Fourteen construction workers are to be assigned to three different tasks. Seven workers are needed for mixing cement, five for laying bricks, & two for carrying bricks. In how many
different ways can the workers be assigned to these tasks?
Answers
To find the total number of ways the workers can be assigned to these tasks, we need to use combinations.
For the first task of mixing cement, we need to choose 7 workers out of the 14 available workers. This can be done in (14 choose 7) ways.(14 choose 7) x (7 choose 5) x 1 = 3432 ways
For the second task of laying bricks, we need to choose 5 workers out of the remaining 7 workers .
To determine the number of different ways the 14 workers can be assigned to the three tasks, you can use the combination formula, which is , where n is the total number of items, r is the number of items to choose, and ! represents the factorial. There are 14 workers, and you need to assign them to specific tasks: 7 for mixing cement, 5 for laying bricks, and 2 for carrying bricks.
First, let's find the number of ways to choose 7 workers for mixing cement from the group of 14:
C(14,7) = 14! / (7!(14-7)!) = 3,432 ways.
Now, we have 7 workers remaining. We need to choose 5 workers for laying bricks: C(7,5) = 7! / (5!(7-5)!) = 21 ways.
Lastly, the remaining 2 workers will be assigned to carrying bricks, so there's only 1 way to do this.
To find the total number of ways to assign the workers to these tasks, multiply the possibilities: 3,432 * 21 * 1 = 72,072 different ways.
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To find the total number of ways the workers can be assigned to these tasks, we need to use combinations. For the first task of mixing cement, we need to choose 7 workers out of the 14 available workers. This can be done in (14 choose 7) ways.(14 choose 7) x (7 choose 5) x 1 = 3432 ways
For the second task of laying bricks, we need to choose 5 workers out of the remaining 7 workers .
To determine the number of different ways the 14 workers can be assigned to the three tasks, you can use the combination formula, which is , where n is the total number of items, r is the number of items to choose, and ! represents the factorial. There are 14 workers, and you need to assign them to specific tasks: 7 for mixing cement, 5 for laying bricks, and 2 for carrying bricks.
First, let's find the number of ways to choose 7 workers for mixing cement from the group of 14:
C(14,7) = 14! / (7!(14-7)!) = 3,432 ways.
Now, we have 7 workers remaining. We need to choose 5 workers for laying bricks: C(7,5) = 7! / (5!(7-5)!) = 21 ways.
Lastly, the remaining 2 workers will be assigned to carrying bricks, so there's only 1 way to do this.
To find the total number of ways to assign the workers to these tasks, multiply the possibilities: 3,432 * 21 * 1 = 72,072 different ways.
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Related Questions
Kylie has $2.10 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Kylie has.
Answers
Answer:
Kylie has 6 Nickels and 18 dimes
Step-by-step explanation:
Variable definitions:
x=the number of nickels
y=the number of dimes
One nickel is worth $0.05, so x nickels are worth 0.05x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.05x+0.10y equals $2.10:
0.05x + 0.10y = 2.10
Since she has a total of 24 coins, we know x+y must equal 24.
x + y = 24
Write System of Equations:
0.05x + 0.10y = 2.10
x + y = 24
Solve for y in each equation:
0.05x + 0.10y= 2.10 x + y = 24
0.10y = 0.05x + 2.10 y = -x + 24
0.10y = -0.05x + 2.10
0.10 0.10
y = -1/2x + 21
The x variable represents the number of nickels and the y variable represents the number of dimes. Since the lines intersect at the point (6,18) we can say:
Kylie has 6 Nickels and 18 dimes
We want to solve a system of equations to see how many nickels and dimes Kyle has. We will see that she has 6 nickels and 18 dimes.
