Answer:
(x + 6)(x + 4)
Step-by-step explanation:
x² + 10x + 24
= x²+ 6x + 4x + 24=0
= x(x + 6)+4(x + 6)
= (x + 6)(x + 4)
Answer:
(x + 6)(x +4)
Step-by-step explanation:
Factorization by splitting the middle term:x² + 10x + 24
Sum = 10
Product = 24
Factors = 6 , 4
{When we multiply 6 and 4, we get 24 & when we add 6 and 4, we get 10}
x² + 10x + 24 = x² + 6x + 4x + 24 {Rewrite the middle term using the factors}
= x(x + 6) + 4 (x + 6)
{Group the first two terms and third & fourth term together. Then take out the common factors}
= (x + 6)(x + 4)
after a long period of time, you observe the chain and see that it is in state 1. what is the conditional probability that the previous state was state 2?
The conditional probability that the previous state was state 2 given that the chain is currently in state 1 is equal to the probability of transitioning from state 2 to state 1.
The conditional probability of transitioning from one state to another in a Markov Chain is dependent on the transition probabilities between the states. In this case, the conditional probability of transitioning from state 2 to state 1 is equal to the probability of transitioning from state 2 to state 1. This probability can be determined by looking at the transition matrix of the Markov Chain. The transition matrix specifies the probability of transitioning from one state to another. Therefore, the conditional probability of transitioning from state 2 to state 1 given that the chain is currently in state 1, is equal to the probability of transitioning from state 2 to state 1 as specified in the transition matrix.
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The regression line for this data set has a slope close to m = , and the correlation coefficient is close to. Based on this information, we can conclude that employees' annual earnings are to their tenure. Employee earnings tenure
1) The slope of the regression line is 35
2) The correlation coefficient is 0.95
3) Employees’ annual earnings are strongly related to their tenure
4) Employee earnings increase with tenure.
The slope of the regression line in this data set is close to 35. In order to determine the slope, two points must be identified that are either on or near the line.
We have the following two points;
(1, 175) and (2.5, 225)
slope = (change in y) / (change in x)
= (225-175)/(2.5-1) = 33.33
This is close to 35.
2) The correlation coefficient of the annual earnings and tenures of employees at Stan & Earl Corp is almost 0.95. This value, known as the coefficient of correlation, shows the level of connection between two variables and the direction of their linear relationship. The scatter-plot demonstrates a strong positive relationship between the employees' annual earnings and their tenure.
Hence the correlation coefficient is close to 0.95.
3) The data suggests a strong connection between an employee's annual earnings and their tenure. The correlation coefficient was estimated to be close to 0.95, which represents a significant positive relationship between the two variables. As a result, it can be concluded that there is a clear relationship between an employee's annual earnings and the length of time they have been with the company.
4) As employees' tenure with the company increases, their annual earnings also increase. This can be deduced from the slope of the regression line which was calculated to be close to 35, indicating a positive relationship between the two variables. The positive correlation coefficient supports this
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The regression line for this data set has a slope close to m = (5.5,35,-50,-2.5) , and the correlation coefficient is close to (0.20,0.40,0.75,0.95) .
Based on this information, we can conclude that employees’ annual earnings are (strongly related, moderately related, weakly related, not related) to their tenure. Employee earnings (increase with, decrease with, are not affected by) tenure.
3. numbers with square roots that are whole
they are called perfect square numbers
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 heres some hope that helps!
How many liters are in 9 quarts
Answer: 8.5 L
Step-by-step explanation: I looked it up l o l
Answer:
Your answer is: 8.51718
Step-by-step explanation:
There's 1.057 quarts in a liter. You multiply that by 9 to get 8.51718.
Attached imagine to answer.
Answer:
A)7y-4xy
Algebraic expressions are just that expressions. No inequality signs or equations. That's what makes them special
Step-by-step explanation:
A wall has paneling made up of rectangles, with an area of 30 square feet each. There are four rectangles along the height and three along the top. The edge of each rectangle in the paneling is (2x+3) feet in width and (4x+2) feet in height. What is the value of x?
