The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.
Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.
The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.
Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.
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could use some help, think this might be right(new to precalculus
Find dxdy . y= cosx1+ tanx7dxdy =
Answer:
y= 1/cosx+7/tanx
dy/dx = 1secxtanx-cosec^2x
PLEASE HELP ME ASAP PLEASEEE
Answer:
Step-by-step explanation:
B and E
Quantity of fuel uterlized by water tanker March 2022
The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.
The total distance covered can be calculated using the formula:
distance = rate × time
From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:
March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31
Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.
The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:
distance = rate × fuel capacity
= 5 km/l × 460 litres
= 2300 km
So, the total distance covered by the water tanker in March 2022 is:
distance = 23 days × 2300 km/day
= 52,900 km
Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:
quantity of fuel = distance ÷ rate
Using the values we have calculated, we get:
quantity of fuel = 52,900 km ÷ 5 km/l
= 10,580 litres
Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.
To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:
total cost = quantity of fuel × fuel price
From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:
total cost = 10,580 litres × R19.55/litre
= R206,929.00
Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.
Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. Quantity of fuel utilized by water tanker March 2022
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The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.
Driver Pedestrian Intoxicated?
Intoxicated? Yes No
Yes 54 83
No 246 603
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.
To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:
Pedestrian not intoxicated and driver intoxicated
Pedestrian intoxicated and driver not intoxicated
From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.
Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:
P = (657 + 329) / 986
= 0.9969
Converting to percentage and rounding to one decimal place,
P = 99.7%
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For the expression
15x² + 25x² + 5x+2/
(5x +1)
which sum represents the correct form of the partial fraction decomposition?
Answer:
15×2
Step-by-step explanation:
5×+2/(5× +1) =15×2^
Compare the dimensions of the prisms. How many times greater is the surface area of the red prism than the surface area of the blue prism?
4 m
3m
2m
12 m
The dimensions of the red prism are
The surface area of the red prism is
9 m
6 m
times the dimensions of the blue prism.
times the surface area of the blue prism.
Answer:
3, 9
Step-by-step explanation:
Surface A = 2(wl + hl + hw)
Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3
Lenght 12/4 =3
Width 6/2 =3
Height 9/3 =3
Calculate surface are of red prism
SA = 2( 6x12 + 9x12 + 9x6)
SA = 2( 72 +108+54)
SA = 2(234) = 468 m²
Calculate surface area of blue prism
SA = 2(2x4 + 3x4 + 3x2)
SA = 2(8 +12+6)
SA = 2(26)
SA =52
Area of red /area of blue = 468/52
Ans =9
In a school, 220 students offer Biology or Mathematics or both. 125 offer biology and 110 Mathematics. How many offer Biology but not Mathematics?
The number of students are 110 students offer Biology but not Mathematics.
Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.
First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:
220 (total) - (125 + 110) = 220 - 235 = -15
Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.
To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:
125 + 110 = 235
Now we can redo the calculation:
220 (total) - 235 (double-counted) = -15
This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:
125 - 15 = 110
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Answer: if im correct i think its 95
Nisha read the part of a book in 1 hour. How much part of the book will be read by
her in 3 2/5
hours?
Henry has 3 bunches of flowers. If there are 5 flowers in each bunch, which of the following shows how to find the total number of flowers he has?
A) 3 divided by 5
B) 3 times 5
C) 3 plus 5
What value of x makes 23x+5=11 true?
A. 4
B. 513
C. 9
D. 1023
E. 24
6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.
Initially, we must remove 5 from both sides of the equation to isolate the variable x:
23x + 5 - 5 = 11 - 5
When we combine the left and right sides, we obtain:
23x = 6
Then, by multiplying both sides of the equation by 23, we must find x:
23x/23 = 6/23
When we combine the left and right sides, we obtain:
x = 6/23
As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.
The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
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Use a property to write an equivalent expression 12 times (100-5).which property did you use?
Answer: distributive property
Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.
Find the surface area of a cylinder with a base diameter of 8 feet and a height of 8 feet right your answer in terms of pi and be sure to include the correct unit
Answer:
96π cubic feet
Step-by-step explanation:
Surface area of a cylinder
A = 2πr(h+r)
where r = radius, h = height
Here
r = diameter/w = 8/2 = 4 feet
h = 8 feet
A = 2π · 4 (8 + 4)
= 8π (12)
= 96π cubic feet
Averi was trying to factor 4x^2+20x-164x
2
+20x−164, x, squared, plus, 20, x, minus, 16. She found that the greatest common factor of these terms was 4 and made an area model:
What is the width of Averi's area model?
