Factorise. 15(k+g)² - 20 (k+g)​

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.

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.

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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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]

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.

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).

[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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Answer:

There is no pie chart to answer it

Step-by-step explanation:

Mark and Lynne have 28 years left on their mortgage. To figure out how old their house is right now, we need to divide the remaining years on the mortgage by 5.

This is because when the mortgage is paid off, their house will be 5 times as old. Therefore, 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. After 28 years, the house will be 33.6 years old.

Mark and Lynne have a mortgage on their house that still has 28 years remaining on it. To figure out the age of the house currently, we need to do a simple calculation. When the mortgage is paid off, their house will be 5 times as old as it is now. Therefore, if we divide the remaining years on the mortgage by 5, we will get the current age of the house. 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. In 28 years, when the mortgage is paid off, the house will be 33.6 years old. It is important to pay off the mortgage in a timely manner, as this will save Mark and Lynne a lot of money in the long run.

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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.

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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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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Domain: [-6,-2], Range: [-4,3) and Function: Yes, this graph can be expressed as a function as it passes the vertical line test.

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, ∞).

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:

Answer:30

Step-by-step explanation:

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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(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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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.

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

The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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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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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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

According to the given information, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

What is 3-4-5 right angle triangle?

A 3-4-5 right triangle is a right triangle where the lengths of the three sides are in the ratio of 3:4:5. In other words, the length of the longest side (the hypotenuse) is 5 times the length of the shortest side, and the length of the remaining side is 4 times the length of the shortest side. This special right triangle has angles of 30 degrees, 60 degrees, and 90 degrees, which are the angles of a 30-60-90 triangle. The sides of a 3-4-5 right triangle can be scaled up or down by any common factor (e.g. 6-8-10, 9-12-15, etc.) and will still form a right triangle with the same angles.

In a 3-4-5 right triangle, the larger acute angle is opposite to the longer leg, which has a length of 4. To find the measure of this angle, we can use the inverse tangent function:

tan(theta) = opposite / adjacent = 3/4

[tex]theta = tan^{-1} (3/4)[/tex]

Using a calculator, we can find that:

theta ≈ 36.87 degrees

Therefore, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

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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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The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.

To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.

In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.

Multiply each term in the second equation by 2, we will get:

4d + 200m = 450

4d + 800m = 600

Now, we can subtract the first equation from the second equation to eliminate d:

(4d + 800m) - (4d + 200m) = 600 - 450

600m = 150

m = 1/4

Substituting this value of m back into either of the original equations, we can solve for d:

4d + 200(1/4) = 450

4d + 50 = 450

4d = 400

d = 100

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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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Answer:hello

Step-by-step explanation:

The required diameter of the actual Ricoffy tin container is approximately 92 mm.

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).

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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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! :)

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)

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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Answer:

Given as steps.

Step-by-step explanation:

Step 2: Transitive Property of Equality
Step 3: SSS Congruency Therom
Step 5: If alt. Interior angles are congruent when two lines are cut by a transversal then the lines are parallel
Step 6: Quadrilateral with opposite sides parallel and congruent is a parallelogram


hope it helps.

Answer:add pic

Step-by-step explanation:

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]

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

Keisha will likely spend any sums over $11 as potential extra money. The response is as follows:

C > 11

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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