What are the dimensions of the wall covered the paneling
The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.
Finding dimensions of wall:To find the dimensions of the wall find the dimensions of the rectangles given in the figure. Calculate the area of the rectangle and factorize the resultant equation for the value of 'x'. Calculate the dimensions of the wall by using the number of panels along the height and top.
Here we have
A wall has paneling made up of rectangles
Area of the rectangle = 30 square feet
Given that the edge of each rectangle in the paneling is (2x+3) feet in width and (4x+2) feet in height.
Area of the rectangle = (2x + 3)(4x +2) = [ 8x²+ 16x + 6 ]
Given that area of the rectangle = 30 ft²
=> 8x²+ 16x + 6 = 30
=> 8x²+ 16x - 24 = 0
=> x² + 2x - 3 = 0
=> x² + 3x - x - 3 = 0
=> x(x + 3) - (x + 3) = 0
=> (x + 3) (x - 1) = 0
=> x = -3 and x = 1
We need to x = 1 [ since height can't be taken in negative ]
Dimensions of the rectangle,
Width, 2x + 3 = 2(1) + 3 = 5 feet
Height, 4x + 2 = 4(1) + 2 = 6 feet
Given that there are 4 rectangles along the height
Height of the wall = 4 × 6 = 24 feet
There are 3 rectangles along the top.
Width of the wall = 3 × 5 = 15 feet
Therefore,
The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.
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grade 4N usually has physical education on a Wednesday at 1:43pm and ends at 2:13 pm. with the new mandated change, at what time will grade 4N PE ends?
Grade 4N usually has physical education on a Wednesday at 1:43 pm and ends at 2:13 pm. with the new mandated change, at 2:28 pm Grade 4N PE will now end
The new regulations require physical education classes to be a minimum of 30 minutes long. Allowing for an extra 15 minutes to the existing PE class brings the end time to 2:28 pm. This is an important change because it ensures that all students receive the recommended amount of physical activity each week.
Physical education is a vital part of a student’s development, as it provides the opportunity for students to become more active, and socially engaged, and learn about the importance of a healthy lifestyle. The extra 15 minutes of physical education also allows for more time for students to learn about safety procedures and the proper way to use the equipment, which is important for the overall well-being of the students.
Additionally, the extra time allows for more time for individual instruction, which can be beneficial for students who need extra help or who may be struggling with a certain skill.
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find the value of y in the proportion (4y+5):3=(y+7):4
The value of y in the given proportion is 1/13.
In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities, typically written as a fraction. For example, if we have two quantities, a and b, then the ratio of a to b is written as a/b.
A proportion is written in the form a/b = c/d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write this as a:b = c:d.
To solve the proportion:
(4y+5):3=(y+7):4
We can cross-multiply and simplify:
4(4y+5) = 3(y+7)
16y + 20 = 3y + 21
Subtracting 3y from both sides:
3y + 20 = 21
Subtracting 20 from both sides:
13y = 1
Dividing both sides by 13:
y = 1/13
Therefore, the value of y that satisfies the proportion is y = 1/13.
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can someone help me with this ik its not math, but there wasn’t a category for band/music. this is due tmr and i’m struggling. i’ll give 50 points!!
1. a break in the music
2. how loud or soft to play
3. bar lines organize the staff into these boxes of music
4. perform two or more notes as one note for the combined sum of all the notes
5. noteheads are placed on the five horizontal lines and four spaces
6. Signifies the end of a piece of music show me your mom
7. Divide the staff in the measures
8. Medium soft
9. Holding note longer than its normal value
10. Fast
11. The style used to begin or end a note
12. A medium tempo
13. Stretch the note to hold it for full value
14. a slow tempo
15. Perform the note with emphasis
16. Gradually getting louder
17. Gradually getting softer same as decrescendo
18. Top number is the number of beats in a measure bottom number is the type of note that receives one beat
19. Gradually getting faster
20. Smoothly connected
the blacked out ones are the ones i’ve already done!!
