Assuming that the meal cost $50, the Shapley values (payments) for each player is: number of possible combination , Player 1: $15 , Player 2: $10 , Player 3: $10 , Player 4: $15
1. Calculate the marginal contribution of each player. This is the amount of money that each player adds to the total cost of the meal.
Player 1: $25
Player 2: $15
Player 3: $10
Player 4: $0
2. Calculate the Shapley Value for each player. This is calculated by taking the average of the marginal contribution of each player, weighted by the number of possible combinations they could have been in.
Player 1: ($25*3 + $15*2 + $10*1 + $0*0) / 6 = $15
Player 2: ($25*2 + $15*3 + $10*2 + $0*1) / 6 = $10
Player 3: ($25*1 + $15*2 + $10*3 + $0*2) / 6 = $10
Player 4: ($25*0 + $15*1 + $10*2 + $0*3) / 6 = $15
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one urn, u1, contains one blue ball (labeled b1) and three red balls (labeled r1, r2, and r3). a second urn, u2, contains two red balls (labeled r4 and r5) and two blue balls (labeled b2 and b3). an experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement.
Two urns contains different numbers of different colour balls. Two balls are randomly chosen from both of urns. The probability that two red balls are choosen is 1/3..
We have given that
First Urn, u₁ contains 3 Red( labelled r₁,r₂,r₃) ; 1 blue ball ,(labelled b₁).
Total number of balls in urn, u₁ = 4 balls
Second Urn, u₂ contains 2 red (labelled r₄,r₅) and 2 blue (labelled b₂, b₃) .
Total number of balls in urn, u₂ = 4 balls
Assume , A = first urn , u₁ is selected
Assume, B = Second urn u₂ is selected
Assume , R = selected balls are red
Case 1 : Urn u₁ is choose and two balls without replacement are withdraw.
Probability to choose the first urn, P(A) = 1/2
Probability that the two withdraw without replacement balls are red in colour, P(A/R)
= 3/4 × 2/3 = 1/2
Case 2 : Urn u₂ is choose and two balls without replacement are withdraw.
Probability to choose the second urn, P(B) = 1/2
Probability that the two without replacement withdraw balls are red in colour, P(B/R)
= 2/4 × 1/3 = 1/6
The required probability= P(A) P(A/R) + P(B)P(B/R) = 1/2(1/2) + 1/2(1/6) = 1/4 + 1/12
= 4/12 = 1/3
Hence, the required probability is 1/3..
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Complete question:
One urn u1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn u2 contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. Probability that two red balls are choosen.
what is answer to 3/7 x 5/2?
Answer:
15/14 or 1 1/14
Step-by-step explanation:
multiple the numerators and deno
3x5=15
7x2=14
15/14 or 1 1/14
Answer:
Step-by-step explanation:
Exact form
15/14
Decimal Form:
1.07142857........
mixed number is
1, 1/14
Two beetles sit at the top edge of a house roof. The roof has two faces. The first face is such that the horizontal shift by 3cm along this face means 2cm shift vertically. Simultaneously, the beetles start moving downwards, the first beetle by the first face, the second - by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the first beetle above the second beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face or is perpendicular to the base
Answer:
16
mark me brainliest
Step-by-step explanation:
Use compatible numbers to determine if 455 + 229 455 + 229 is more than 650 650 . Drag the numbers to the table to show each compatible number. Numbers may be used once or not at all. Is it more than one answer for each box or just the one I already selected
The required compatible number of the given two number are 500 and 200 and sum is 700.
What is Compatible Numbers?In math, compatible numbers are the numbers that are not difficult to add, deduct, duplicate, or gap intellectually. compatible number are close in worth to the real numbers that make assessing the response and figuring issues more straightforward. We can adjust the numbers to the closest ten, hundred, thousand or 10,000 to make them viable numbers. For example, in the event that we need to add 493 and 549, we can make the numbers viable by gathering them together to the closest tens or hundreds. 490 and 550 (adjusted to the closest tens) or 500 and 500 (adjusted to the closest hundreds) are a lot simpler to settle.
According to question:So, the compatible number of 455 is 500 and that of 225 is 200.
Then,
Compatible sum = 500 + 200 = 700.
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Write the equation of the piecewise function whose graph is shown
Please help will give brainlist only if correct!
Answer:
C.
Step-by-step explanation:
Also what you picked
PLEASE HELP WILL GET BRAINLIEST!!
