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Related Questions
A hiker has various cans of food of assorted sizes that are to be placed in a knapsack. Unfortunately, the knapsack is not large enough to hold all the cans. Therefore, the hiker must determine which cans are to be included in the knapsack Suppose that a hiker's knapsack will hold no more than 0.8 cubic feet of canned goods. The hiker would like to make a selection that will maximize the total protein content of the food in the knapsack. Some food items that are being considered for inclusion in the knapsack are shown in Table below
Item Volume, cubic feet Grams of protein
1 0.2 12
2 0.5 40
3 0.2 15
4 0.2 20
5 0.3 10
a. How should the hiker pack his bag? Build a model in Excel to answer this question.
b. Suppose the hiker wants to include item 2 and 3 for sure. What would the optimal solution be?
c. Suppose now the hiker has to include at least one of the items 2 and 3 (both are also allowed, but not neither). What would the optimal solution be?
Answers
a. The hiker should pack the bag by selecting the items with the highest protein density first, based on grams of protein per cubic foot. Add the items to the knapsack until the volume limit of 0.8 cubic feet is reached. b. If the hiker wants to include item 2 and 3 for sure, the optimal solution would be to add those two items first and then continue selecting additional items based on protein density until the volume limit is reached. c. If the hiker has to include at least one of the items 2 and 3, the optimal solution would be to select the item with the highest protein density among the two and add it to the knapsack first. Then continue selecting additional items based on protein density until the volume limit is reached.
a. To determine how the hiker should pack the bag to maximize the total protein content, we can use a knapsack problem algorithm. We will create a model in Excel to solve this problem. The model will include the following steps:
1. Create a table with columns for the item number, volume, and grams of protein.
2. Add additional columns to calculate the protein density for each item by dividing the grams of protein by the volume.
3. Sort the table in descending order based on the protein density column.
4. Add additional columns to calculate the cumulative volume and cumulative protein for each item as we add them to the knapsack.
5. Starting from the top of the sorted list, add items to the knapsack as long as the cumulative volume does not exceed 0.8 cubic feet.
6. Once we reach the maximum volume, check if adding the next item would increase the total protein content. If it does, include it in the knapsack.
7. Repeat step 6 until there are no more items or the cumulative volume exceeds 0.8 cubic feet.
b. If the hiker wants to include items 2 and 3 for sure, we can modify the model as follows:
1. Start by adding items 2 and 3 to the knapsack.
2. Follow the same steps as mentioned above to determine if adding more items would increase the total protein content without exceeding the maximum volume.
c. If the hiker has to include at least one of the items 2 and 3, we can modify the model as follows:
1. Start by adding either item 2 or item 3 to the knapsack, whichever has a higher protein density.
2. Follow the same steps as mentioned above to determine if adding more items would increase the total protein content without exceeding the maximum volume.
By building and running the Excel model with these modifications, the hiker can determine the optimal solution based on the given constraints.
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A bottle of water of 34 liters of capacity, has only half of liquid, what amount of liters of water has the bottle?
Answers
Find the measure of a negative angle coterminal with 100°.
Answers
Answer:
-260
Step-by-step explanation:
to find a coterminal angle, you add or subtract 360 from it. since the question asks for a negative angle, it should be subtracting 360 from 100
Why
is i= 0.058?
17. A business owner wants to build a reserve fund. To have \( \$ 50,000 \) in the fund at the end of 10 years, the amount the owner will need to invest annually, assuming an annual return of \( 5 \%
Answers
The annual investment amount required to accumulate a reserve fund of $50,000 in 10 years, assuming an annual return of 5%, is approximately $3,720.
To calculate this, we can use the formula for the future value of an ordinary annuity: \[FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right),\] where \(FV\) is the future value (desired reserve fund amount), \(P\) is the annual investment amount, \(r\) is the annual interest rate (in decimal form), and \(n\) is the number of years. Rearranging the formula to solve for \(P\), we have: \[P = \frac{{FV \times r}}{{(1 + r)^n - 1}}.\]Substituting the given values into the formula, we get: \[P = \frac{{50000 \times 0.05}}{{(1 + 0.05)^{10} - 1}} \approx 3720.\]Therefore, the business owner would need to invest approximately $3,720 annually to accumulate a reserve fund of $50,000 at the end of 10 years, assuming a 5% annual return.
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-2(x-2)-4x=3(x+1)-9x
Answers
Answer:
No solution
Step-by-step explanation:
There are no values of x that make the equation true.
