The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems
A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.
The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.
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Question 16
SALARY Sondra just started a job with an annual salary of $45,000. Each year, her salary will increase by 7%. If Sondra continues to work at
this job, what will be her total earnings in the first 4 years, rounded to the nearest dollar?
OA) $48,359
OB) $58,986
OC) $199,797
OD) $213,783
The solution is Option C.
The total amount of earnings of Sondra after 5 years is $ 169,113
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the annual salary of Sandra be A = $ 30,000
Now , the percentage increase in salary = 6 %
So , the equation will be
First year :
The increase in first year = annual salary of Sandra + percentage increase in salary x annual salary of Sandra
The increase in first year = 30000 + ( 6/100 ) x 30000
= 30000 + 1800
= $ 31,800
Second year :
The increase in second year = increase in first year + percentage increase in salary x increase in first year
The increase in second year = 31800 + ( 6/100 ) x 31800
= 31800 + 1908
= $ 33,708
Third year :
The increase in third year = increase in second year + percentage increase in salary x increase in second year
The increase in third year = 33708 + ( 6/100 ) x 33708
= 33708 + 2022.48
= $ 35,730.48
Fourth year :
The increase in fourth year = increase in third year + percentage increase in salary x increase in third year
The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48
= 35730.48 + 2143.8288
= $ 37,874.3088
Now , the equation is
The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary
The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088
The total amount earnings of Sondra is = $ 169,112.7888
Therefore , the total amount earnings = $ 169,113
Hence , The total amount of earnings of Sondra after 5 years is $ 169,113
Answer:
C) $199,797
Step-by-step explanation:
Adding 7% of a number to the number is the same as multiplying the number by 1.07
First year: $45,000
Second year: $45,000 × 1.07 = $48,150
Third year: $48,150 × 1.07 = $51,520.50
Fourth year: $51,520.50 × 1.07 = $55,126.94
Total = $199,797.43
Answer: C) $199,797
Which equations represent linear functions?
f(x) = 10x + 10
k(x)=10/x
m(x)=10
h(x)=1/10x
g(x)=10^x
j(x)=10x^2+10
help me with this please hurry
Answer: Its A
Ive took this test :3
radius = 14m, angle of sector=ø area of sector = 462m². Find ø
Answer:
HERE'S YOUR ANSWERStep-by-step explanation:
HOPE IT WILL HELP YOU!!(✿^‿^)(✿^‿^)Answer:
Step-by-step explanation:
can you pls tell me the answer for ixl
Answer:
the P is 25% for all positions
Step-by-step explanation:
P = (1/n)
P = probability
1 = the total of the whole
n = number of options
P = 1/4
P = .25
Find the coordinate of the midpoint segment for(7, 0), (3, 4)
a.2,5
b.5,2
c.7,4
d.2, 5
Write a equation and solve.
A car moves 660 feet every 10 seconds. How far does it go if it moves for 10 sec, 20 sec, and 30 sec
Answer: 10sec 660 feet, 20sec = 1320 feet, 30 sec = 1980 feet.
Step-by-step explanation:
It states that a car moves 660 feet in 10sec.
10sec = 660 feet
20sec: 660+660=1320f
30sec: 660+660+660=1980f
Divide then show a model
50 points for thorough explanation!
I’m a bit stuck can someone help me please
Answer:
x < 6/5 and x > 32/5
Step-by-step explanation:
|x| means taking the absolute value, or the distance from 0. This means that |-8| = 8, because -8 is 8 from 0
if |14-5x|>8, 14-5x > 8, or 14-5x < -8 because the absolute value of any number less than -8 is more than 8
for 14 - 5x > 8, -5x > -6, 5x < 6, x < 6/5
for 14 - 5x < -8, -5x < -32, 5x > 32, x > 32/5
I NEED HELP ON THIS ASAP!
Answer:
(-2,4) is quadrant 2, (8,4) is quadrant 1, (6,-2) is quadrant 4
Step-by-step explanation:
The amount of money in a bank account can be expressed by the exponential equation
A = 500 (1.04) ¹2t, How many years will it take for the amount in the account to be
more than $5000?