Answer:
235.5
Step-by-step explanation:
cylinder volume formula
V = pi * r^2 * h
V = 3.14 * 5^2 * 3
V = 3.14 * 25 * 3
V = 3.14 * 75
V = 235.5
A four-sided figure with four-right angles
Answer:
Square and Rectangle
The table shows the transportation method of employees at a certain company. What percent of the employees walk to work?
A. 0.5 %
B. 1 %
C. 5 %
D. 7 %
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. 0.5% of employees walk to work.
What percent of the employees walk to work?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given,Employees who use;
Car: 758
Bus: 530
Walk: 7
Other: 105
Total = 758+530+7+105 = 1400
Employees percentage who walk to work
=No of employees who walk /Total number*100
Percentage =700/1400 =0.5%
0.5% of employees walk to work.
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DIG DEEPER You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and ( 45w + 25) dollars in checking account. how much money do you save each week?
The sum of both accounts' expression in its most basic form is 55w + 145.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the instructions given in the question,
Amount in savings account = 10w + 120
Amount in checking account = 45w + 25
Then, total money shaved each week will be,
(10w + 120) + (45w + 25)
10w + 45w + 120 + 25
= 55w + 145
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How many miles are in 54.74 kilometers? Round to the nearest whole
number, if necessary.
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles.
So to convert 54.74 kilometers to miles, you can multiply 54.74 by 0.621371:
54.74 kilometers * 0.621371 miles/kilometer = 34.09 miles
Rounded to the nearest whole number, this is 34 miles.
Step-by-step explanation:
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles. To convert 54.74 kilometers to miles, you can multiply the number of kilometers by the conversion factor:
[tex]54.74 kilometers * 0.621371 miles/kilometer = 34.08 miles[/tex]
Rounded to the nearest whole number, there are approximately 34 miles in 54.74 kilometers.
Step-by-step explanation:
X1,..., X are i.i.d. standard normal variables. Denote by An the sample mean of the squares of these variables: 1.:- x - - * - }(x2 + x3 + .. + x2). 1 Recall An= = x. For very large n, the distribution of (An-a) is approximated best by ... (In the choices below, the parameter for the normal distributions N (4,0") are the mean w and the variance o?.) O N (0,1) O N (0,2) O N (0,n) O N (0,2n) O x x. Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
Answer:
Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
Step-by-step explanation:
Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
The correct characterization of the limit distribution and other Questions are answered in the following steps.
For the first question, the distribution of (An-a) is approximated best by N(0, n) because the variance of the sample mean of i.i.d. standard normal variables is 1/n.
For the second question, since An converges in probability to a constant, Bn = 4An also converges in probability to 4a. Therefore, the sequence of random variables (Bn-b) does converge in distribution.
For the third question, the limit distribution of (Bn-b) is N(0, 4^2 * n) because the variance of the product of a random variable and a constant is the constant squared times the variance of the random variable.
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Estimate y when x = 8 from the best fitted straight line y = 13.06 + 0.6x.
Answer:
17.86
Step-by-step explanation:
You want to find y when x=8 using the equation y = 13.06 +0.6x.
EvaluationPut the value of the variable in place of the variable in the equation, and do the arithmetic.
y = 13.06 +0.6x
y = 13.06 +0.6·8 . . . for x=8
y = 13.06 +4.8
y = 17.86
The estimated value of y for x=8 is 17.86.
A cat gave to 3 kittens who each had a different mass between 147 znd 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.
Kitten Mass (in grams)
Archer 147
Nate 153
Lisa 159
Bob 57
How will the birth of the 4th kitten affect the mean and median?
Choose 1 answer
A. Both the mean and median will increase, but the median will increase by more than the mean.
B. Both the mean and median will increase, but the mean will increase by more than the median.
C. The mean will increase, and the median will decrease.
The affect of mean and median due to the birth of the 4th kitchen is B. Both the mean and median will increase, but the mean will increase by more than the median.
The median is the middle value when the values are ordered from smallest to largest. In this case, the median of the first 3 kittens is 153 because it is the middle value of (147, 153, 159). The median of all 4 kittens is 153 because it is the middle value of (57, 147, 153, 159). The median does not change because the addition of the 4th kitten does not change the position of the middle value.
The mean is calculated by adding up all the values and dividing by the number of values. In this case, the mean of the first 3 kittens is:
(147 + 153 + 159) / 3 = 153
The mean of all 4 kittens is:
(147 + 153 + 159 + 57) / 4 = 128
The mean increases because the addition of the 4th kitten with a lower mass pulls the overall average down.
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Suppose your PRNG uses the following formula: X = X * 3 - 2. And suppose that X is 5. What are the next three numbers that would be generated?