Finding the system of equations:
First, let's define the variables, we will use:
x = number of nickelsy = number of dimes.We know that there are 24 coins, then:
x + y = 24
We know that the total whort of the coins is $2.10, then:
x*$0.05 + y*$0.10 = $2.10
Then the system of equations is:
x + y = 24
x*$0.05 + y*$0.10 = $2.10
Solving the system of equations.Here we need to graph both equations and find where they do intercept, the graph of the system can be seen below:
We can see that the intersection is at the point (6, 18)
So this means that she has:
6 nickels and 18 dimes.
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Which of the following is equivalent to (5y + 3x) + 9x?
Answers
Answer:
12x+5y
Step-by-step explanation:
Combine 3x and 9x to get 12x.
hope it helped :)
what must be the beta of a portfolio with e(rp) = 18%, if rf = 6% and e(rm 14)
Answers
the beta of a portfolio given the expected return of the portfolio will be 1.5.
The beta of a portfolio measures its sensitivity to market movements. It is calculated as the covariance between the returns of the portfolio and the market divided by the variance of the market returns. Mathematically, the formula for beta (β) is: β = Cov(rp, rm) / Var(rm),
where Cov(rp, rm) represents the covariance between the portfolio returns (rp) and the market returns (rm), and Var(rm) represents the variance of the market returns.
Given that e(rp) = 18% (expected return of the portfolio), rf = 6% (risk-free rate), and e(rm) = 14% (expected return of the market), we can use these values to calculate the beta.
First, we need to determine the excess return of the portfolio and the market:
Excess Return of Portfolio (ERP) = e(rp) - rf = 18% - 6% = 12%
Excess Return of Market (ERM) = e(rm) - rf = 14% - 6% = 8%
Next, we can calculate the beta using the formula:
β = Cov(rp, rm) / Var(rm) = ERP / ERM
Plugging in the values, we have: β = 12% / 8% = 1.5
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what is \( {i}^{84} \)I need extra help with imaginary numbers
Answers
The given expression is
\(i^{84}\)Remember that i = -1, so.
\((-1)^{84}\)We know by definition that all powers with even exponents give a positive number. So,
\((-1)^{84}=1\)Therefore,\(i^{84}=1\)10. The cost price of an article is $40 and it was sold to make a profit of $20. What is the
selling price of the article?
a) S40.20
b) $48.00
c) $50.00
d) $60.00
Answers
Answer:
D
Step-by-step explanation:
40 + 20 = 60 lol
What are 3 examples of value?
Answers
Thousands, hundreds and tens are three examples of values and there are many more.
What is value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
What is the value of 4?The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.
Thousands, hundreds and tens are three examples of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.
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Find the values of a and b that make f continuous everywhere.
f(x) =
(x2 − 4)/(x − 2) if x < 2
ax2 − bx + 3 if 2 ≤ x < 3
2x − a + b if x ≥ 3
Answers
The values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.
What is the limit?The limit is a concept in mathematics that describes the behavior of a function near a particular value, called the limit point. The limit of a function gives the value that the function approaches as the input (variable) approaches the limit point.
For f(x) to be continuous everywhere, the function must have the same value and the same limit as x approaches 2 from the left and the right. In other words, f(2-) = f(2+) and the limit of f(x) as x approaches 2 from the left and the right must be equal.
Let's start by finding f(2-), which is the value of f(x) as x approaches 2 from the left. In this case, f(x) = (x2 - 4)/(x - 2) for x < 2, so as x approaches 2 from the left, f(x) approaches (2^2 - 4)/(2 - 2) = 0.
Next, let's find f(2+), which is the value of f(x) as x approaches 2 from the right. In this case, f(x) = ax^2 - bx + 3 for 2 <= x < 3, so as x approaches 2 from the right, f(x) approaches a(2^2) - b(2) + 3 = 4a - 2b + 3.