It will take approximately 58.71 years for the amount in the account to be more than $5000.
We can solve for the number of years it will take for the amount in the account to be more than $5000 by setting the given equation equal to 5000 and solving for t:
5000 = 500 (1.04)^t
Dividing both sides by 500, we get:
10 = (1.04)^t
To solve for t, we can take the logarithm of both sides.
1 = t * log(1.04)
Simplifying, we get:
t = 1/log(1.04)
Evaluate
t ≈ 58.71
Therefore, it will take approximately 58.71 years for the amount in the account to be more than $5000.
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A bag contains tiles with letters that spell the word OUTCOME. Which letter should we expect to appear more than the others when tiles are chosen from the bag?
A.) letter O
B.) letter C
C.) letter E
D.) letter T
Answer: O
Step-by-step explanation: if the bag is only filled with the letters in OUTCOME then there are more O’s than the rest
Hello please help I’m having trouble answering this question
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Answer:
2 + x = 5 2 + x = 5 x + 1 = 4 2 + x = 5 x + 1 = 4 - 5 + x = - 2Step-by-step explanation:
2 + x = 5 2 + x = 5 x = 5 - 22x = 32x = 3x + 1 = 4 2x = 3x + 1 = 4 x = 4 - 12x = 3x + 1 = 4 x = 4 - 1x = 32x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 22x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 2x = -2 + 52x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 2x = -2 + 5 x = 3Consider a chemical reaction, where “A” is one of the reactants.
Therefore, the reaction is first-order with respect to the concentration of "A".
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown values, and constants, which are known values. The goal in solving an equation is to find the values of the variables that satisfy the equation, that is, make it true. Equations can be linear or nonlinear, and they may involve one or more variables. Some common types of equations include polynomial equations, trigonometric equations, exponential equations, and logarithmic equations.
Here,
1. Table completion:
Time (s) [A] (M)
0 1.0
50 0.81
100 0.65
150 0.53
200 0.43
250 0.35
300 0.28
350 0.23
400 0.19
450 0.15
500 0.12
2. To determine the reaction order with respect to the concentration of "A", we need to manipulate the above equation for the different orders of the reaction and re-plot the tabulated numbers to determine the order.
For zero-order: [A]t = [A]o - kt
Taking the natural logarithm on both sides:
ln [A]t = ln [A]o - kt
This gives a straight line equation of the form y = mx + b, where y = ln[A]t, x = t, m = -k, and b = ln[A]o.
For first-order: ln [A]t = ln [A]o - kt
Taking the reciprocal on both sides:
1/[A]t = kt + 1/[A]o
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o.
For second-order: 1/[A]t = 1/[A]o + kt
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o. We can then plot the given data in Excel with the appropriate equation and check which equation gives us the best straight line fit. The slope of the line will give us the reaction order. Using Excel, we find that the first-order equation gives the best straight line fit with a slope of -0.0077.
3. To calculate the rate constant 'k', we can use the slope of the straight line fit obtained above.
From the equation ln [A]t = ln [A]o - kt, we have k = -slope.
Therefore, k = 0.0077 s⁻¹.
To estimate the half-life of "A", we can use the equation for the half-life of a first-order reaction:
t1/2 = ln 2/k
Substituting the value of k obtained above, we get:
t1/2 = ln 2/0.0077 s⁻¹
= 89.9 s
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what is the sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's
The sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's is 8/3.
The sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's is 8/3. To prove this, we can use the following equation:
(1/2) + (1/3) + (1/4) + (1/6) + (1/8) + (1/9) + (1/12) + (1/18) = 8/3.
Here, 1/2, 1/3, 1/4, and 1/6 are all reciprocals of numbers whose prime factors are only 2's and/or 3's,
and the sum of these four fractions is 2/3.
To complete the sum, we can add the reciprocals of 8, 9, 12, and 18, which are 1/8, 1/9, 1/12, and 1/18, respectively.