Answer:
no solution
Step-by-step explanation:
-2(x-2)-4x = 3(x+1)-9x
-2x+4-4x = 3x+3-9x
-6x+4=-6x+3
4 ≠ 3
No solution
Find the seventh term of the geometric sequence from the given information. Express the term as an integer or simplified fraction.
a2 = -7 and r = 1/2
Answers
The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term
To find the seventh term of a geometric sequence, we can use the formula:
[tex]an = a1 * r^(n-1),[/tex]
where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, we are given a2 = -7 and r = 1/2.
Using the formula, we can find a1 by substituting n = 2:
a2 = a1 * (1/2)^(2-1).
We know that a2 = -7, so we can rewrite the equation:
-7 = a1 * (1/2)^1,
-7 = a1 * (1/2).
Now, let's solve for a1:
a1 = -7 * (2/1),
a1 = -14.
We have found that the first term, a1, is equal to -14.
Now, we can find the seventh term, a7, by substituting n = 7 into the formula:
a7 = (-14) * (1/2)^(7-1),
a7 = (-14) * (1/2)^6,
a7 = (-14) * (1/64),
a7 = -14/64,
a7 = -7/32.
Therefore, the seventh term of the geometric sequence is -7/32.
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What is the product?
Answers
Answer:
d. is the correct answer
What is the image point of (−8,−1) after a translation left 3 units and up 4 units?
Answers
Answer:
i think it is
( 3,-11) or
(-4,-4) as
the
answer
Consider the following system of linear equation in three unknowns x1, x2, x3:
4x1+2x2-x3=9
-5x1+9x2+x3=0
2x1-2x2+10x3=12
Perform the LU decomposition of A i.e. A=LU, where A is the coefficient matrix of system (1) above, L is a lower triangular matrix with ones on the main diagonal, and U is upper triangular.
Answers
The LU decomposition of the given Matrix A is given as A = LU = [1 0 0][-5/4 1 0][1/2 -2/19 1][4 2 -1][-5 9 1][2 -2 10]
The LU Decomposition of a matrix is a way of representing it as the product of a lower triangular matrix L and an upper triangular matrix U. The process of LU Decomposition can be done in various ways.
One common method for LU Decomposition is called the Gaussian Elimination method or the Crout method.
The LU decomposition of a given matrix is a factorization of a matrix A into two matrices L and U such that L is a lower triangular matrix and U is an upper triangular matrix.LU Decomposition of the given system of linear equation in three unknowns x1, x2, x3 is performed as follows
:Given system of linear equations is:4x1+2x2−x3=9−5x1+9x2+x3=02x1−2x2+10x3=12The corresponding matrix form of the given system of equations is given by A x = B where A is the coefficient matrix, x is the column matrix of unknowns (x1, x2, x3) and B is the column matrix of constan ts.The coefficient matrix A of the given system of equations is given as follows:A = 4 2 -1 -5 9 1 2 -2 10We will perform the Gaussian elimination method to find the LU decomposition of matrix A.To find the LU decomposition, we will perform the following steps:
Step 1: Write the augmented matrix [A|B].
Step 2: Convert the matrix [A|B] to the upper triangular form using the Gaussian elimination method.
Step 3: Extract the lower triangular matrix L from the upper triangular matrix U, and rewrite the upper triangular matrix U.
Step 1: Augmented Matrix [A|B]The augmented matrix [A|B] of the given system of linear equations is given as follows:[4 2 -1 9 | 0][-5 9 1 0 | 0][2 -2 10 12 | 0]
Step 2: Upper Triangular FormUsing the Gaussian elimination method, we will reduce the augmented matrix [A|B] to the upper triangular form as follows:[4 2 -1 9 | 0][-5 9 1 0 | 0][2 -2 10 12 | 0]
We will multiply the first row by -5/4 and add it to the second row. Similarly, we will multiply the first row by 1/2 and add it to the third row. The resulting matrix is given as follows:[4 2 -1 9 | 0][0 19/4 3/4 45/4 | 0][0 0 101/19 39/19 | 0]We have obtained the upper triangular matrix U of the given matrix A. The corresponding lower triangular matrix L is obtained as follows:
Step 3: Lower Triangular Matrix LThe lower triangular matrix L is obtained as follows:L = [1 0 0][-5/4 1 0][1/2 -2/19 1]We have obtained the lower triangular matrix L and upper triangular matrix U for the given system of linear equations using the Gaussian elimination method.