The next three numbers that would be generated are 13, 37, and 109.
What is formula?Formula is a mathematical expression that is used to calculate the value of a particular quantity, such as a number, a quantity of a certain type of material, or a number of elements. The most common form of a formula is an equation, which contains two or more variables and is written in the form of a mathematical expression. Formulas are used in many disciplines, including physics, chemistry, engineering, and economics, to solve problems and determine relationships between quantities.
This is because the formula applies the operation of multiplying the current number by 3 and then subtracting 2. Applying this formula to 5 gives 13, and then applying the formula to 13 gives 37, and so on. The resulting sequence is 5, 13, 37, 109, and so on. This is a simple PRNG that can be used to generate sequences of random numbers.
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Jessica earns 35 for 7 hours of babysitting she is saving to buy a 160 radio how many hours will Jessica have to buysit to have enough money to buy the radio
To have enough money to buy the radio, Jessica will have to babysit for 32 hours
How to determine the number of hours Jessica will have to babysit?From the question, we have the following parameters that can be used in our computation:
Earnings = $35 for 7 hours
This means that the hourly rate can be calculated as
Hourly rate = $35/7 hours
Using the above as a guide, we have the following:
Evaluate the quotients
Hourly rate = $5 per hour
The number of hours Jessica will have to babysit is calculated as
Number of hours = 160/Hourly rate
Substitute the known values in the above equation, so, we have the following representation
Number of hours = 160/5
Evaluate
Number of hours = 32
Hence, the number of hours is 32
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A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
a. Write a system of linear equations that represents this situation. Let x represent the cost of an adult ticket and y represent the cost of a student ticket.
System of equations: x=
x+
y=1040
Question 2
b. What is the cost of each ticket?
The cost of an adult ticket is $
.
The cost of a student ticket is $
.
The system of linear equations, that models the problem is represented as x = 2 and 64x + 132y = 1040 while the cost of adult and student tickets is $8 and $4 respectively.
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = cost of adult tickety = cost of student ticketa)
x = 2y ...eq(i)
64x + 132y = 1040 ...eq(ii)
b)
From equation (i)
64(2y) + 132y = 1040
y = 4
Put y = 4 into equation (i)
x = 2(4)
x = 8
The cost of adult ticket is $8 and student ticket is $4
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(4+ square root3x-2 (4+square root 13x-2)
How do you foil this?
The solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is 4 + √(3x⁻²) and 4 + √(13⁻²). The expression will be solved as,
E = {[4 + √(3x⁻²)]} { {4 + √(13x⁻²).]}
E = {4 + [√3 / √x²] { [4 + √13 / √x²]}
E = ( 4 + √3 / x) ( 4 + √13 / x).
Therefore, the solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).
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NO LINKS!!
Find the binomial coefficient
( 11)
(6)
Evaluate using Pascal's Triangle
4_C_1
Answer:
462; 4------------------------------
The binomial coefficients can be found using Pascal's triangle.
Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.
For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.
Calculation of the binomial coefficient is as follows:
[tex]\[ \binom{11}{6} = _{11}C_6=\cfrac{11!}{6!(11-6)!}=\cfrac{6!*11*10*9*8*7}{6!5!} =\cfrac{11*10*9*8*7}{5*4*3*2} =462[/tex][tex]\[ \binom{4}{1} = _4C_1=\cfrac{4!}{1!(4-1)!} =\cfrac{4!}{3!} =\cfrac{3!*4}{3!} =4[/tex]c) If the gradient of a line, C, is a 2/3 , what is the gradient of the line which is perpendicular to C?
Any line perpendicular to line C must have a slope equal to -3/2.
Which is the slope of a line perpendicular to line C?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the slopes is -1, then if the slope of the line perpendicular to line C is x, then we can write:
x*(2/3) = -1
Solving for x we get:
x = -3/2
That is the slope of the perpendicular line.
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What is equivalent to 1:9
Answer:
2 : 18
Step-by-step explanation:
to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.
1 : 9 ( multiply both parts by 2 )
= 2 : 18
or
1 : 9 ( multiply both parts by 3 )
= 3 : 27
and so on...
FILL IN THE BLANK alona is examining the impact of the 2011 penn state scandal on student morale and school spirit by distributing number-scaled surveys in her introduction to sociology class. alona is employing a______research method.
Alona is using a quantitative approach to her studies.
What is Quantitative research?The goal of quantitative research is to quantify the data collection and processing process.
It is based on a deductive method that emphasizes the validation of the hypothesis and is influenced by positivist and empiricist theories.