Since f(x) must be continuous at x = 2, we need to have f(2-) = f(2+), so we can set f(2-) = f(2+) and solve for a and b:
0 = 4a - 2b + 3
2b = 4a - 3
b = 2a - 3/2
Now that we have an expression for b in terms of a, we can substitute b = 2a - 3/2 into the expression for f(x) for x >= 3 to find the value of a that makes f(x) continuous everywhere:
f(x) = 2x - a + b for x >= 3
f(x) = 2x - a + (2a - 3/2) for x >= 3
f(x) = 2x + 3/2 - a for x >= 3
Since f(x) must be continuous at x = 2, we need to have f(2+) = f(2+), so we can set f(2+) = f(2+) and solve for a:
4a - 2b + 3 = 2x + 3/2 - a for x >= 3
4a - 2(2a - 3/2) + 3 = 2x + 3/2 - a
4a - 4a + 3 + 3/2 = 2x + 3/2 - a
3/2 = 2x + 3/2 - a
a = 2x
So, the values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.
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State the explicit formula for the sequence below and find the 8th term.
-4, 16, -64, 256,...
O an = -4(4)n-1; n = 8 is-262,144
O an = -4(-4)-1; n = 8 is 65,536
O an = 4(4)n-1; n = 8 is 65,536
O a = 4(-4)n-1; n = 8 is 261,144
6.25 pts
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Answers
The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536
The given sequence is -4, 16, -64, 256,...
If we observe the sequence it is a geometric sequence
aₙ=a.rⁿ⁻¹
a is the first term and r is the common ratio
From the sequence the first term is -4 and common ratio is -4
aₙ=(-4).(-4)ⁿ⁻¹
Plug in the value n as 8
a₈=(-4).(-4)⁷
The value of minus four power seven is minus sixteen thousand three hundred eighty four
a₈=(-4)(-16384)
When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six
a₈= 65536
Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536
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Raymond has a motion detector light which gets activated an average of 15 times every 2 hours during the night. In order to find the probability that the motion detector light will be activated exactly 8 times in a 55 minute period during the night using the Poisson distribution, what does the random variable X represent
Answers
Answer:
The random variable X is the number of activations that occur in the 55 minute time period.
Step-by-step explanation:
The random variable X represents the number of occurrences of an event in the time interval of interest. The time interval of interest is the fixed time period for which the probability of an event is being sought. In this case, the time interval of interest is 55 minutes. The random variable X is the number of activations that occur in the 55 minute time period.
In the given Poisson Distribution, the random variable X represents the number of activation in 55 minutes. Hence, the 4th option is the right choice.
What is Poisson Distribution?A Poisson distribution is a probability distribution used in statistics to illustrate how many times an event is expected to occur over a certain time period. It is, in other words, a count distribution. Poisson distributions are frequently used to analyze independent events that occur at a consistent rate during a specified time frame. It was named after Siméon Denis Poisson, a French mathematician.
The Poisson distribution is a discrete function, which means that the variable may only take values from a (possibly endless) list. To put it another way, the variable cannot accept all values in any continuous range. The variable in the Poisson distribution may only take whole integer values (0, 1, 2, 3, etc.), no fractions or decimals.
How to solve the question?In the question, we are informed that Raymond has a motion detector light that gets activated an average of 15 times every 2 hours during the night.
We are asked what the random variable X represents, to find the probability that the motion detector light will be activated exactly 8 times in 55 minutes during the night using the Poisson distribution.
The formula for the Poisson Distribution is given as,
\(P(X = x) = e^{-\lambda}\frac{\lambda^x}{x!}\)
where e is the Euler's number, x is the number of occurrence, and λ is the expected value.
The term X is the variable over which the distribution is defined.
Thus, in the given Poisson Distribution, the random variable X represents the number of activation in 55 minutes. Hence, the 4th option is the right choice.
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Refer to the attachment for the complete question.
PLEASE HELP FASTT!!!!!!!
In a relation, the input values can also be referred to as the_____?
Answers
Answer:
Domain
Step-by-step explanation:
Answer: the x values
Step-by-step explanation:
the pithag tells us how the ____ lengths of ______ triangles are related
Answers
Pythagorean theorem tells us how the side lengths of right triangles are related.