Therefore, the LU decomposition of the given matrix A is given as A = LU = [1 0 0][-5/4 1 0][1/2 -2/19 1][4 2 -1][-5 9 1][2 -2 10]
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kingda ka in new jersey is the tallest and fastest roller coaster in the world. riders travel at an average speed of 61 feet per second for 3118 feet. They reach a maximum speed of 187 feet per second.
a. if x represents the total time that the roller coaster is in motion for each ride, write an expression to represent the situation.
b. how long is the roller coaster in motion?
Answers
Answer:
(a) 3118=61*t
(b) The amount of time the roller coaster is in motion is 51.11 seconds.
Step-by-step explanation:
Speed is a magnitude that expresses the relationship between the space traveled by an object, the time used for it and its direction. In other words, speed is associated with the change in position of a body over time and can be expressed as:
[tex]speed=\frac{distance}{time}[/tex]
Then the distance traveled can be expressed as:
distance=speed*time
(a) If x represents the total time that the roller coaster is in motion for each ride, the average speed is 61 feet per second and the distance is 3118 feet then the expression to represent the situation is:
3118=61*x
(b) To calculate the amount of time the roller coaster is moving, you simply need to solve the expression found in (a). Dividing 61 to both sides:
[tex]\frac{3118}{61} =\frac{61*x}{61}[/tex]
51.11 seconds=x
The amount of time the roller coaster is in motion is 51.11 seconds.
What will be the ones place digit of the square of 269?
Answers
Answer:
hi
Step-by-step explanation:
it wuold be nine
Answer: The ones place digit would be 9
the standard form of a linear equation -2x+3=4y
Answers
Answer:
ax+b=0
Step-by-step explanation:
linear equation
Which of these ordered pairs is a solution of 3x−y=12? Choose all that apply.
Answers
American Heart Association Recipes >... Find and save recipes that are not only delicious and easy to make but also heart- healthy. All of our recipes are lower in sodium, lower in fa
Answers
The American Heart Association provides a variety of delicious and easy-to-make recipes that are not only tasty but also heart-healthy.
These recipes are designed to be lower in sodium and lower in fat, making them a great choice for maintaining a healthy heart.
To find and save these recipes, you can visit the American Heart Association's official website or use their mobile application. They offer a wide range of recipes in various categories, including breakfast, lunch, dinner, snacks, and desserts. You can search for recipes based on your dietary preferences, ingredients, and cooking time.
By incorporating heart-healthy recipes into your meal planning, you can enjoy flavorful and nutritious meals while taking care of your cardiovascular health.
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Q.2) (30 p.) Answer each section given as follows: A. (10 p.) Examine and determine which one of the following functions is even, odd, or neither. Show your results as much as possible. I II III IV V —————————————————————————————————————————————————
f(x)=x²-2x³ x f(x) = x² + x -1 f(x)= x/ x⁴ + 1 f(x)= x² sin(x) - x cos(x²) f(x) = log (2-x²)/(2 + x)² x cos(x²) B. (20 p.) Obtain the Fourier series representation of f(x) of given function f(x) = { 1,π < x < 0
{ 0, 0 < x < π, and has period 2 Sketch a graph of f(x) in the interval -2 < x < 2π
——————————————————————
Answers
Among the given functions, function II (f(x) = x² + x - 1) is even, function III (f(x) = x / (x⁴ + 1)) is odd, and the remaining functions I, IV, and V are neither even nor odd.
To determine if a function is even or odd, we can analyze its symmetry properties.
A function is even if it satisfies f(-x) = f(x) for all x in its domain. This means that the function is symmetric about the y-axis.
A function is odd if it satisfies f(-x) = -f(x) for all x in its domain. This means that the function is symmetric about the origin.
Let's analyze each function:
I. f(x) = x² - 2x³
To check for evenness or oddness, we substitute -x for x in the function:
f(-x) = (-x)² - 2(-x)³ = x² + 2x³
Since f(-x) ≠ f(x) and f(-x) ≠ -f(x), function I is neither even nor odd.
II. f(x) = x² + x - 1
To check for evenness or oddness, we substitute -x for x in the function:
f(-x) = (-x)² + (-x) - 1 = x² - x - 1
Since f(-x) = f(x), function II is even.
III. f(x) = x / (x⁴ + 1)
To check for evenness or oddness, we substitute -x for x in the function:
f(-x) = (-x) / ((-x)⁴ + 1) = -x / (x⁴ + 1)
Since f(-x) = -f(x), function III is odd.
IV. f(x) = x² sin(x) - x cos(x²)
To check for evenness or oddness, we substitute -x for x in the function:
f(-x) = (-x)² sin(-x) - (-x) cos((-x)²) = x² sin(-x) - x cos(x²)
Since f(-x) ≠ f(x) and f(-x) ≠ -f(x), function IV is neither even nor odd.