This research technique, which is related to the natural, applied, formal, and social sciences, encourages the unbiased empirical exploration of observable phenomena to test and comprehend correlations.
This is accomplished using a variety of quantification techniques and procedures, demonstrating the wide application of this approach as a research strategy across numerous academic fields.
So, in the given situation, Alona is using the quantitative research method.
Therefore, Alona is using a quantitative approach to her studies.
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What is the slope of linear relationship?
Photo goes with qustion
A. 1/4
B. -4/1
C. 4/1
D. -1/4
how many shapes are drawn based on the code below? def drawshapes(centerx, centery, radius, points, color): star(centerx, centery, radius, points, fill
6 shapes can be drawn by the given code.
Describe shapes.Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many types. The shapes are typically enclosed by an outline or boundary that is composed of points, lines, curves, etc. Geometric figures and figures composed of fixed lines or curves are other names for forms. There are two types of shapes: closed shapes and open shapes. Examples of shapes in daily life are the Sun, Earth, Doors, Windows, Watches, Wall Clocks, and so forth.
Given
Codes are def draw shapes( centerx , centery, radius, points, color): star(centerx, centery, radius, points, fill.
6 shapes can be drawn by the given code.
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Which line is an irregular line of blank verse?
“He only says, ‘Good fences make good neighbours.’”
“If I could put a notion in his head:”
“And on a day we meet to walk the line”
“And set the wall between us once again.”
THE ANSWER IS THE FIRST ONE
Identify the irregularity in the line.
THE ANSWER IS THE SECOND ONE
The line that is an irregular line of a blank verse is A . “ He only says , ‘Good fences make good neighbours. ”
The irregularity of the line is that it has 11 syllables while other lines have 10 syllables .
What is a blank verse ?Unrhymed but metric poetry with usually always iambic pentameter is referred to as "blank verse" in literature.
Going by the definition, the three bottom lines are regular lines in a blank verse as they have 10 syllables. However, the first line, has 11 syllables, thereby making it irregular.
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Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1).
1, 1/2, 1/6, 1/24, 1/120, . . .
a_n =
Answer:
The apparent nth term of the given sequence is given by the formula:
a_n = 1 / n!
where n! is the factorial of n, defined as the product of all positive integers less than or equal to n.
For example, the first term of the sequence is 1/1! = 1/1 = 1, the second term is 1/2! = 1/2 = 1/2, the third term is 1/3! = 1/6, and so on.
Therefore, the expression for the apparent nth term of the sequence is:
a_n = 1 / n!
Answer:
[tex]a_n=\dfrac{1}{n!}[/tex]
Step-by-step explanation:
Given sequence:
[tex]1,\; \dfrac{1}{2},\; \dfrac{1}{6}, \; \dfrac{1}{24}, \; \dfrac{1}{120}, \; ...[/tex]
Analyse each term in the sequence:
[tex]a_1=\dfrac{1}{1}=\dfrac{1}{1 \times 1}=\dfrac{1}{1!}[/tex]
[tex]a_2=\dfrac{1}{2}=\dfrac{1}{2 \times 1}=\dfrac{1}{2!}[/tex]
[tex]a_3=\dfrac{1}{6}=\dfrac{1}{3 \times 2 \times 1}=\dfrac{1}{3!}[/tex]
[tex]a_4=\dfrac{1}{24}=\dfrac{1}{4 \times 3 \times 2 \times 1}=\dfrac{1}{4!}[/tex]
[tex]a_5=\dfrac{1}{120}=\dfrac{1}{5 \times 4 \times 3 \times 2 \times 1}=\dfrac{1}{5!}[/tex]
The exclamation mark "!" placed after a number means factorial.
It means to multiply all whole numbers from the given number down to 1. Example: 4! = 4 × 3 × 2 × 1
Therefore, the equation for the nth term of the given sequence is:
[tex]a_n=\dfrac{1}{n!}[/tex]
a random sample of 100100 observations from a population with standard deviation 17.037078307720517. yielded a sample mean of 93.1). Given that the null hypothesis is μ≤90 and the alternative hypothesis is μ>90 using α=.05, find the following:(a) Test statistic(b) P-value:(c) The decision for this test is:i. Reject the null hypothesis.ii. Fail to reject the null hypothesis.
1)Test Static: 1.82
2)P-Value: < 0.05
3)Decision: i. Reject the null hypothesis.
To test the claim that the population mean is greater than 90, we can use a one-sample t-test.