Answer:
1. rest
2. dynamics
3. measure
4. chord
5. staff
6. double bar line
7. bar line
8. mezzo-piano
9. fermata
10. allegro
11. articulation
12. moderato
13. tenuto
14. larghetto?
15. accent
16. crescendo
17. diminuendo
18. time signature
19. accelerando
20. slur
5. A regular hexagon is a six-sided figure with congruent sides and
congruent angles. A regular hexagon can be composed of six equilateral
triangles. Write and solve an equation to determine the value of x on the
regular hexagon shown. Then determine the sum of the six interior angles
of a regular hexagon.
I need this answer ASAP
The sum of the interior angles of a regular hexagon is S = 720° and each angle of the regular hexagon x = 120°
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the interior angles of the hexagon be S
Now , the number of sides for a hexagon = 6
And ,Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
Substituting the values in the equation , we get
6θ = 180 ( 6 - 2 )
On simplifying the equation , we get
6θ = 180 x 4
6θ = 720°
Therefore , the sum of angles is 720°
And , the value of x = 720 / 6 = 120°
Hence , the sum of interior angles of hexagon is 720°
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Select all the equations where x=3 is a solution.
Answer: 2,4,6
Step-by-step explanation: All of these have x=3 as a solution.
Answer:
Step-by-step explanation:
6=2x
x^2=9
x-3=0
ra 1 Y. Write exponential functions: word problems LZW
Mr. Olsen, the owner of Trading Card Depot, purchased a rare baseball card valued at $98.70.
He expects the card's value to double each year.
Write an exponential equation in the form y = a(b)* that can model the card's value, y, in
dollars, x years after Mr. Olsen purchased it.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y = 98.70()
0
O
O
Submit
(
What can Mr. Olsen expect the card's value to be 5 years after he purchased it?
M
31
D
●
Answer:
Here's the exponential equation to model the card's value:
y = 98.70 * 2^x
where x is the number of years after Mr. Olsen purchased the card.
To find the value of the card after 5 years:
x = 5
y = 98.70 * 2^5 = 98.70 * 32 = $3162.40
So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.
Step-by-step explanation:
Answer:
Step-by-step explanation:
m
Classify each statement about the function f(x)=2x3+8 as true or false.
The domain of the function is all real numbers.
The range of the function is (0, ∞).
The y-intercept is (0, 0).
The center of symmetry is (0, 8).
Answer:
The answer to the classification of the statements is:
1.True
2.False
3.False
4.True
Answer:
True
False
False
True
Step-by-step explanation:
You want to buy a pet hamster that costs $42. You already have $15 and plan to save $8 per week. If w represents the number of weeks until you have enough money to buy the hamster, what equation represents your plan to afford the hamster.
I need help I can't think of what the equation would be!
Answer: 42 = 8w + 15
Step-by-step explanation:
Is this right please help now ASAPppp
Answer: Pretty much correct except one thing is wrong.
Step-by-step explanation:
In place of CB you should write AB because the sides doesn't match when you flip the triangle CED.
Hope it helps!
find median of each of the following distributions
A science class planned a field trip for which the total costs were $80. When four additional students decided to go on the trip, the cost per student was reduced by $1. How many students went on the trip?
Answer:
There were 8 student who went on a trip.
Step-by-step explanation:
Let's call the original number of students "x". The total cost of the trip was $80, so the cost per student was $80/x.
When four more students decided to go, the new number of students became x + 4, and the cost per student was reduced by $1, to $80/x - $1.
We can set up an equation to solve for x:
$80/x = $80/(x + 4) - $1
Expanding the right side:
$80/x = $80/x + $80/4 - $1
Combining like terms:
$80/x = $80/4 + $80/x - $1
Solving for x:
$80/4 = $80/x - $1
$80/4 + $1 = $80/x
$20 + $1 = $80/x
$21 = $80/x
Finally, solving for x:
x = 80/$21 = 80/21 = 3.81 (rounded to nearest whole number)
So, there were 4 students on the original trip.