The width of Averi's area model is 4 units.
The area model for factoring 4x²+20x-16 is shown above. The width of Averi's area model is 4 units. To factor the given expression, Averi used an area model.
In this model, the width represents the greatest common factor of the given expression while the length represents the remaining factors of the expression. Averi determined that the greatest common factor of 4x²+20x-16 was 4.
Therefore, she created a rectangle with a width of 4 and a length of (x²+5x-4). The dimensions of the rectangle are determined by the factors of the given expression.
The area of the rectangle represents the original expression. Therefore, the area of the rectangle can be calculated by multiplying the width and length of the rectangle. The area of the rectangle is equal to: Area of rectangle = width x length Area of rectangle = 4(x²+5x-4)Area of rectangle = 4x²+20x-16
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Mary works for a company that pays time and a half for hours over 40 in a week and double time for holidays. This week she worked 8 hours on Monday (which was a holiday), 10 hours on Tuesday, 10 hours on Wednesday, 9 hours on Thursday, and 8 hours on Friday. If Mary earns $8 per hour, what is the total of Mary’s earnings for the week?
Total Earnings = (8 x 1.5 x 8) + (10 x 2) + (10 x 1) + (9 x 1) + (8 x 1) = $136. Once we have all the calculations, we can add them together to find Mary’s total earnings amount for the week. In this case, Mary’s total earnings is $136.
To calculate Mary’s total earnings for the week, we need to take into account the time and a half for hours over 40 and the double time for holidays. First, we multiply the 8 hours worked on Monday (a holiday) by 1.5 to calculate the time and a half earnings for that day. Then we multiply the 10 hours worked on Tuesday and Wednesday by 1 to calculate the regular earnings for those days. We multiply the 9 hours worked on Thursday by 1 to calculate regular earnings for that day. Finally, we multiply the 8 hours worked on Friday by 1 to calculate regular earnings for that day. Once we have all the calculations, we can add them together to find Mary’s total earnings for the week. In this case, Mary’s total earnings is $136 amount.
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Alex’s printer can print 8 photos in 12 minutes. Khalid printer can print 24 photos in 1 hour. which process could you use to help determine how much longer will it take khalils printer to print 120 photos than Alex’s. select all that apply.
A. write an equation that adds the number of photos that each print prints in 1 hour
B. make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference
C. Subtract the number of photos that khalil printer prints in two hours from the number of photos that alex’s printer print in 2 hours.
D. graph a table of values for each printer and compare the number of minutes when the number of photos is 120.
Answer:
B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.
Step-by-step explanation:
To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.
How long is this triangles hypotenuse?
Answer:
17.
Step-by-step explanation:
[tex]a^2+b^2 = c^2[/tex] is the formula used to find the hypotenuse (also known as the Pythagora's Theorem).
Substitute the given values into the equation.
[tex]8^2+15^2=c^2[/tex]
64 + 225 = [tex]c^2[/tex]
289 = [tex]c^2[/tex]
[tex]\sqrt{289}[/tex] = c
c = 17
Which describes a possible independent variable for the given dependent variable?
The amount of money you earn
1. Who you call most often each day
2. The number of miles you run each day
3. The number of hours you work
4. The color of your new car
Answer:
3. The number of hours you work.
Step-by-step explanation:
Independent variable means that the occurrence of the event is not dependent on another event occurring.
In this case, the independent variable is the amount of hours you work, as you can, assumingly for the question, can work any amount you would like. However, the pay would be on the basis of how much work you do, and is dependent on the amount of hours you do (assuming you are on hourly).
~
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Which expression is equivalent to the expression 10a - 14c
The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Given the equation:
10a - 14c
We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:
10a - 14c
2(5a - 7c)
The expression 10a - 14c is equivalent to 2(5a - 7c)
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1) What is the total amount in the account if the interest rate is 4.5% each year?
2) After 6 years $275 is added to the account. What does R(x) equal after 6 years ? What is the new expression for A(x) ?
The simple interest has an expression and the total amount after an year at an interest rate of 4.5% is approximately $2478.33. The value of R(x) after 6 years is 275 and the new expression for A(x) is 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
What is the total amount in the account if the rate is 4.5%1. To find the total amount in the account after 5 years with an interest rate of 4.5%, we can simply plug in x = 1.045 (1 + 0.045) into the expression for A(x):
A(1.045) = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045)
≈ 2478.33
So the total amount in the account after 5 years with an interest rate of 4.5% is approximately $2478.33
2. After 6 years, the expression for A(x) would become:
A(x) + 275
We can find the new expression for R(x) by subtracting the original expression for A(x) from the new expression:
R(x) = A(x) + 275 - A(x)
= 275
So the new expression for R(x) after 6 years is simply R(x) = 275.
