The sample mean is -0.0417 standard deviations from the population mean.
What is standard deviation?Standard deviation is a measure of the dispersion or spread of a set of data.
What is mean?The mean, also known as the arithmetic mean or average, is a measure of the central tendency of a dataset.
(sample mean - population mean) / standard deviation
Plugging in the values from the problem, we get:
(245.05 - 246) / 3.60 = -0.15 / 3.60 = -0.0417
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Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
7 and one fourth pounds
8 and one half pounds
10 and one half pounds
14 and one fourth pounds
The number of pounds of clay used to make 21 small vases is 10 and one half pounds.
How to find the number of pounds of clay used to make vases?Sandy uses three and one half pounds of clay to make 7 small vases. Using proportion, the number of pounds of clay that she can use to make 21 small vases can be calculated as follows;
Therefore,
7 small vases = 3 1 / 2 pounds of clay(7 / 2)
21 small vases = ?
cross multiply
pounds of clay used to make 21 small vases = 7 / 2 × 21 ÷ 7
pounds of clay used to make 21 small vases = 147 / 2 ÷ 7
pounds of clay used to make 21 small vases = 147 / 2 × 1 / 7
pounds of clay used to make 21 small vases = 21 / 2
Therefore,
pounds of clay used to make 21 small vases = 10 1 / 2
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If point C lies on the line y = −1, what is the x-value of point C?
Answer:
0
Step-by-step explanation:
If it lies on the y line then it is horizontal. This means the slope is 0 and so is the x value.
in parts (a) and (b), identify whether the events are mutually exclusive, independent, or neither (events cannot be both disjoint and independent). a) you and a randomly selected student from your class both earn a's in this course. mutually exclusive neither independent b) you and your class partner both earn a's in this course. mutually exclusive neither independent c) if two events can occur at the same time, they must be independent. false true
By looking at the definition of mutually exclusive and independent event, the statement for both events are true.
What is meant by mutually exclusive?A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.
What is independent event?Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.
(a) True. The given event is both mutually exclusive as well as independent
(b)True. The given event is both mutually exclusive as well as independent
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Simplify the expression 10^log5
Answer:
5
Step-by-step explanation:
The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."
Using this definition, we can simplify the expression "10^log5" as follows:
10^log5 = 10^y
Where "y" is the exponent to which the base "10" must be raised to produce the result "5."
To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:
log(10^y) = y
Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:
log(5) = y
Solving for "y," we find that "y = log(5)."
Therefore, the expression "10^log5" can be simplified to:
10^log(5) = 10^(log(5)) = 5
So the simplified result is 5.
A chemist is investigating a new reaction to synthesize barite crystals. She finds that eight grams are synthesized every five minutes. If there are 111 grams of barite after an hour, how many grams of barite did the chemist start with?
possiable answers
0
8
15
71
Answer:
The answer is 71
What is chemist?
A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.
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Answer: the answer is 15
Step-by-step explanation:
9) Rachel has $46 she can spend on food and toys for her cats. PetSmart sells the
food her cats like for $8 per bag. They also have a sale on cat toys that will cost her
$4 per toy. Write a linear inequality that describes how many bags of food and how
many toys Rachel can buy for her cats.
Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.
We can write the linear inequality as follows:
8x + 4y ≤ 46
What is inequality?An inequality is a mathematical statement that shows the relative size of two values.
What is linear inequality?A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.
This inequality can be rewritten as follows:
x + 0.5y ≤ 5.75
This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.
Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.
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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.
We can write the linear inequality as follows:
8x + 4y ≤ 46
What is inequality?
An inequality is a mathematical statement that shows the relative size of two values.
What is linear inequality?
A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.
This inequality can be rewritten as follows:
x + 0.5y ≤ 5.75
This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.
Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.
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an expert archer hits a bullseye 89% of the time. if she shoots 15 shots in a row, what is the probability she hits at least 13 bullseye\
Using the formula for binomial probability distribution and the provided values, The answer is 0.775 .
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What is binomial distribution and it's formula?The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (p) and fail—is known as the binomial distribution with parameters n and p in probability theory and statistics (1-p).