There were 4 students on the original trip and 4 more students joined, so in total, there were 4 + 4 = 8 students who went on the trip.
Answer: 8 student
Step-by-step explanation:
in a bacteria growing experiment, a biologist observes that the number of bacteria in a certain culture triples every 4 hourse. after 12 hours, it is estimated that there are 1 million bacteria in the culture. what is the doubling time for the population?
The bacteria's population increases exponentially, and its equation is
P(t) = P[tex]_{0}[/tex]e[tex]^{kt}[/tex]
Where,
P[tex]_{o}[/tex] is the initial population t is the number of hours.
k is the growth rate.
It is given that the population of the bacteria after one hour triples itself. i.e
P(1)=3P[tex]_{o}[/tex]
3P[tex]_{o}[/tex]=Pe[tex]k^{(l)}[/tex]
3=e[tex]^{k}[/tex]
In 3 = In e[tex]^{k}[/tex]
In 3=k ln e
In 3 = k(1)
k = ln (3)
Thus, the rate of growth is k= ln (3)
Substitute k = ln (3) in the equation P(t) = P[tex]_{o}[/tex]e[tex]^{kt}[/tex].
P(t) = P[tex]_{o}[/tex]e[tex]tln^{(3)}[/tex]
It is given that there are 1 million bacteria after 5 hours. i.e. P(5)=10,00,000
P(5) = P[tex]_{o}[/tex]e[tex]^{(5)} ln^{(3)}[/tex]
10,00,000 Pe[tex]^{(5)}ln^{(3)}[/tex]
10,00,000 = P[tex]_{o}[/tex]e[tex]ln^{(3)^{5} }[/tex]
10,00,000 = P[tex]_{o}[/tex][tex](3)^{5}[/tex]
P[tex]_{o}[/tex] = 10,00,000 / [tex]3^{5}[/tex]
P[tex]_{o}[/tex] = 10,00,000 / 243
Thus, the formula for any t is P(t) = (10,00,000 / 243) e[tex]ln^{(3)^{t} }[/tex]
Find the doubling time for the bacteria population.
Let X= 10,00,000 / 243 then the equation for the doubling time for the bacteria is
2X = Xe[tex]ln^{(3)t[/tex]
2 = e[tex]ln^{(3)t}[/tex]
t= ln (2) / ln (3) ≈ 0.63094 hours
Or t=37.8564 minutes.
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Hector wants to send a parcel to Spain.
His parcel is a cuboid with dimensions 10 cm, 10 cm and 40 cm.
10 cm
10 cm
He looks at the prices of two companies,
WeGoFast and ParcelsFly.
Not drawn
to scale
WeGoFast
Total cost: Sum, in cm, of the 3 dimensions * £1. 20F
GXF420 Find the cost of sending the
parcel with each company.
Give each of your answers
Parcels Fly
in pounds (£).
Total cost: Volume measured in cm' * £0. 02
The cost for sending the parcel with each company is £72 via WeGoFast and £80 by ParcelsFly.
In product, exploration, retail, and account, a cost is the value of plutocrat that has been used up to produce commodity or deliver a service, and hence isn't available for use presently. In business, the cost may be one of accession.
Hector needs the parcel to be send.
Dimension for his cuboid parcel is given by 10 cm by 10 cm by 40 cm.
10cm x 10cm x 40cm
Sum of the three dimension in cm
= (10 + 10 + 40) cm
= 60 cm.
Volume of the parcel in = (10 × 10 × 40) = 4000 cm³
Price charge by WeGoFast
= Sum of the three dimensions in cm × £1.20
= £ (60 × 1.20) = £72.
Price charged by ParcelsFly
= Volume measured in × £0.02
= £ (4000 × 0.02) = £80
Therefore, The cost of sending the parcel with each company is £72 by WeGoFast and £80 by ParcelsFly.
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Compute the requested operating costs as indicated, based on the preceding table and the following information.