V. f(x) = log((2-x²) / (2 + x)²) x cos(x²)
To check for evenness or oddness, we substitute -x for x in the function:
f(-x) = log((2-(-x)²) / (2 + (-x))²) (-x) cos((-x)²) = log((2-x²) / (2 + x)²) (-x) cos(x²)
Since f(-x) ≠ f(x) and f(-x) ≠ -f(x), function V is neither even nor odd.
In summary, function II is even, function III is odd, and functions I, IV, and V are neither even nor odd.
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What is the length of each side of quadrilateral ABCD?
Answers
Answer:
AB = 5
CD = 5
DA = 3
CB = 3
Step-by-step explanation:
Just count the cubes from one point to the other which gives you the answers I gave above.
Hope it Helps! :D
Triangle A B C is reflected across the line of reflection m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point B prime 270 degrees to form triangle A double-prime B double-prime C double-prime. Which rule describes the composition of transformations that maps ΔABC to ΔA"B'C"?
Answers
Answer: D
Step-by-step explanation: edge 2022
Answer:
B - a reflection across line n followed by a 270° rotation about point P
Step-by-step explanation:
got it correct on edge
A carton has a length of 1 2/3 feet, width of 1 1/6 feet, and height of 1 1/5 feet. What is the volume of the carton?
Answers
Answer:
Step-by-step explanation:
Volume= (length)(width)(height)
step 1: make sure all the measurements have the same unit (ft)
step 2: convert mixed fractions to improper fractions
1 2/3= 5/3 1 1/6= 7/6 1 1/5 = 6/5
multiply the length by width and height
(5/3)(7/6)(6/5)
=7/3 ft^3
The following table shows the time it takes to ride the elevator to three different floors of a skyscraper.
Answers
Answer:
the answer would be no hope this helps
Answer: it is proportional
Step-by-step explanation:
I got it right on khan
f(x)= sin(x-90°)
circle the value of f(0°)
a= 1
b= 0
c= -1/2
d= -1
Answers
Answer:
d = -1
Step-by-step explanation:
Step 1: Define
f(x) = sin(x - 90°)
f(0) is x = -
Step 2: Substitute and Evaluate
f(0) = sin(0° - 90°)
f(0) = sin(-90°)
We know from the unit circle that -90° is equal to 270° or 3pi/2. The value of 3pi/2 is (0, -1). sin is always y, so our answer is -1.
24 lb turkey for 15 people
Answers
Answer:
Each person gets 1.6 of the turkey
Step-by-step explanation:
24/15 = 1.6
how do you find an expression for a cubic function when given f(1)=6 and f(-1)=f90)=f(2)=0
Answers
Answer:
f(x) = -3x(x +1)(x -2)
Step-by-step explanation:
You want a cubic function with zeros at x=-1, 0, 2, that passes through point f(1) = 6.
FactorsEach zero x = p corresponds to a factor (x -p). The factored form of the required function is ...
f(x) = a(x +1)(x -0)(x -2)
Scale factorThe value of f(1) is ...
f(1) = a(1 +1)(1 -0)(1 -2) = -2a = 6
a = -3
FunctionThen the desired function is ...
f(x) = -3x(x +1)(x -2)
__
Additional comment
In expanded form, the function is ...
f(x) = -3x³ +3x² +6x
<95141404393>
8x + 4y = 3x - 6 is a Linear equation or not?
Answers
Yes, it is, as it has variables with the degree one, and a linear equation only has variables that are of degree one.
Answer:
No it's not linear equation
Does the equation y=4x+2 show a proportional relationship between x and y
Answers
Answer:
I'm slow. I think so because remember y=mx+b
b is the y intercept and the mx is the slope which is x.
So 4x is the slope which is the x, and 2 is the y intercept.
Step-by-step explanation:
correct me anyone if im wrong
What is the y-intercept "b" of the linear function y= -1x - 3?
Answers
Answer:
y=3-1x not answering to question
The height of a plant was 133 centimeters. After one week, it grew by 37 centimeters, and after three more weeks, the new height was 238 centimeters.
How much did the plant grow in three weeks?
______ centimeter(s)
Answers
The plant grew by approximately 41.75 centimeters in the following three weeks.
