Answer: 7,656.46
Step-by-step explanation:
Given is the Present Value of annuity, PV = 1,200,000 dollars.Given that 4.6% APR compounded monthly i.e. r = 4.6%/12 = 0.003833Given that 20 years of investment i.e. N = 20x12 = 240It says to find monthly income from the annuity.We know the formula for Periodic Payment (when PV is known) is given as follows :-Hence, Monthly Income would be
7,656.46 dollars.
It will take Peter approximately 12.5 years to earn back his initial investment.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
For calculate the number of years it will take Peter to earn back his initial investment of $1,200,000 with an APR of 4.6% compounded monthly for a period of 20 years, we can use the formula for the future value of an annuity:
⇒ FV = P ((1+r)ⁿ - 1) / r
Where: P = Payment per period
r = Interest rate per period
n = Number of periods
We need to solve for n, so we can rearrange the formula as;
n = (log(FV × r/P + 1)) / log(1+r)
Plugging in the given values, we get:
P = $6,601.34 ($1,200,000 / (12 × 20))
r = 0.046 / 12 = 0.00383333
FV = $1,200,000
n = (log(1,200,000*0.00383333/6,601.34 + 1)) / log(1+0.00383333)
n ≈ 12.5 years
Therefore, it will take Peter approximately 12.5 years to earn back his initial investment. The answer is option B.
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A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
What was the total bill?
well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.
so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x[/tex]
so "x" plus the tax will just be x + 0.08x = 1.08x.
The tip was 15% of that 1.08x, and we happen to know that was $1.05.
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48[/tex]
The average amount of time until a car accident on a particular 60 mile stretch of road is 60 minutes. Assume (unreasonably) that car accidents are independent, and that two accidents cannot occur at the same time.
(a) What is the probability of a car accident occurring in the two hours?
(b) What is the probability of a car accident occurring between 45 and 75 minutes?
(c) What is the variance of the time until a car accident occurs?
(d) If a car accident has not happened in 3 hours, what is the probability it will happen in the next two hours?
(a) The probability of a car accident occurring in the two hours is 0.3679.(b) The probability of a car accident occurring between 45 and 75 minutes is 0.3935 (c) The variance of the time until a car accident occurs is 0.0167 d) If a car accident has not happened in 3 hours, the probability it will happen in the next two hours is 0.7385
Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-120/60) * (120/60)^1) / 1! = 0.3679[/tex]
So the probability of a car accident occurring in the two hours is 0.3679.
Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-30/60) * (30/60)^1) / 1! = 0.3935[/tex], So the probability of a car accident occurring between 45 and 75 minutes is 0.3935.
The variance of a Poisson distribution is equal to the average rate, so the variance of the time until a car accident occurs is: [tex]Var(X) = 1/60 = 0.0167[/tex]Given that no car accident has occurred in the previous 180 minutes. We can use the conditional probability formula to find this probability:
[tex]P(X = 1 | X = 0) = P(X = 1 and X = 0) / P(X = 0) = (e^(-120/60) * (120/60)^1) / (e^(-180/60) * (180/60)^0) = 0.3679 / 0.0498 = 0.7385[/tex]
So the probability of a car accident occurring in the next two hours, given that no car accident has occurred in the previous 3 hours, is 0.7385.
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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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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 piano teacher schedules either 30-minute lessons or 60-minute lessons with her students. Last week, the teacher gave 9 lessons which lasted for a total of 7 hours. How many 30-minute lessons did the teacher give last week?
Let's use algebra to solve this problem. Let x be the number of 30-minute lessons that the teacher gave last week, and let y be the number of 60-minute lessons. We know that the teacher gave a total of 9 lessons, so we can write:
x + y = 9
We also know that the total time spent on lessons was 7 hours, which we can convert to minutes:
30x + 60y = 420
Now we have two equations with two unknowns, which we can solve using substitution or elimination. Let's use substitution:
x + y = 9 -> y = 9 - x
30x + 60y = 420 -> 30x + 60(9 - x) = 420
Simplifying and solving for x:
30x + 540 - 60x = 420
-30x = -120
x = 4
Therefore, the teacher gave 4 30-minute lessons last week. To find the number of 60-minute lessons, we can substitute x = 4 into either equation:
x + y = 9 -> y = 9 - x -> y = 9 - 4 -> y = 5
So the teacher gave 5 60-minute lessons last week.
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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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:
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:
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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Type your answer in to the boxes. The three points marked on the graph are the vertices (corners) of a parallelogram Y 10 q 8 5 B 3 2 2 3 5 6 7 8 9 10 X What are the coordinates of the fourth vertex?
The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
What is cοοrdinate?A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.
First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:
Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]
Distance Yq = [tex]\sqrt{8 + 25 }[/tex]
Distance Yq =[tex]\sqrt{ 33}[/tex]
Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]
Distance 5B = [tex]\sqrt{2}[/tex]
Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:
x = (33/2)
Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,
Slοpe Yq = (10-5)/(8-10) = -5/2
Slοpe B-missing vertex = -5/2
write the equatiοn οf the line passing thrοugh B and the missing vertex:
y - 2 = (-5/2)(x - 3)
Simplifying, we get:
y = (-5/2)x + (19/2)
Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.
Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
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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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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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what is the measure of angle DEB?
30,60,120,150 explanation
Answer:30
Step-by-step explanation:
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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−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:
the ricoffy tin container no dimensions that container is 2,5 times smaller then what it is in reality the actual weight of coffees 750g , measure the diameter of the diameter of the tin in mm and write down the real diameter in mm
The required diameter of the actual Ricoffy tin container is approximately 92 mm.
Explain about Container.By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).
According to question:Let the diameter of the actual Ricoffy tin container be d mm.
Since the volume of the tin container is proportional to the cube of its dimensions, and the tin container is 2.5 times smaller than its actual size, we have:
[tex]$(\frac{d}{2.5})^3 = \frac{1}{2.5} \times d^3 = \frac{3}{4} \times 750\text{ g} = 562.5\text{ g}$$[/tex]
where we have used the fact that the actual weight of the coffee is 750g.
Solving for d, we get:
[tex]$$d = \sqrt[3]{\frac{562.5\text{ g}}{\frac{1}{2.5}}} \approx 91.98\text{ mm}$$[/tex]
Therefore, the diameter of the actual Ricoffy tin container is approximately 92 mm.
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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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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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PLEASE HELP!!! Using technology, graph these functions and find the solution to the system.
f(x) = x²+x-4
g(x) = -2x2-2x+14
(-2.5, 5) and (1.5, 5)
(-4, 14)
(-3, 2) and (2, 2)
No solution: They do not intersect.
The solution of the functions given will be (-3, 2) and (2, 2) as we can see in graph.
What is the definition of a function?
In mathematics, a function is a rule that associates each element in one set, called the domain, with a unique element in another set, called the range. In other words, a function is a relation between two sets such that each element in the domain is paired with exactly one element in the range.
A function can be represented by an equation, a graph, a table, or a verbal description. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input (or independent variable). The output (or dependent variable) is then given by f(x).
Now,
For functions f(x) = x²+x-4
g(x) = -2x²-2x+14
the graph will be made as shown in image
and their intersection points will be the solution of the given functions
Hence,
The solution of the functions given will be (-3, 2) and (2, 2) as shown in graph.
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Question 10
Which equation represents the line parallel to the line whose equation is 4x+2) = 14 and
passing through the point (2, 2)?
03²=-2x+6
0y=-2x
Oy-x+1
2 pts
Oy-x
Answer:
First choice, y = -2x+6
Step-by-step explanation:
Convert the original equation to slope-intercept form, where y = mx + b.
We are looking for a parallel line so keep x, y, and the slope. turn the 7 into an intercept variable. Plug in (2,2) for (x,y). Solve for b. b = 6. Rewrite the equation with the same slope and the new y-intercept.
y = -2x + 6
If X equals seven what is X times by 7÷2
Answer:
24.5
Step-by-step explanation:
we know that x=7
so 7x/2 (just a fancy way of saying x multiplied by 7/2)=
7*7/2= 24.5
Hope this helps! :)
Keisha will spend more than 27$ on gifts. So far, she has spent 16$. What are the possible additional amounts she will spend?
Use C for the additional amount (in dollars) Keisha will spend.
Write your answer as an inequality solved for C.
pls give me the answer and how to write it
Keisha will likely spend any sums over $11 as potential extra money. The response is as follows:
C > 11
what is addiction?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, in addition. This operator is used to combine two or more objects or numbers. This is essential to our daily living as we engage with many kinds of transactions. Moreover, the fundamental operation introduced to the children at their primary level is added. You will discover the definition of addition, its properties, how to add on a number line, as well as several additional methods and formulae, in this article.
from the question:
Let C represent the extra money Keisha will spend (in dollars).
We are aware that Keisha will purchase gifts for more than $27. This can be written as follows:
16 + C > 27
We can take 16 away from both sides of the inequality to solve for C:
C > 27 - 16
C > 11
Hence, all sums over $11 represent potential extra expenditures by Keisha. The response is as follows:
C > 11
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f
According to the given information, the value(s) of x for which[tex]$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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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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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
If A = and B = , find BA
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 )
Write the polynomial in factored form. x 3 − 3 x 2 − 10 x show work
Answer:
x(x - 5)(x + 2)
Step-by-step explanation:
[tex]x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)[/tex]
x² - 3x - 10
Now, we look for two integers which when added give (-3) and when multiplied give (-10). The factors are 2 and (-5).
Sum = -3
Product = -10
Factors = 2 , (-5) {2*(-5) = -10 and 2 + (-5) = -3}
x² - 3x - 10 = x² - 5x + 2x - 10 {Rewrite the middle term using the factors}
From the first and second term, take out the common factor 'x' & take out the common factor 2 from the third and fourth term.
= x(x - 5) + 2(x - 5)
= (x -5)(x + 2)
[tex]x^3 - 3x^2 - 10x = x(x -5)(x + 2)[/tex]
the graph shows that you are traveling at a constant rate three of the statements are true, which is not
Step-by-step explanation:
Find unit rate :
90 miles in 1.5 hrs
90 /1.5 = 60 miles/hr
that is one mile per minute 20 miles takes 20 minutes
120 miles takes 120 minutes = 2 hours
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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