The sum of these four fractions is 6/3, and the sum of 2/3 and 6/3 is 8/3.
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A student mows lawns on the weekends. It takes him 110 minutes to mow 2 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 10 hours to mow 12 lawns.
It will take him 11 hours to mow 12 lawns.
It will take him 17 hours to mow 12 lawns.
It will take him 48 hours to mow 12 lawns.
Answer:
It will take him 11 hours to mow 12 lawns
Step-by-step explanation:
110/2=55 (meaning it takes him 55 minutes to mow 1 lawn)
55x12=660 (meaning it takes him 660 minutes to mow 12 lawns)
660/60=11 (meaning it takes him 11 hours to mow 12 lawns)
Why 660/60? Because there is 60 minutes in 1 hour.
Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?
A.{x | x R, x < 5}
B.{x | x R, x > 5}
C.{x | x R, x ≤ 5}
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
What exactly is a set?
In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.
Now,
The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.
In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.
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I don't understand this, can someone please help me?
Answer: You'll have to plug each function into a calculator and match the corresponding ones with each other.
for example Sin45° = B cos 45°
Step-by-step explanation:
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are: 10 are red, 8 are blue, 5 are green, and 2 are white
Based on the random sample results, how many of the 200 gumballs are red?
The proportion of red gumballs in the random sample is 0.4, meaning 40% of the 200 gumballs are red. To estimate the number of red gumballs in the entire population of 200 gumballs, we multiply the proportion of red gumballs by the total number of gumballs, 0.4 x 200 = 80.
What is proportion?Proportion in mathematics refers to the equality of two ratios. It asserts that two ratios are comparable. A ratio is a fractional comparison of two numbers or quantities, such as a/b or c/d.
To estimate how many of the 200 gumballs are red, we can use the proportion of red gumballs in the random sample and apply it to the entire population of 200 gumballs.
The proportion of red gumballs in the random sample is:
10/25 = 0.4
This means that 40% of the gumballs in the random sample are red.
To estimate the number of red gumballs in the entire population of 200 gumballs, we can multiply the proportion of red gumballs by the total number of gumballs:
0.4 x 200 = 80
Therefore, we can estimate that there are approximately 80 red gumballs in the machine.
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Please solve 2x-y greater than or equal to 3
This is the inequality in slope-intercept form, where the slope is 2 and the y-intercept is -3. the solution to the inequality[tex]2x - y \geq 3[/tex] is represented by the shaded region above the line. [tex]y=2x-3[/tex].
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Thet learn more about degree being compared can be numbers, variables, or expressions.
An inequality expresses that one value is smaller or larger than another, or that they are not equal. For example, x > 5 is an inequality that says x is greater than 5, while y ≤ 10 is an inequality that says y is less than or equal to 10.
by the question.
To solve 2x - y ≥ 3, we need to isolate y on one side of the inequality.
First, we can add y to both sides to get:
[tex]2x \geq y + 3[/tex]
Next, we can subtract 3 from both sides to get:
[tex]2x - 3\geq y[/tex]
Alternatively, we can switch the inequality sign and write:
[tex]y \geq 2x - 3[/tex]
So, the solution is:
[tex]y \leq 2x - 3[/tex]
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Where does the graph of [tex]y=-2x+1[/tex] intersect the [tex]x[/tex] -axis?
Answer:
x = 1/2
Step-by-step explanation:
You want to know the x-intercept of the graph of y = -2x +1.
X-interceptThe x-axis corresponds to a y-value of 0. The graph of any relation will intersect the x-axis where the output value is 0. We can find those points by solving the relation after setting y=0.
y = -2x +1 . . . . . . . given relation
0 = -2x +1 . . . . . . . equation with y=0
2x = 1 . . . . . . . . . . . add 2x
x = 1/2 . . . . . . . . . . . divide by 2
The graph intersects the x-axis where x = 1/2.
Prove that 5^7 + 5^6 is divisible by 60
Answer:
I think it is not ?