The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.
This relationship can be written as the equation:
\(a^2 + b^2 = c^2\)
where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
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Hal, Zelda, Maya, and Jason each recorded the height and age of five classmates. They used the data to create the tables below
Answers
Answer:
Please which data and tables are you talking about?
Compute the answers for this fish tank containing water.
Compute the mass of water filling this tank.
0.25 g
20 g
250 g
Answers
Answer:
Option (3)
Step-by-step explanation:
Since density on an element = \(\frac{\text{Mass}}{\text{Volume}}\)
Volume of the water in the aquarium = volume of the aquarium
= Length × width × height
= 10 × 5 × 5
= 250 cm³
We know density of the water = 1 gram per cm³
By putting these values in the formula,
1 = \(\frac{\text{Mass}}{250}\)
Mass = 250 g
Therefore, Option (3) will be the answer.
read the picture plsssssssssss
Answers
2. 2x - 5(3x^2)
3. 8x + 2x/3 +6
4. x + 3 - y - 6
The company made $700,000 the first quarter and $343,000 the second
quarter. Which shows the change from the first quarter to the second
quarter?
a) –357,000
B) 357,000-
C) 357,000+
D) +357,000
Hi! i need help, can someone help me please
Answers
Answer:
b
Step-by-step explanation:
The change from the first quarter to the second quarter is +357,000. Therefore, the correct answer is option D.
Given that, the money made by company in first quarter = $700,000 and in the second quarter = $343,000.
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
The difference in money made by company from first quarter to second is
700,000-343,000
= +357,000
Therefore, the correct answer is option D.
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a model rocket is launched with an initial upward velocity of 175 ft/s the rocket's height is represented by h (in feet) after t seconds is given by the followingh = 175t - 16t^2find all values of t for which the rockets height id 85 feetand i need to round the answer to nearest hundredth
Answers
Given relation between height and time is:
\(h=175t-16t^2\)Now put the value of h=85 ft in given relation:
\(85=175t-16t^2\)Solving it for t:
\(\begin{gathered} 16t^2-175t-85=0 \\ t=\frac{175\pm\sqrt[]{(-175)^2-4\times16\times85}}{2\times16} \\ t=\frac{175\pm\sqrt[]{30625-5440}}{32} \\ t=\frac{175\pm\sqrt[]{25185}}{32} \\ t=\frac{175\pm158.6}{32} \\ t=0.51\text{ or }10.43\text{ second} \end{gathered}\)Please help, I'm stuck
Suppose ten distinct, positive integers have a median of $10$. ("Distinct integers" means that no two integers are the same.)
What is the smallest the average of those ten integers could be?
Explain your answer in complete sentences.
Answers
Answer:
8 (or 8.4)
Step-by-step explanation:
First, the problem states the words: Distinct and positive.
That means that the smallest number we can use is 0.
We can make 10 blanks for 10 numbers for us to fill in.
_ _ _ _ _ _ _ _ _ _
Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.
In this case, our two numbers are the 5th and 6th blank.
Any two numbers can be used, as long as they are the same actual value from 10.
Let us first put in the numbers we can, which are the numbers before the two middle blanks.
0,1,2,3, _ _ _ _ _ _
To find the median between two numbers, we can do:
(a+b) divided by 2 = median
We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.
Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.
4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.
Now let's place the other numbers in for these two equations.
0,1,2,3,4,16,17,18,19,20
0,1,2,3,9,11,12,13,14,15
If we add the numbers of each together, we get:
0,1,2,3,4,16,17,18,19,20=100
0,1,2,3,9,11,12,13,14,15= 80
If we now divide each sum by 10 (to find the average) we get:
10
8
Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.
Since the smaller answer we got was 8, the answer must be 8.
(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process
If the base of a rectangle is 39cm and the area is 245 cm², what is the height
of the rectangle?