Car: V-8 sedan
Year driven: third
Miles driven: 10,000
In dollars and cents the depreciation for this vehicle using method 2 will be $
.
The repairs and maintenance charges for this vehicle are 207 dollars and 0 cents.
What is the meaning of an operating cost?Operating costs are continuous expenses paid as a result of the usual day-to-day operations of an organization. Operating costs comprise both the cost of goods sold and additional operating expenditures, which are sometimes referred to as selling, general, and administrative costs.
here, we have,
From the data provided in the table, we can deduce the repair and maintenance charges of the vehicle.
The name of Car 8 implies that they are talking about Version V-8 of the Sedan Car.
Year-driven third implies the third year which alludes to the 6th column of the table.
Number of miles driven = 9000
From the repair and maintenance cents per mile in the table:
The total cost for this service = number of miles driven × repair and maintenance cost
The total cost for this service = 9000 × 2.3
The total cost for this service = 20700 cents
The total cost for this service in dollars and cents
= $207.00
The total cost for this service is 207 dollars and 0 cents.
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To graph the shape on the coordinate grid, click on a point that represents a vertex, then repeat this process for each vertex point of the shape. To complete the shape, click on the first vertex point. The shape will be shaded in once it is completed.
Check the picture below.
Grace rakes led s every day for one week. She fills the same number of bags with leaves o each of the 5 weekdays. She fills 11 bags over the weekend. At the end of the week, Grace has filled a totallof 26 bags. She wants to know how many bags she filled each weekday.
bags filled on weekdays + bags filled on weekend = total bags filled
Let b equal the number of bags Grace filled each weekday.
5b + 11 = 26
How many bags of leaves did Grace fill each weekday?
Answer:
3 bags of leaves each weekday
Step-by-step explanation:
5b + 11 = 26
Subtract 11 from both sides.
5b = 15
Divide 5 on both sides.
b = 3
Grace filled 3 bags of leaves each weekday.
grace read 1/3 of a book in the morning some at night and by the end of the day she still had 2/5 left how much did she read at night
Grace read 4/7 of the book at night.
To solve this problem, we need to use the fractions to calculate the amount of the book that Grace read in the morning and the amount of the book that she read at night.
The total amount of the book that Grace read in the day is 1/3 + 2/5 = 7/15.
Since she read 1/3 of the book in the morning, then the amount of the book that she read at night is 7/15 - 1/3 = 4/15.
To calculate the amount of the book that she read at night as a fraction of the total book, we need to divide 4/15 by 7/15.
4/15 ÷ 7/15 = 4/7
Therefore, Grace read 4/7 of the book at night.
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Need some help please
Answer:
10x+15y-10
Step-by-step explanation:
5(2x+3y-2)
=10x+15y-10
A social media website had 500,000 followers in 2012. The number y of followers increases by 19% each
year.
a. Write a function that represents the number of followers t years after 2012.
b. How many people will be following the website in 2019? Round your answer to the nearest thousand
Function representing number of followers for different situation are:
a. Number of followers in 't' years N = 500,000 ( 1 + 19/100 )^t.
b. Number of people following in 2019 are 1,690,000 ( nearest thousand )
Total number of followers of social media website in 2012 = 500,000
Followers increases by 19% every year.
let 'N' represents the number of followers.
a. Function to represents the number of follower in 't' years after 2012 is:
N = 500,000 ( 1 + 19/100 )^t
b. Number of people following website in 2019 is:
t = 2019 -2012
= 7
N = 500,000 ( 1 + 19/100 )^7
⇒ N = 500,000 ( 1.19 )^7
⇒ N = 500,000 × 3.379
⇒ N= 1689657.7
⇒ N = 1,690,000 ( nearest thousand )
Therefore, the number of followers represented for different condition are:
a. Function to represent number of followers in 't' years is
N = 500,000 ( 1 + 19/100 )^t
b. Number of followers in 2019 are 1,690,000 ( nearest thousand )
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A total of
330
330 children and adults attended a school play. There were
21
21 times as many children in attendance as there were adults.
This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children.
As a result, 315 pupils attended the school play.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
The first equation in the system is given by the total number of attendees:
c + a = 330
The second equation is given by the number of children being 21 times the number of adults:
c = 21a
We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:
21a + a = 330
Combining the two terms on the left-hand side, we have:
22a = 330
Dividing both sides by 22, we have:
a = 15
So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:
c = 21a = 21 * 15 = 315
So there were 315 children in attendance at the school play.
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A person invests 7000 dollars in a bank. The bank pays 6. 25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 11300 dollars?
It takes 3.9 years long the person have to leave the money in the bank until it reaches 11300 dollars
Suppose that the initial amount of something is P.
Let after one unit of time, it increases by R% [per unit time] end compounds on the resultant total of that quantity, then, after T such units of time, then the quantity would increase to:
[tex]A=P\left(1+\frac{R}{100}\right)^{nT}[/tex]
A person invests 7000 dollars in a bank. The bank pays 6.25 % interest compounded semi-annually.
Given that:
Principal =7000
Interest (r) = 6.25 % compounded semi annually
As compounded semi annually n = 2
Calculate time, t, if final amount A = 11300
Using the compound interest formula
[tex]A=P\left(1+\frac{R}{100}\right)^{nT}[/tex]
A = Final amount
n = number of times interest is applied per period
11300 = 7000 [tex](1+0.0625)^{2t[/tex]
113 = 70 [tex](1.0625)^{2t[/tex]
1.614 = [tex](1.0625)^{2t[/tex]
Take the log of both sides
log 1.614 = 2t log 1.0625
0.2079 = 2t (0.0263)
0.2079 = 0.0526 t
t = 3.9
Time period will be 3.9 years.
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Chris says that he can find the surface area faster by
thinking of the box as a triangular prism on top of a
rectangular prism. He finds the surface area of each one
and adds them together. Does his method make sense?
Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism is a valid and useful approach.
What is Surface area?
The surface area of a solid item is a measurement of the total area occupied by the object's surface.
Yes, Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism makes sense.
A box can be thought of as a combination of a triangular prism and a rectangular prism because a box is made up of six faces, with three rectangular faces and three triangular faces. By finding the surface area of the triangular prism and the rectangular prism separately, and then adding them together, one can find the total surface area of the box.
This method can make finding the surface area of a box faster and easier because one can use formulas that are specifically designed for finding the surface area of triangular prisms and rectangular prisms. By breaking down the box into its constituent parts, one can simplify the calculation and avoid having to use a more complex formula for finding the surface area of a box.
In summary, Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism is a valid and useful approach.
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how much will the optimal solution increase if the limit of the second constraint is increased by 10?
The optimal solution amount will increase by the amount that the additional 10 units of the second constraint can be used to benefit the overall solution.
The optimal solution amount will increase with the addition of 10 units to the second constraint. This is because the additional 10 units can be used to benefit the overall solution by providing more of the resources that are necessary to reach the optimal solution. For example, if the second constraint is a limit on the amount of a certain resource that can be used, then the additional 10 units can be used to increase the amount of resources available, which can lead to a better overall solution. In addition, the additional 10 units can also be used to increase the efficiency of the solution, by allowing the solution to use the same amount of resources more efficiently.
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What does the ordered pair (5,200) represent in this situation
The ordered pair (5,200) represent in this situation is a straight line passing through y = 20x.
Having zero width and extending on all sides, a line is a geometry object. An unbent line is, to put it simply, a straight line. A straight line is one that doesn't curve and extends indefinitely on both sides.
We have ordered pair (5,200),
x = 5
so y = 200
so y = 5 x 40
so we have y = 40x
This is a straight line passing through the origin on the point (5,200), through any point.
An ordered pair consists of two items. Because the ordered pair differs from the ordered pair unless a = b, the order of the objects in the pair is important. Other names for ordered pairs include 2-tuples and 2-length sequences.
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Complete question:
What does the ordered pair (5, 200) represent in this situation?