Step-by-step explanation:
You get a remainder at the end when you solve it and that's the opposite of what divisible means
"(of a number) capable of being divided by another number without a remainder."
Answer:
Not divisible
Step-by-step explanation:
5^7 is 78125
5^6 is 15625
15625 + 78125 = 93750
93750/60 = 1562.5
Therefore it is not fully divisible by 60.
What is the theoretical probability of selecting a vowel from the word orange?
A. 10%
B. 75%
C. 20%
D. 50%
Answer:50%
Step-by-step explanation: Since there are 6 letters in orange, and there are 3 vowels in the word (o,a,e), that would mean there is a 3/6 chance (50%) of selecting a vowel.
what is the unit rate if the car traveled 300 km within 2.5 hrs
The unit rate of the given expression through which the relation is satisfied is 300km / 2.5 hrs = 120 km / hr
What about unit rate?
In mathematics, a unit rate is a ratio between two quantities in which one quantity is expressed in terms of one unit of measure. It is commonly used to compare the cost or value of two or more items. For example, if a store charges $4 for 2 pounds of bananas, then the unit rate is $2 per pound of bananas.
The general formula for calculating unit rate is:
Unit rate = Quantity of one item ÷ Cost or value of that item
This formula can be used to find the unit rate of any item or quantity, as long as the quantity and cost or value are known. Unit rate is a useful tool in mathematics, as it allows for easy comparison of different quantities or values, and helps to make complex calculations more straightforward.
According to the given information:
The unit rate = [tex]\frac{Distance}{Time}[/tex]
i.e , unit rate = 300/2.5 = 120
⇒ 120km/hr.
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Micaela is going to invest $360 and leave it in an account for 12 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Micaela to end up with $670?
The required in order for Micaela to end up with ,n = 365 , t = 12, P = $360, and A = $670
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A binary relation from A to B is made up of these ordered pairs (a,b),
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), here the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
According to our question-
r=7.5%
Thus, 7.5% would be required in order for Micaela to end up with $670.
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a faulty car odometer proceeds from digit $3$ to digit $5$, always skipping the digit $4$, regardless of position. for example, after traveling one mile the odometer changed from $000039$ to $000050$. if the odometer now reads $002005$, how many miles has the car actually traveled?
The car has actually travelled 1745 miles, even though the odometer reads 2005. This is because the odometer skips the digit 4, so the number of valid readings must be counted and subtracted from the odometer reading.
We can approach this problem by counting the number of valid readings on the odometer between 3000 and 5000. We can then subtract the number of invalid readings (i.e., readings that contain the digit 4) to determine the actual number of miles the car has travelled.
The valid readings between 3000 and 5000 are: 3001, 3002, 3003, 3005, 3006, 3007, 3008, 3009, 3010, ..., 4997, 4998, 4999, 5000.
There are a total of 2001 valid readings in this range.
However, we need to subtract the number of invalid readings, which are the readings that contain the digit 4. Since the odometer skips the digit 4, we can think of each valid reading as having four possible digits (0, 1, 2, or 5) for each of its four places. Therefore, the number of invalid readings is 4 x 4 x 4 x 4 = 256.
So the actual number of miles the car has travelled is 2001 - 256 = 1745.
Therefore, the car has actually travelled 1745 miles.
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The graph of y = 4x? - 4x - 1 is shown.
Use the graph to find estimates for
the solutions
The estimates for the solutions are x = -0.25 and 1.25 when y = 0 and x = -0.5 and 1.5 when y = 2
Finding estimates for the solutionsFrom the question, we have the following parameters that can be used in our computation:
y = 4x² - 4x - 1
When y = 0, we have
4x² - 4x - 1 = 0
From the graph, we can see that
x = -0.25 and 1.25 when y = 0
When y = 2, we have
4x² - 4x - 1 = 2
From the graph, we can see that
x = -0.5 and 1.5 when y = 2
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pls answer!!!
worth 60 points <33
Answer:
a. 4
b. -2
c. 0,5
Step-by-step explanation:
1. 4
2.2
3.0,5
IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS