expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers/variables and at least οne math οperatiοn in it.
An expressiοn that includes variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn in mathematics (additiοn, subtractiοn, etc.). Terms cοmbine tο fοrm expressiοns.
Given expressiοn :
[tex]6^{-10}\times6 -10[/tex]
This simplifies tο -9.9999
Any given expressiοns in the options that simplifies to -9.9999 are equal to [tex]6^{-10}\times6 -10[/tex] ( since the expressions in the οptions are not clear, mentiοning the value)
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f
According to the given information, the value(s) of x for which[tex]$f(G(x)) = g(f(x))$[/tex] is x = 1 or x = -2/3.
What is the slope?The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
According to the given information:[tex]To find the inverse of $G(x)$:Replace $G(x)$ with $y$: $y = x - x^2 + 1$Solve for $x$: $x^2 - x + (1 - y) = 0$Apply the quadratic formula: $x = \frac{1 \pm \sqrt{1 - 4(1)(1-y)}}{2} = \frac{1 \pm \sqrt{-3 + 4y}}{2}$The inverse of $G(x)$ is therefore: $G^{-1}(x) = \frac{1 \pm \sqrt{-3 + 4x}}{2}$To find the value of $x$ for which $f(G(x)) = g(f(x))$:Start with $f(G(x))$: $f(G(x)) = f(x^2 - x + 2)$[/tex]
[tex]Replace $f(x)$ with $3 - 2x$: $f(G(x)) = 3 - 2(x^2 - x + 2) = -2x^2 + 2x - 3$Replace $G(x)$ with $y$: $y = x^2 - x + 2$Replace $g(y)$ with $y - x^2 + 1$: $g(y) = y - x^2 + 1$Set $f(G(x))$ equal to $g(f(x))$ and solve for $x$:$-2x^2 + 2x - 3 = (3 - 2x) - x^2 + 1$Simplify and solve for $x$: $x = 1$ or $x = -\frac{2}{3}$[/tex]
Therefore, according to the given information, the value(s) of x for which [tex]$f(G(x)) = g(f(x))$[/tex]is x = 1 or x = -2/3.
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2.731 ÷ 1000
[tex]2.731 \div 1000[/tex]
how do U do the for multiplying and dividing decimals
A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 508.68yd . What is the surface area of the sphere? Use 3.14 for .
The surface area οf the sphere is apprοximately 82,203.84 square yards.
Let's start by using the fοrmula fοr the circumference οf a circle C = 2πr
where C is the circumference, π is the cοnstant pi (which is apprοximately equal tο 3.14), and r is the radius οf the circle. We knοw that the circumference οf the widest circle οf the sphere is 508.68 yards, sο we can set up an equatiοn as fοllοws:
508.68 = 2πr
Sοlving fοr r, we get:
r = 508.68 / (2π)
r = 80.99 yards (rοunded tο twο decimal places)
Nοw that we knοw the radius οf the sphere, we can use the fοrmula fοr the surface area οf a sphere:
A = 4πr²
Plugging in the value οf r, we get:
A = 4π(80.99)²
An ≈ 82,203.84 square yards
Therefοre, the surface area οf the sphere is apprοximately 82,203.84 square yards.
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The relative frequency of ordering a hamburger is about .....%
The relative frequency of ordering a cheeseburger and onion rings compared to the total amount of orders for onion rings is about ....%.
A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.
For hamburguers, the outcomes are given as follows:
Desired: 58 people order hamburguer.Total: 300 people.Hence:
58/300 x 100% = 19.33%.
For cheeseburger and onion rings compared to the total amount of orders for onion rings, the outcomes are given as follows:
Desired: 74 cheeseburgers and onion rings.Total: 103 onion rings.Hence:
74/103 = 71.84%.
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6 marks
2. As an engineer you inspect a 2, 500-foot sewer pipe and find that a 150-foot portion is
damaged. You get estimates for two different solutions. The first estimate is for
spot repair of the damaged portion at a cost of $375.00 per foot. The second estimate is
for relining the full length of the entire sewer pipe at a cost of $65.00 per foot. How much
could you save in immediate costs by choosing the lower estimate?
Answer:add pic
Step-by-step explanation:
Write 2^15 ÷ 2^9 in the form 2^k where k is an integer to be found
Answer:
[tex]2^{6}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]
then
[tex]2^{15}[/tex] ÷ [tex]2^{9}[/tex] = [tex]2^{(15-9)}[/tex] = [tex]2^{6}[/tex] ( with k = 6 )
6. Last month, Lucie had total expenditures of $900. The pie chart below breaks down these
expenditures by category. The category in which Lucie's expenditures were greatest is what
percent of her total expenditures, to the nearest 1%?
a. 24%
b. 28%
c. 32%
d. 34%
e. 39%
gas- $120
insurance- $182
clothes- $254
entertainment- $125
food- $219
Answer:
There is no pie chart to answer it
Step-by-step explanation:
PLEASE HELP the question is on paper
a. The solution to the system of equations that is graphed in the diagram is: (6, -1).
b. This is the point where the lines intersect each other.
How to Find the Solution of System of Equations Graphically?To find the solution of the system of equations graphically, we plot the equations as lines on a coordinate plane and look for the point of intersection, which represents the solution to the system. If the lines are parallel, there is no solution, and if they overlap, there are infinitely many solutions.
a. The solution as shown in the graph given is: (6, -1).
b. We know this because the point where the two lines intersect is the solution of a system of equations.
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Points L, M, and N lie on the surface of a sphere with
its center at point O. Point T lies in the interior of the
sphere. Which segment represents a chord of the
sphere?
A: OT
B: LM
C: LT
D: ON
The chord of the sphere is represented by OT.
The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.
The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.
So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.
Hence, the chord of the sphere is represented by OT.
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $2000 and his stock in Company B was worth $4240. The stock in Company A has increased 1% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage increase in the investor's stock account is 3.7%.
What is the percentage increase?
Percentage increase refers to the amount by which a value or quantity has grown or increased, expressed as a percentage of its original value. It is calculated by dividing the difference between the new value and the original value by the original value, and then multiplying by 100 to express the result as a percentage. The formula for calculating percentage increase is:
Percentage increase = [(New value - Original value) / Original value] x 100%
To find the total percentage increase in the investor's stock account, we need to first calculate the new value of each stock and then add them together.
For Company A:
The stock has increased by 1%, which means its new value is 1% higher than $2000.
The increase in value is 0.01 * $2000 = $20.
The new value of the stock in Company A is $2000 + $20 = $2020.
For Company B:
The stock has increased by 5%, which means its new value is 5% higher than $4240.
The increase in value is 0.05 * $4240 = $212.
The new value of the stock in Company B is $4240 + $212 = $4452.
Now, we can find the total value of the investor's stock account by adding the new values of both stocks:
$2020 + $4452 = $6472
To find the percentage increase, we need to compare the total new value to the original total value:
The original total value was $2000 + $4240 = $6240
The total percentage increase is [(New total value - Original total value) / Original total value] x 100%
Plugging in the numbers: [(6472 - 6240) / 6240] x 100% = 3.7%
Therefore, the total percentage increase in the investor's stock account is 3.7%.
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A small company has five employees. Let X denote the number of employees absent during a
given week. Suppose the pmf of X is as follows:
X 0 1 2 3 4 5
___________________________________________________
P(x) 0.12 0.15 0.20 0.25 0.19 0.09
Find the probability of the following events.
a) Exactly 3 employees are absent during a given week.
b) At least 3 employees are absent during a given week.
c) At most 3 employees are absent during a given week.
d) At most 2 employees are absent during a given week.
e) Between 2 and 4 employees inclusive are absent during a given week.
f) Strictly between 2 and 4 employees are absent during a given week.
g) More than 3 employees are not absent during a given week.
The probability that exactly 3 employees are absent during a given week is 0.25.
The probability that at least 3 employees are absent during a given week is 0.19 + 0.09 + 0.25 = 0.53.
The probability that at most 3 employees are absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 + 0.25 = 0.72.
The probability that at most 2 employees are absent during a given week is P(X ≤ 2) = 0.12 + 0.15 + 0.20 = 0.47.
The probability that between 2 and 4 employees inclusive are absent during a given week is P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.19 = 0.64.
The probability that strictly between 2 and 4 employees are absent during a given week is P(2 < X < 4) = 0.25 + 0.19 = 0.44.
The probability that more than 3 employees are not absent during a given week is P(X ≤ 3) = 0.12 + 0.15 + 0.20 = 0.47, and the probability that more than 3 employees are absent during a given week is P(X > 3) = 0.19 + 0.09 = 0.28. The probability that more than 3 employees are not absent is the complement of the probability that more than 3 employees are absent. Therefore, the probability that more than 3 employees are not absent during a given week is 1 - 0.28 = 0.72.
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Giving Brainliest!!!
Answer:
216 cubic cm
Step-by-step explanation:
Answer:
3174.538707cm³
Step-by-step explanation:
SurfaceArea of Cube=S²
volume of cube=S³
SA=216cm²
S=
[tex] \sqrt{216} [/tex]
S=
[tex]6 \sqrt{6} [/tex]
Volume of cube =S³
V=
[tex](6 \sqrt{6} )^{3} [/tex]
: . V= 3174.538707cm³
Coins are placed into a treasure chest, and each coin has a radius of 1.2 inches and a height of 0.0625 inches. if there are 250 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? round to the nearest hundredth and approximate using π = 3.14. a. 0.28 in3 b. 70.65 in3 c. 117.75 in3d. 282.60 in3
From the given data, the answer is approximately 26.5 cubic inches. The closest option is b. 70.65 inches³.
The volume of each coin can be calculated as follows:
Volume of a coin = π × radius² × height
Volume of a coin = 3.14 × (1.2 inches)² × 0.0625 inches
Volume of a coin = 0.106 cubic inches
The total volume of all the coins can be found by multiplying the volume of one coin by the number of coins:
Total volume of coins = 0.106 cubic inches/coin × 250 coins
Total volume of coins = 26.5 cubic inches (rounded to the nearest tenth)
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One side of a square is 14x + 14 feet. What is the perimeter of the square?
A. 42x + 3/4 feet
B. 56x + 1 feet
C. 14/4x feet
D. 28x + 1/2 feet
Answer:
The perimeter of a square is given by the formula P = 4s, where s is the length of one side.
Here, one side of the square is given as 14x + 14 feet. Substituting this into the formula, we get:
P = 4(14x + 14) feet
P = 56x + 56 feet
Therefore, the answer is option B: 56x + 1 feet.
The crosswalk in front of a school intersects the sidewalk at
an angle of 99º. Find the value of x.
The value of x, considering that 3x and 99º are supplementary angles, is given as follows:
x = 27.
What are supplementary angles?Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if two angles are supplementary, then the sum of their measures is 180 degrees.
Supplementary angles can be adjacent (share a common vertex and a common side) or non-adjacent (do not share a common vertex or side). When two angles are supplementary, they form a straight line, and are sometimes referred to as a linear pair of angles.
For this problem, the angles 3x and 99º are a linear pair, hence the value of x is obtained as follows:
3x + 99 = 180
3x = 81
x = 81/3
x = 27.
Missing InformationThe image is presented at the end of the answer.
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a fair 6 -sided die is rolled 10 times and the resulting sequence of 10 numbers is recorded. how many different sequences are possible?
There are 60,466,176 different sequences that are possible.
Permutation represents a method of arranging things in order. In a fair 6-sided die rolled 10 times and the resulting sequence of 10 numbers is recorded, the different possible sequences are calculated as shown below:
When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. As there are ten rolls, each roll has six possible outcomes. Thus, the total number of different sequences will be calculated as follows:6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60,466,176. Therefore, there are 60,466,176 different sequences that are possible.
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Consider a Newsvendor problem with a single product that sells at a price of p and costs $3 per item.
Assume that the store holds 5 products and that the demand is a Poison random variable with rate
10€-(P-3)
(a) (6 points) Compute the expected profit if the price if $4.
(b) (10 points) Find the price $p that maximizes the profit.
Type in the answers in the following way: a= ..., b=..; use 2 significant figures when plugging the answers. You can also answer "a=. or "b=..." and get partial grades if the answer is correct.
Based on the given scenario, the expected profit if the price is $4 is $11.91, while the price that maximizes the profit is $5.47.
What is the Newsvendor problem?
The Newsvendor problem is a problem in inventory theory that tries to answer the question of how much inventory should be ordered to maximize profit, given limited shelf space or warehouse space, uncertain product demand, and a fixed order quantity. This problem is often encountered in newspaper, magazine, and perishable food industries, and the answer lies in balancing the risk of stocking out (not having enough inventory to meet demand) with the cost of holding excess inventory.
Newsvendor problem with a single product that sells at a price of p and costs $3 per item. Assuming that the store holds 5 products and that the demand is a Poison random variable with rate 10€-(P-3), let’s answer the two questions.
a. Compute the expected profit if the price is $4.The expected profit (EP) is given by:
EP = Revenue - Cost =
EP = (p*min{Demand, Quantity}) - (3*Quantity)
For the given problem, Quantity is 5, and Demand is a Poison random variable with rate 10€-(P-3). Therefore:
EP(p) = (p*min{Demand, 5}) - (3*5)EP(p)
EP(p) = {p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15.
Using p = $4:
EP(4) = {(4*(1 - exp[-7])) + (5*(1 - exp[-7]))} - 15EP(4)
EP(4) = $11.91
Therefore, the expected profit is $11.91 when the price is $4.
b. Find the price $p that maximizes the profit.The profit function is given by:
P(p) = (p*(1 - exp[-10€-(p-3)] + (5*(1 - exp[-10€-(p-3)]))} - 15
To maximize the profit, we need to take the derivative of the profit function with respect to p, set it equal to zero, and solve for p:
P'(p) = {1 - exp[-10€-(p-3)]} + p*{10€-(p-3)}*exp[-10€-(p-3)] - 5*{10€-(p-3)}*exp[-10€-(p-3)] = 0
Rearranging and using numerical methods to solve for p, we find:
p = $5.47
Therefore, the price that maximizes the profit is $5.47.
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