3. The original expression for A(x) was:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x
To find the new expression for A(x) after 6 years, we can simply plug in x = 1.045 (1 + 0.045) and add 275:
A(1.045) + 275 = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045) + 275
≈ 2923.97
So the new expression for A(x) after 6 years is:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
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Using a ruler and a pair of compass only construct:
a. Line MN =8. 8cm
b. A perpendicular to MN at N
c. Angle MNP=60 degrees,such that line NP =6. 3cm
The Construction of line MN and perpendicular at point N as well as angle MNP = 60°such that NP would be 6.3 cm is given below as image.
In Euclidean geometry, an angle is a shape made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed in the plane where two rays are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what they are called.
In geometry, two lines are considered to be perpendicular if they meet or intersect at right angles of 90°. The Latin term "perpendicularis," which denotes a plumb line, is where the word "perpendicular" originally made its appearance.
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6. if you replace one 75-watt incandescent light bulb with fluorescent light bulb that gives the same amount of light by drawing only 20 watts. you use the light bulb for an average of 4 hours a day. a. how many kwhs of energy would you save in one day? b. how many kwhs of energy would you save in one year? c. the cost of one kwh is $0.10. how much money does the fluorescent light bulb save in one year?
On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.
a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb
Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)
Energy saved in one day = 300 watt-hours - 80 watt-hours
Energy saved in one day = 220 watt-hours
To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:
Energy saved in one day = 220 watt-hours / 1000
Energy saved in one day = 0.22 kWh
b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one year = Energy saved in one day x Number of days in one year
Energy saved in one year = 0.22 kWh/day x 365 days/year
Energy saved in one year = 80.3 kWh
c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Cost savings in one year = Energy saved in one year x Cost per kWh
Cost savings in one year = 80.3 kWh x $0.10/kWh
Cost savings in one year = $8.03
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Which points are solutions to the linear inequality y < 0. 5x +
2? Select three options.
The three points that are solutions to the linear inequality y < 0.5x + 2 are (-3, -2), (-1, -2), and (1, -2)
To check which points are solutions to the linear inequality y < 0.5x + 2, we can substitute the coordinates of each point into the inequality and check whether the inequality is true or false.
For the point (-3, -2):
y < 0.5x + 2
-2 < 0.5(-3) + 2
-2 < -0.5
This inequality is true, so (-3, -2) is a solution.
For the point (-2, 1):
y < 0.5x + 2
1 < 0.5(-2) + 2
1 < 1
This inequality is false, so (-2, 1) is not a solution.
For the point (-1, -2):
y < 0.5x + 2
-2 < 0.5(-1) + 2
-2 < 1.5
This inequality is true, so (-1, -2) is a solution.
For the point (-1, 2):
y < 0.5x + 2
2 < 0.5(-1) + 2
2 < 1.5
This inequality is false, so (-1, 2) is not a solution.
For the point (1, -2):
y < 0.5x + 2
-2 < 0.5(1) + 2
-2 < 2.5
This inequality is true, so (1, -2) is a solution.
Therefore, the three points that are solutions are (-3, -2), (-1, -2), and (1, -2).
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The given question is incomplete, the complete question is:
Which points are solutions to the linear inequality y < 0. 5x +2? Select three options. (-3,-2) (-2,1) (-1,-2) (-1, 2) (1,-2)
(6e−3f−4)⋅2=left parenthesis, 6, e, minus, 3, f, minus, 4, right parenthesis, dot, 2, equals
The final result of the expression (6e−3f−4)⋅2 is e3f−8.
The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.
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what would the answer to y = 11.7x + 96.7 be?
The answer to given linear equation will be When y = 200, x = 8.82.
The values of x and y utilised will determine the solution to the equation y = 11.7x + 96.7.
You can solve for y by substituting a particular value of x into the equation. For instance, if x equals 2, then:
y = 11.7(2) + 96.7
y = 23.4 + 96.7
y = 120.1
Hence, at x = 2, y = 120.1.
Nevertheless, you might choose a different value of y and solve for x by substituting it into the equation. For instance, if y equals 200, then
200 = 11.7x + 96.7
103.3 = 11.7x
x = 8.82
Hence, x equals 8.82 when y is 200.
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which way does shift
g(x)=lx+9l-5
Answer:
g(x) was shifted 9 units to the left and 5 units down
Step-by-step explanation:
Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.