The initial height of the plant was 133 centimeters. After one week, it grew by 37 centimeters, so its height became:
133 + 37 = 170 centimeters
After three more weeks, the new height was 238 centimeters. If we subtract the initial height (133 centimeters) from the final height (238 centimeters), we can find the total growth in four weeks:
238 - 133 = 105 centimeters
We can then subtract the growth in the first week (37 centimeters) to find the growth in the following three weeks:
105 - 37 = 68 centimeters
Therefore, the plant grew by 68 centimeters in three weeks.
Alternatively, we can find the average growth rate per week by dividing the total growth in four weeks by the number of weeks:
(238 - 133) / 4 = 26.25 centimeters per week
Multiplying the growth rate by the number of weeks in the following three weeks, we can find the expected growth in that period:
26.25 * 3 = 78.75 centimeters
Subtracting the initial growth from the expected growth, we can find the growth in the following three weeks:
78.75 - 37 = 41.75 centimeters
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What is an angle with no point?
Answers
hope this helps:)
Answer:
Adjacent angles
Step-by-step explanation:
A truck is hauling earth from a construction site. The truck has the following specifications: T
Bank density
Loose density
110 pcf
100 pef
The productivity, in bank measure (yd
3
/hr), of this operation is most nearly: (A) 38.8 (B) 35.3 (C) 32.3 (D) 29.5
Answers
The productivity of the truck in bank measure is most nearly 32.3 (option C).
To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.
The formula to convert loose density to bank density is as follows:
Bank Density = Loose Density / (1 + Moisture Content)
Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.
Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:
Productivity = Truck Capacity / Cycle Time
However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.
Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).
Using these values, we can calculate the productivity as follows:
Productivity = Truck Capacity / Cycle Time
Productivity = 20 / 0.5
Productivity = 40 cubic yards per hour
However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.
Adjusted Productivity = Productivity * (Loose Density / Bank Density)
Adjusted Productivity = 40 * (100 / 110)
Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)
Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).
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the graph of the line x y=b is a perpendicular bisector of the line segment from (0,3) to (6,9). what is the value of b?
Answers
Answer:
Step-by-step explanation:
the graph of the line x y=b is a perpendicular bisector of the line segment from (0,3) to (6,9). what is the value of b?
rose has a combined total of 25 nickels, dimes, and quarters that together have a value of $3.20. the number of dimes exceeds the number of nickels by 4. how many coins of each kind does she have?
Answers
Rose has 5 nickels, 9 dimes, and 10 quarters. To solve the problem, we used a system of equations, where the first equation was the sum of the number of nickels, dimes, and quarters, and the second equation was the value of the coins.
Let the number of nickels = x
Let the number of dimes = y
Let the number of quarters = z
According to the given question, rose has a combined total of 25 nickels, dimes, and quarters:
Therefore, x + y + z = 25
The total value of coins is $3.20.
So, the value of x nickels, y dimes and z quarters is:
$0.05x + $0.10y + $0.25z = $3.20
The number of dimes exceeds the number of nickels by 4. Therefore, y = x + 4
Now we have three equations: x + y + z = 25
$0.05x + $0.10y + $0.25z = $3.20y = x + 4
Solving for the equations: x + (x + 4) + z = 25
2x + 4 + z = 25
2x + z = 21$0.05x + $0.10(x + 4) + $0.25z = $3.20
0.05x + 0.10x + 0.40 + 0.25z = 3.20
0.15x + 0.25z = 2.80
Substituting 2x + z = 21 in 0.15x + 0.25z = 2.80, we get:
x = 11, y = 15, z = -1
This means that Rose has 11 nickels, 15 dimes and -1 quarters.
However, she can't have -1 quarters, so let's check again.
x = 11, y = 15, z = -1 (from 2x + z = 21)
5x + 10y + 25z = 800 (multiply by 100 to get rid of decimal places)
$0.05x + $0.10y + $0.25z = $3.20
$0.55x + $1.5y + $0.25z = $7.20
Add the equations: 5x + 10y + 25z = 800
$0.55x + $1.5y + $0.25z = $7.20
5.5x + 15y + 2.5z = 72
But we also know that: x + y + z = 25
If we add 10 to both sides, we get: x + y + z + 10 = 35
If we multiply both sides by 0.05, we get:
$0.05x + $0.10y + $0.25z + $0.50 = $1.75
But we know that: $0.05x + $0.10y + $0.25z = $3.20
Therefore, $3.20 + $0.50 = $3.70, which is the value of 10 quarters.
This means that z = 10, and we can substitute it into x + y + z = 25 to get:
y = x + 4y + x + z = 25
2x + 14 = 25
2x = 11
x = 5, y = 9
Therefore, Rose has 5 nickels, 9 dimes, and 10 quarters.
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