Answers
The the height of the rectangle 6.3cm
How to find the height?A rectangle is a polygon of four sides whose opposite sides are equall and parallel
The given parameters that will help us to solve for the height are
Area = 245 cm²Lenght = 39cmHeight = hcmthe area of a rectangle is the space the rectangle occupies
The area is denoted by :
Area= Lenght * Height
245 = 39 * h
h= 245/39
Height = 6.3cm
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Which, if any, of the following generalized formulas does not exist for interhalogen compounds? (X and Y represent different halogens.)
XY
XY2
XY3
XY5
All the above can represent stable interhalogen compounds.
Answers
All the above can represent stable interhalogen compounds. Interhalogen compounds are formed when different halogens combine with each other.
The general formula for interhalogen compounds is given by XYn, where X and Y represent different halogens, and n represents the number of Y atoms bonded to the X atom. The interhalogen compounds can have different stoichiometries, resulting in different values of n. Therefore, all the given formulas, XY, XY2, XY3, and XY5, can represent stable interhalogen compounds, depending on the specific combination of halogens and their bonding arrangements.
Hence, none of the given formulas does not exist for interhalogen compounds, as all of them can be valid representations of stable interhalogen compounds.
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q - r - 3s = p solve for q
Answers
Answer:
q = p + r + 3s
Step-by-step explanation:
q - r - 3s = p solve for q
q - r - 3s = p
add r to both sides:
q - r - 3s + r = p + r
q - 3s = p + r
add 3s to both sides:
q - 3s + 3s = p + r + 3s
q = p + r + 3s
Solve the initial value problem: 5x + yy' = 0, y (2) = 5 What is the largest value of x for which this solution is defined? If needed enter your answer to 2 decimal places. _____
Answers
The largest value of x for which this solution is defined is 2.45 (approx.).Hence, the required answer is 2.45.
To solve the initial value problem 5x + y y' = 0, y (2) = 5, we need to first solve the differential equation and then plug in the value of y(2) = 5 to find the value of the constant C. Finally, we need to find the largest value of x for which this solution is defined. Steps to solve the initial value problem: Given, 5x + y y' = 0y (2) = 5 Separating the variables and integrating,5x + y y' = 0 => y d y = -5xdx Integrating both sides, we get y²/2 = -5x²/2 + C.... .. (1)Now, we need to find the value of the constant C
To do so, plug in the value of y(2) = 5 in equation (1),5²/2 = -5(2)²/2 + C => C = 15Thus, the solution to the initial value problem is given by, y²/2 = -5x²/2 + 15 => y² = -5x² + 30The solution will be defined only if y² > 0.
Thus, -5x² + 30 > 0 => x < √6 or x > -√6.The largest value of x for which this solution is defined is therefore √6 ≈ 2.45 (rounded to 2 decimal places).Therefore, the largest value of x for which this solution is defined is 2.45 (approx.).Hence, the required answer is 2.45.
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(3) Predator-prey System Model
x
˙
=rx(1−
k
x
)−αxy
y
˙
=−βy+γxy
Answers
The predator-prey system model is described by the following set of differential equations:
\(\dot{x} = rx(1 - \frac{k}{x}) - \alpha xy\)
\(\dot{y} = -\beta y + \gamma xy\)
In these equations, \(x\) represents the population of the prey species, \(y\) represents the population of the predator species, and \(\dot{x}\) and \(\dot{y}\) represent their respective rates of change over time.
The first equation represents the growth of the prey population, which is influenced by the growth rate \(r\), the carrying capacity \(k\), and the interaction with the predator population \(y\). The term \(rx(1 - \frac{k}{x})\) describes the prey's intrinsic growth rate that is limited by the carrying capacity. The term \(-\alpha xy\) represents the predation effect, where the predator species consumes the prey species, resulting in a negative impact on the prey population.
The second equation represents the growth of the predator population. The term \(-\beta y\) represents the natural mortality rate of the predator species, where \(y\) decreases over time. The term \(\gamma xy\) represents the predation effect, where the predator population is positively influenced by the availability of prey \(x\).