It's formula is:
[tex]P(x) = C(n,x)*p^{x}*q^{n-x}[/tex]
p = 0.89
q= 1-p = 0.11
n=15
P(x>=13) = P(13)+P(14)+P(15)
=0.279+0.322+0.174
=0.775
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How would i solve for E
Answer:
5/13
Step-by-step explanation:
[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]
The cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet. It costs $3,000 to paint a room with a surface area of 1,500 square feet. Determine an equation that gives the relationship between c and a.
The equation that gives the relationship between cost (c) and area (a) is c = 2a
How to determine an equation that gives the relationship between cost and area?A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet
We can write:
c α a
c = ka
where k is the constant of proportionality
since c = $3,000 and a = 1500
c = ka
3000 = 1500k
k = 3000/1500
k = 2
Thus, the equation of the relationship is c = 2a
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Points B, D, and F are midpoints of the sides of
AACE. EC 32 and DF = 20. Find AC.
The diagram is not to scale.
A
F
B
The value of the side AC is 40 if the points B, D, and F are midpoints of
the sides of ΔACE.
What is the mid-point of a triangle?The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."
Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.
Given,
The points B, D, F are midpoints of the sides of a triangle ACE.
And also given that,
EC =32 and DF=20, AC=?
So, FD=1/2(AC)
AC=2(FD)
AC=2(20)
AC=40
Therefore, the value of the side AC is 40 if the points B, D, and F are
midpoints of the sides of ΔACE.
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The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 6:19. There are 57 gallons of gasoline. How many ounces of oil are there?
2 ounces
18 ounces
24 ounces
180.5 ounces
According to the specified ratio , we obtain The gasoline contains 18 ounces of oil.
What's does ratio mean?The number, volume, or size difference between two or more items is known as their proportion.We got the word "ratio" directly from the Latin word, which is also called "suitable ratio." The mathematics and English ratios were derived from the Latin ratio, which had multiple meanings, ranging from "reason" to "calculation" to "proportion."Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.The fuel for a chain saw is a mix of oil and gasoline.
The ratio of ounces of oil to gallons of gasoline is 6:19.
So oil : gas = 6:19
There are 57 gallons of gasoline
⇒ oil : gas = 6:19
Let there are x gallons of ounces of oil
So x : 57 = 6:19
Convert ratio to fraction
⇒ x/57 = 6/19
Multiply both sides by 57
⇒ x = (6/19)57
⇒ x = 18
Hence, there are 18 ounces of oil in the fuel.
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in how many ways can four people line up in a straight line if the youngest person cannot be first in line?
Total number of ways four people line up in the straight line with the given condition is equal to 18 ways.
As given in the question,
Total number of people = 4
Given condition :
First position can not occupied by youngest person:
First position occupied in 3 ways
Second position occupied in 3 ways
Third position occupied in 2 ways
fourth position occupied in 1 ways
Total number of ways = 3 × 3 × 2 × 1
= 18 ways
Therefore, the number of ways four people stand in straight line is equal to 18 ways.
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what is the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order?
The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.
This is calculated by probability of independent events.
We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.
So, P(A and B occurring together )= P(A)P(B) if A and B are independent.
And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)
This is because, being the probability of independent events , they are multiplied.
so, the total probability is 6.5.4.3.2.1/6^6 = 1.54
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Which of the following equations has a different value of x than the others?(1 point
x + 9/8 = 7/4
x − 7/8 = −3/2
x + 0.875 = 1.5
x − 0.025 = 0.6
Answer: The equation [tex]x-7/8=-3/2[/tex] has a different value of x than the others. The value of x here is -0.625, while in all the other equations, the value of x is 0.625.
Step-by-step explanation: Simplifying the equation [tex]x+9/8=7/4[/tex], we get:
[tex]x=7/4-9/8[/tex]
[tex]x=0.625[/tex]
Simplifying the equation [tex]x-7/8=-3/2[/tex], we get:
[tex]x=-3/2+7/8[/tex]
[tex]x=-0.625[/tex]
Simplifying the equation [tex]x+0.875=1.5[/tex], we get:
[tex]x=1.5-0.875[/tex]
[tex]x=0.625[/tex]
Simplifying the equation [tex]x-0.025=0.6[/tex], we get:
[tex]x=0.6+0.025[/tex]
[tex]x=0.625[/tex]
Therefore, [tex]x+9/8=7/4[/tex] has a different value of x than the others.
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Find the approximate distance between the points A (2,-1) and B(-4,5)
Answer:
d ≈ 8.5 units
Step-by-step explanation:
calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (2, - 1 ) and (x₂, y₂ ) = B (- 4, 5 )
d = [tex]\sqrt{(-4-2)^2+(5-(-1))^2}[/tex]
= [tex]\sqrt{(-6)^2+(5+1)^2}[/tex]
= [tex]\sqrt{36+6^2}[/tex]
= [tex]\sqrt{36+36}[/tex]
= [tex]\sqrt{72}[/tex]
≈ 8.5 units ( to 1 decimal place )
Help me answer this question for a 10 on my homework
Answer:
1. 4
2. rise = 2; run = 1; slope = 2
3. y = 2x + 4
Step-by-step explanation:
1. Look at the graph. On the y-axis, the line passes through 4. The line crosses the y-axis at 4, so 4 is the y-intercept, and b = 4 in the equation y = mx + b.
2. Choose any two points on the line. I choose the y-intercept, (0, 4) and point (-1, 2).
slope = rise/run
We need to go from point (-1, 2) to point (0, 4) by only moving vertically and horizontally. Start at (-1, 2). Go up 2 units. That is a ris of 2. Now go right 1 unit to arrive at point (0, 4). that is a run of 1.
slope = rise/run = 2
3. We have b = 4, and m = 2.
y = mx + b
y = 2x + 4
Somebody please help I’m studying for finals and I’m losing my mind
The perimeter of the image is 70 meters and its area is 210 square meters.
What is meant by perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.
There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.
Area=(1/2)×base× height
=(1/2)×21×20
=210 square meters
Perimeter=a+ b+ c
=21+20+29
=70meters
Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.
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An element with a mass of 240 grams decays by 17.4% per minute. To the nearest
tenth of a minute, how long will it be until there are 20 grams of the element remaining?
It will be 13min until there are 20 grams of the element remaining.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, and is the initial amount, b is the decay factor, and y is the final amount.
Here, we have
This is a compound decay problem, which goes by the formula:
F = P(1-r)ˣ
Where
F is the future amount (we want it to be 20)
P is the present amount (240 now)
r is the rate of decay per minute (17.4% = 17.4/100 = 0.174)
x is the time it takes (what we want to find)
Substitute all values in the formula and we get
20 = 240(1-0.174)ˣ
20 = 240(0.826)ˣ
0.0833 = 0.826ˣ
㏑0.0833 = ㏑0.826ˣ
㏑0.0833 = x ㏑0.826
x = ㏑0.0833/㏑0.826
x = 13
Hence, it will be 13min until there are 20 grams of the element remaining.
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Noah is baking cookies. the recipe he is using makes 48 cookies and uses 1/4 cup of sugar. How much sugar will Noah need to make 72 cookies?
Answer: Approx. 0.375 cups of sugar
Step-by-step explanation:
1/4=0.25
0.25 cups of sugar per 48 cookies = 0.25/48= (about) 0.00520833333 per cookie
0.00520833333 cups of sugar x 72 cookes= 0.375 cups of sugar for 72 cookies
Answer question #9
The response is incorrect and I need help on getting the correct answer
Answer:
congruence is compatibility or agreement while equal is the same or equivalent to one another.
Yo can yall answer this for me??
8 ÷ 640 x 100,000 = 12,500 defective computer chips
Scaling calculationWe can anticipate that a larger sample of 100,000 chips will exhibit the same rate of defects if the sample of 640 chips produced 8 defective ones.As a result, 8/640 Equals x/100,000, where x is the quantity of flawed chips. x = 8000 can be used to sum up this. As a result, we may anticipate that out of every 100,000 computer chips produced, there will be about 8,000 that are flawed.However, this presupposes that the defect rate stays constant and that the 640 chip sample is typical of the 100,000 chip population as a whole.Additionally, when the overall number of chips manufactured rises, the defect rate could either rise or fall.To ensure accuracy and reliability of this prediction, it is important to collect more data from larger sample sizes.To learn more about scaling calculation refer to:
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please help with this
The function, f(x) = -50 and g(x) = -17
What is the function?A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.
Instance: f(x) = x/2 ("f of x equals x divided by 2")
we are given that f(x) = -3[tex]x^{2}[/tex] -2 and g(x) = 4x - 1
we need to find f(4) and g(-4)
f(4) = -3([tex]4^{2}[/tex]) - 2
f(4) = -3*16 - 2
f(4) = -48-2
f(4) = -50
g(x) = 4x - 1
g(-4) = 4 *-4 -1
g(-4) = -16-1
g(-4) = -17
The function f(x) = -50 and g(x) = -17
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what is the conditional probability that a randomly-generated 4-bit string contains two consecutive 1s, given that the first bit of the string is a 1?
The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .
total length of four-bit strings = 16
Let S represent the collection of all four-bit bit strings.
Let A represent the occurrence of a randomly generated string beginning with 1.
Let B represent the scenario where a string created at random contains two consecutive 0s.
S has 8 strings that begin with the letter "1."
P( A ) = 8 / 16 = 1 / 2
Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100
P(A ∩ B) = 3 / 16
Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,
3/16 / 1/2
= 3 / 8
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A piece of cheese is shaped like a triangle. It has a height of 2.5 inches and a base that is 4.75 inches long. If 1 inch = 2.54 centimeters, find the area of the cheese in square centimeters. Round the answer to the nearest square centimeter. Please answer this thank you!
Answer:
[tex]A \approx 38 \, \textrm{cm}^2[/tex]
Step-by-step explanation:
The area of a triangle is defined as:
[tex]A_\triangle = \dfrac{1}{2}bh[/tex]
where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.
So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.
[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]
And simplify.
[tex]A \approx 38 \, \textrm{cm}^2[/tex]
Evaluate. Remember Order of
Operations! (PEMDAS)
8 x 3²- (14+ 6) = [?]
Answer:
52
Step-by-step explanation:
Order of Operations says to do Parenthesis first, then exponents.
8 x 3²- (14+ 6)
= 8 x 3²- (20)
= 8 × 9 - 20
Then multiply before subtracting in this question.
= 72 - 20
= 52
Insert terms to make a identity replace *
(*-0.2n)^2=*-1.2mn+0.04n^2
The unidentified term is 3m.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²
We know that, (a-b)² = a²-2ab+b²
Comparing the given equation with the above identity, we get,
a = x, b = 0.2n and 2ab = 1.2mn
Therefore, 2x×0.2n = 1.2mn
x = 3m
Hence, the unidentified term is 3m
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One group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house. At which house will they first meet?
The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.
How to calculate the multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.
Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.
From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.
It should be noted that this will be illustrated through tye lowest common multiple.
Multiples of 6 = 6, 12, 18, 24
Multiples of 8 = 8, 16, 24
Therefore, they'll meet at the 24th house.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y= 3x + 5
Step-by-step explanation:
Some examples
(1,8)
8= 3 (1) + 5
8 = 3 + 5
8= 8
(2,11)
11= 3 (2) + 5
11= 6 + 5
11= 11
Laura is going to tile her dining room floor. The room is in the shape of a rectangle, and the dimensions are 18 feet by 12 feet. The tile she wants to use costs $9 per square foot. How much will the tile cost for the dining room floor?
Answer:
$1944
Step-by-step explanation:
18x12=216
216x$9=$1944
Answer:
£1944
Step-by-step explanation:
The area of the floor is 216 feet²
18 x 12 = 216
216 x 9 = 1944
if w denotes weight, n denotes number of items, m denotes maximum capacity constraint, and x =0 or 1, what would be the valid bounding condition/conditions for the sum of the subset problem?
So the valid bounding conditions for the sum of the subset problem are:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
The valid bounding condition for the sum of the subset problem is:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).
The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.
So the valid bounding conditions for the sum of the subset problem are:
0 <= x[i] <= 1 (for all i such that 1 <= i <= n)
∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)
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