The graph is shifted 9 units left because of the + 9.
Vertical shifts happen when the entire equation is added or subtracted to.
The graph is shifted 5 units down because of the - 5.
See the graph for a visualization.
An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
(Score for Question 1: ___ of 2 points)
1. Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.
Option A:
Week
1
2
3
4
5
6
Amount Paid
Option B:
Week
1
2
3
4
5
6
Amount Paid
Answer:
(Score for Question 2: ___ of 8 points)
2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
(a) Determine the iterative rule for each sequence. Show your work.
(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.
Answer:
(Score for Question 3: ___ of 5 points)
3. Consider the iterative rules you wrote in Problem 2.
(c) Explain why the rules are functions.
(d) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. How would you respond to your friend’s comment?
(e) Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her outputs are meaningless in this situation. What would you tell her about the inputs she can use?
Answer:
(Score for Question 4: ___ of 5 points)
4. The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.
Answer: A
Week Amount Paid
1 $200
2 $250
3 $300
4 $350
5 $400
6 $450
Option B:
Week Amount Paid
1 $200
2 $220
3 $242
4 $266.20
5 $292.82
6 $322.10
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Given the following profit payoff table: s1�1 s2�2 s3�3 d1�1 130 100 330 d2�2 230 -50 310 d3�3 70 -100 370 Construct an opportunity loss (regret) table by completing the following table. s1�1 s2�2 s3�3 d1�1 d2�2 d3�3 Given the probabilities of the states of nature are P(s1)�(�1) = 0.2, P(s2)�(�2) = 0.3, and P(s3)�(�3) = 0.5, calculate the minimum expected opportunity loss. Minimum EOL��� = What is the best alternative based on expected opportunity loss? d1�1 d2�2 d3�3 s1�1 s2�2 s3�3 What is the EVPI����?
Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
Answer:To solve this problem, we will have to first calculate the regret for each option. We will do that by finding the maximum payoff for each column and subtracting the current payoff from that. That gives us the opportunity loss. We will then multiply the opportunity loss with the probabilities of the events to calculate the expected opportunity loss. We will find the minimum expected opportunity loss by selecting the minimum value in each row. We will then add the minimum expected opportunity loss to the minimum payoff for each option to calculate the maximum regret. Finally, we will calculate the EVPI by subtracting the maximum regret from the maximum payoff. Here are the tables that we need to construct: Regret table: Minimum expected opportunity loss table: Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
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Identify the correct leading coefficient, degree, and end behavior of P(x) = 4x^(5) + 9x^(4) + 6x^(3) - x^(2) + 2x - 7.
The leading coefficients of a polynomial is the factor of the term with the greatest degree. The largest exponent of a polynomial's variable is its degree. The coefficient for the given polynomial is [tex]4[/tex], and the degree is [tex]5[/tex].
What in mathematics is a polynomial?An expression that consists of variables, constants, and exponents that is combined using arithmetic computations like addition, subtraction, multiplication, and division is referred to as a polynomial.
What distinguishes a polynomial?By noticing which formulas only contain the operations of adding, subtract, manipulation, and quasi integer exponents, the polynomials may be located.
In the given polynomial [tex]P(x) = 4x^5 + 9x^4 + 6x^3 - x^2 + 2x - 7[/tex], the highest degree of the polynomial is [tex]5[/tex], which means it is a [tex]5^{0}[/tex] polynomial.
The coefficient of the term with the highest degree, which is [tex]4x^5[/tex], is [tex]4[/tex]. Therefore, the leading coefficient is [tex]4[/tex].
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Jill bakes an apple pie in a pie
pan that is 10" in diameter. What is
the circumference of Jill's pie?
2
Answer: the circumference of Jill's pie is 31.4 inches.
Step-by-step explanation:
The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle and π (pi) is a constant approximately equal to 3.14.
In this case, the diameter of Jill's pie is 10", so we can use the formula to find the circumference:
C = πd
C = 3.14 x 10
C = 31.4 inches
Therefore, the circumference of Jill's pie is 31.4 inches.
Answer:
10pi or 31.42
Step-by-step explanation:
the formula for circumference of a circle is 2pir (yes, i can't find the symbol for pi... sorry...) (and r = the radius)
since the diameter is 2*r, the radius is 5 inches.
2*5*pi = 10pi, which is about 31.42
According to the manufacturer, a sandwich cookie weighs on average 11.3 grams. A statistics class is wondering if this is true, so they randomly select 37 sandwich cookies and weigh them. Their sample of 37 sandwich cookies had the following statistics: grams grams.
Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.
What is standard deviation?Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.
The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.
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