These equations capture the dynamic interactions between predator and prey populations. The model shows that the growth and decline of each species are influenced by both intrinsic factors (such as growth rates and carrying capacity) and interactions between the two species. By studying and analyzing this model, we can gain insights into the dynamics of predator-prey relationships and the factors that affect population dynamics in ecological systems.
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The director of the CO-Tech startup needs to decide what salaries to offer
its employees for the coming year. In order to keep the employees satisfied,
she needs to satisfy the following constraints:
Tom wants at least $20 000 or he will quit;
Peter, Nina, and Samir each want to be paid at least $5000 more than Tom;
Gary wants his salary to be at least as high as the combined salary of Tom and Peter;
Linda wants her salary to be $200 more than Gary;
the combined salary of Nina and Samir should be at least twice the
combined salary of Tom and Peter;
Bob’s salary is at least as high as that of Peter and at least as high as that of Samir;
the combined salary of Bob and Peter should be at least $60 000;
Linda should not make more money than the combined salary of Bob and Tom.
(b) Write an LP that will determine salaries for the employees of CO-tech that satisfy each of these constraints while minimizing the salary of the highest paid employee.
Answers
The linear program is as follows:
T - M ≤ -20,000
P - T ≤ -5,000
N - T ≤ -5,000
S - T ≤ -5,000
G - T - P ≤ 0
L - G ≤ -200
N + S - 2T - 2P ≤ 0
B - P ≤ 0
B - S ≤ 0
B + P ≤ 60,000
L - B - T ≤ 0
Let's define decision variables for each employee's salary as follows:
Let T, P, N, S, G, L, and B represent the salaries of Tom, Peter, Nina, Samir, Gary, Linda, and Bob, respectively.
Our objective is to minimize the salary of the highest paid employee. We can achieve this by introducing another variable, M, that represents the maximum salary among all employees. Therefore, our objective is to minimize M.
Minimize: M
Subject to:
T ≥ 20,000
P ≥ T + 5,000
N ≥ T + 5,000
S ≥ T + 5,000
G ≥ T + P
L ≥ G + 200
N + S ≥ 2(T + P)
B ≥ max(P, S)
B + P ≥ 60,000
L ≤ B + T
Now, we can write the linear program in standard form by moving all variables to the left-hand side of the constraints and adding slack variables:
Minimize: M
Subject to:
T - M ≤ -20,000
P - T ≤ -5,000
N - T ≤ -5,000
S - T ≤ -5,000
G - T - P ≤ 0
L - G ≤ -200
N + S - 2T - 2P ≤ 0
B - P ≤ 0
B - S ≤ 0
B + P ≤ 60,000
L - B - T ≤ 0
All variables are non-negative.
This linear program can be solved using a linear programming solver to find the minimum value of M that satisfies all the constraints. Once we have the optimal solution, we can retrieve the salaries of each employee from the linear program solution.
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A truck that can carry no more that 7700 lbs is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250lbs and each piano weighs 475lbs. Write a graph an inequality to show how many pianos the truck could carry. Will 16 refrigerators and nine pianos overload the truck?
Answers
The quantity of pianos that the truck will be able to carry would be = 11 pianos
What is weight?Weight is defined as the total amount of matter that is contained in an object which is measured in Kilograms, grams of pounds(Ibs).
The weight of goods that the truck can carry generally= 7700 Ibs.
The weight of each refrigerator = 250 lbs
The weight of each piano = 475 Ibs.
The total weight of both items = 725 Ibs
The weight of piano that makes up the weight of truck;
= 475/725 × 7700/1
= 3657500/725
= 5,045
To find the number of pianos is as follows:
= 5,045/475
= 11 ( approximated to the nearest whole number)
Therefore, nine pianos won't overload the truck..
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A cartoon contains 5 1/2 cups of juice. One serving is 3/4 of a cup. How many servings of juice are in the cartoon?
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can Someone Answer This Please! The Question Is on the Attached Photograph Below: Thanks!
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Answer:
a^5÷a^3=a^5×a^-3=a^5+-3=a^2
Answer:
\(a) \: \: {a}^{2} \)
\(b) \: \: c\)
Step-by-step explanation:
\(a) \: \: {a}^{5} \div {a}^{3} \\ = (a \times a \times a \times a \times a)(a \times a \times a) \\ = a \times a \\ = {a}^{2} \)
\(b) \: \: \frac{ {c}^{4} }{ {c}^{3} } \\ \frac{(c \times c \times c \times c)}{(c \times c \times c)} \\ = c\)
Hope it is helpful.....Hình tròn lớn và hình tròn nhỏ có cùng tâm O. Tính diện tích hình tròn lớn, biết rằng diện tích hình tròn nhỏ là 12,56m2.
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Answer:
Hình tròn lớn và hình tròn nhỏ có cùng tâm O. Tính diện tích hình tròn lớn, biết rằng diện tích hình tròn nhỏ là 12,56m2.
Step-by-step explanation:
Hình tròn lớn và hình tròn nhỏ có cùng tâm O. Tính diện tích hình tròn lớn, biết rằng diện tích hình tròn nhỏ là 12,56m2.
Suppose, as in American Roulette, the wheel has an additional zero, which is denoted ' 00 ′
', the so-called 'double zero'. In other words you can bet on any of the following 'numbers': 00,0,1,2,3,4,…,36 The payoffs are the same for both American and European Roulette. 9. What is the house advantage associated with any given bet in American Roulette? (Express your answer as a \% win for the house, correct to three decimal places. Do not enter the \% sign) 10. Which game has the lowest expected reward from a player's point of view? Select the correct option: American Roulette / European Roulette / Neither, they are designed to be equal
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The correct option is: European Roulette.
The probability of winning an American Roulette game is given by n/N, where n is the number of ways to win and N is the number of possible outcomes.
So, The number of possible outcomes (without betting) is 38, while the number of winning outcomes is 1 (if you bet on 00, which is unique to American Roulette), 18 (if you bet on black), and 18 (if you bet on even).
Thus, the probability of winning if you bet on black or even is given by 18/38 = 0.47368 (rounded to five decimal places).
The probability of winning if you bet on 00 is given by 1/38 = 0.02632 (rounded to five decimal places).
In American Roulette, the house advantage is given by 1 - n/N.
So,The house advantage for black or even is given by 1 - 18/38 = 0.05263 (rounded to five decimal places).The house advantage for 00 is given by 1 - 1/38 = 0.02632 (rounded to five decimal places).
Thus, the house advantage associated with any given bet in American Roulette is 5.263%. 10. Game that has the lowest expected reward from a player's point of viewIt is known that the expected reward of a European Roulette game is equal to 2.7%.
And since the payoffs are the same for both American and European Roulette. Therefore, European Roulette has the lowest expected reward from a player's point of view.
Thus, the correct option is: European Roulette.
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Given: AQ ≅ RQ
∠YAF and ∠FRY are right angles.
Prove: AQY ≅ RQF
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Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.
How to explain the informationGiven: AQ ≅ RQ
∠YAF and ∠FRY are right angles.
Prove: AQY ≅ RQF
1. AQ ≅ RQ (Given)
2. ∠YAF and ∠FRY are right angles (Given)
3. ∠AQY = ∠RQF (Vertical angles are congruent)
4. AQ = RQ (Given)
5. AY = RY (Side-Angle-Side Congruence)
6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)
7. AQY ≅ RQF (SAS Congruence)
Therefore, AQY ≅ RQF.
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Given: AQ ≅ RQ
∠YAF and ∠FRY are right angles.
Prove: AQY ≅ RQF
The nullspace of nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors.
A. True
B. False
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The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.
Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.
Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.
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