(a) The test statistic for the one-sample t-test is calculated as:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))Plugging in the values, we get:
t = (93.1 - 90) / (17.037078307720517 / sqrt(100)) = 3.1 / (17.037078307720517 / 10) = 3.1 / 1.7037078307720517 = 1.82(b) To find the p-value for the test, we can use a t-table or a statistical software package to find the probability of observing a t-value as extreme or more extreme than the one we obtained, given that the null hypothesis is true. For a one-tailed test with α = 0.05 and df = 99 (the sample size - 1), the critical value for t is approximately 1.65. Since our test statistic (1.82) is greater than the critical value, the p-value is less than 0.05.
(c) Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that the population mean is indeed greater than 90. Therefore, the decision for this test is: i. Reject the null hypothesis.
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Maximum revenue Imagine this scenario: You are trying to fulfill you dream of opening your own business, designing and selling coffee mugs. After many years and hours of studying for college, you feel that there is a big demand for coffee mugs. You are trying to get a contract with a local store to be the sole provider of coffee mugs. You and your company partner are researching how many coffee mugs must be produced and sold for maximum revenue. After extensive research, you concluded that you could give away 50 coffee mugs without charging anything. If you charge $10.00, nobody will buy the coffee mugs. Your job is to find the maximum possible revenue from selling the coffee mugs. Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S . Hint: To give away 50 coffee mugs means when the price p=0 , S(0) = 50. Plot that point on the graph. Find one more point using the other given condition. Keep in mind S(p) is a linear function.
2. Find the equation of the linear function S(p) that describes the situation.
3. The revenue is determined by R = S p. Express the revenue as a function of the price p.
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be made to maximize the revenue?
8. What is the maximum revenue? 9. How many coffee mugs must be sold to make at least $50 in revenue?
Therefore at $5 you selling 15 mugs will generate the maximum revenue.
What is a graph?In discrete mathematics, a graph is made up of points called vertices, and the connecting lines between them are called edges. Simple graphs, linked and unconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and linked and unconnected graphs are only a few of the numerous varieties of graphs.
Here,
For $0 for , 50 mugs be sold
For $10 for , 0 mugs be sold
Thus, from graph
1) Slope= 50/-10 =-5
2) m(p)= -5(p-10) =-5p +10
=> m(p) =10 -5p
3)Revenue R(p) = m(p)
R(p) = 10 -5p
4) point(5,15)
5) at price p =0 , p=5 , we do not make any money
6)At $5 most revenue is made
7)when p=5
R(p) = 10 -5(5)
R(p) = 15
Thus , 15 coffee mugs will yield max revenue
8)Max revenue = $45
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Evaluate the expression when c=4 and d=5.
d+6 c
Answer:
29 is the correct answer
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Use the properties of exponents to determine which functions (if any) are the same.
f(x)= 3^x + 11
g(x) = 2^(3x+5)
h(x)= 32(8^x)
a. f(x) = g(x)
b. f(x) = h(x)
c. g(x)=h(x)
d. All three functions are equal
e. None of the functions are equal
Answer:
c. g(x) = h(x)
Step-by-step explanation:
Given functions:
[tex]f(x) = 3^x+11[/tex]
[tex]g(x)=2^{3x+5}[/tex]
[tex]h(x)=32(8^x)[/tex]
Rewrite function g(x) using exponent rules.
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies g(x)=2^{3x} \cdot 2^5[/tex]
[tex]\implies g(x)=2^{3x} \cdot 32[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies g(x)=(2^3)^{x} \cdot 32[/tex]
[tex]\implies g(x)=8^{x} \cdot 32[/tex]
[tex]\implies g(x)=32(8^{x})[/tex]
Therefore, g(x) = h(x).
A circular cake has radius 12 cm and height 7 cm. The uniform cross-section of a slice of the cake is a sector with angle 22°. The top and the curved surface of the slice, shaded in the diagram, are covered with chocolate. Calculate the area of the slice which is covered with chocolate.
Therefore, the given area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]
What is area ?Area is a mathematical notion that describes the size of a region on a planar or curved surface. A surface area is the area of an open surface or the border of a three-dimensional object, whereas a plane region's or plane's area's refers to a shape's or planar lamina's area.
Here,
Given :
circular cake radius = 12 cm
circular cake height = 7 cm
thus,
the area of the slice which is covered with chocolate = θ/360 *π[tex]r^{2}[/tex]
=> 22/360 * 3.14 *12*12
=> 22/360 * 3.14 *144
=>69.08/360 * 144
=> 276.57 c[tex]m^{2}[/tex]
Therefore the given area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]
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