The papers graded exponentially at the end of 5 days are 134, and it will take approximately around 12 days to complete 6000 papers.
What is exponential function?A function is considered to be exponentially growing if its value rises faster than any polynomial. The function e^x, serves as a good illustration.
The exponential growth is given by the following formula:
[tex]A = Pe^{rt}[/tex]
where, A is the final amount, P is the initial amount, r is the rate and t is the time.
For t = 0, the number of papers graded are, 9, hence the value of P = 9.
To calculate the rate at which the work is done, substitute the value of P = 9, A = 27 and t = 2 in the equation:
[tex]27 = 9 e^{2r}\\3 = e^{2r}[/tex]
Taking ln on both sides of the equation:
[tex]ln (3) = ln(e^{2r})\\\\ln(3) = 2r[/tex]
1.09 = 2r
r = 0.54
To calculate the number of papers graded in five days, substitute the value of P = 9, t = 5 and r = 0.54.
[tex]A = 9 e^{(0.54)(5)}[/tex]
A = 134
Hence, the papers graded at the end of 5 days are 134.
To complete grading 6000 papers, the time taken will be:
6000 = 9e^(0.54)(t)
666.66 = e^(0.54)(t)
Taking ln on both sides of the equation:
ln (666.66) = ln(e^(0.54)(t))
6.50 = (0.54)(t)
t = 12.04
Hence, it will take approximately around 12 days to complete 6000 papers.
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please help don't ignore :(
Answer:
Its either .5 or 5
Step-by-step explanation:
im not sure which one though lol
:)
Events A and B are mutually exclusive. Events B and C are non-mutually exclusive. which Venn diagram could represent this description?
The Venn diagram that represents the description on Events A and B would be the A. First Diagram.
What does mutually exclusive mean ?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.
This means that Events A and B cannot happen at the same time and therefore cannot share circles on the Venn diagram.
Events B and C are non - mutually exclusive however and so will share a circle on the Venn Diagram as shown below.
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Answer: D
last one
Step-by-step explanation: just did the test
Sarah is cycling at a speed of -8 mph. If she starts at the zero point what will her position be after 45 minutes?
Answer:
-8mph
It is not possible for Sarah to have a speed of -8 mph, as speed is a scalar quantity and cannot be negative. Speed is defined as the magnitude of velocity, which is a vector quantity that has both magnitude and direction. A negative speed would indicate that the direction of Sarah's motion is opposite to what is stated. It is likely that you meant to ask about Sarah's velocity, which could be -8 mph. But since the question does not specify her direction, it is impossible to give an accurate answer.
Step-by-step explanation:
Benita buys 2 shirts for the same price s the sales tax rate is 6.5
Write an expression to represent the total cost of the shirt in two different ways .
The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Benita buys 2 shirts for the same price s the sales tax rate is 6.5%
1 way, paid the cost of 2 shirts jointly
The total cost of the two shirts becomes,
Total cost = 2[ s + 0.065s]
Total cost = 2.13s
2nd way paid the cost of two shirts individually,
total cost = s + 0.065s + s + 0.065s
= 2.13s
Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
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the sum of 8 and 11 times a number
The sum of 8 and 11 times a number will be (8+11x).
What does a math sum mean?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms. The result or conclusion of adding two or more numbers or sentences is known as the sum.
Let x be the number.
The result is 11 times the number, or 11x.
The result of adding the number's multiples of 8 and 11 is 8+11x.
What is sum, for instance?The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of addends 14 and 6.
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A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold? show it in a graphhhhhh!!! THANK YOU!!!!
Answer: We can use a system of equations to solve this problem. Let x be the number of oranges sold and y be the number of apples sold. Then we know that:
x + y = 15 (the total number of fruits sold)
1x + 2y = 25 (the total cost of the fruits sold)
We can use the first equation to solve for one variable in terms of the other.
For example, we can solve for x:
x = 15 - y
Now we can substitute this expression into the second equation:
1(15 - y) + 2y = 25
15 - y + 2y = 25
3y = 10
y = 10/3 = 3.333
We can round it to 3 apples sold
So we have 3 apples and 12 oranges sold.
This can be represented in a graph with a point (12,3)
Alternatively, we can solve for y:
y = 15 - x
Now we can substitute this expression into the second equation:
1x + 2(15 - x) = 25
1x + 30 - 2x = 25
-x = -5
x = 5
So we have 5 oranges and 10 apples sold.
This can be represented in a graph with a point (5,10)
Both solutions represent the same values, the number of oranges and apples sold, but represented in a different way.
Step-by-step explanation:
write the measure in degrees 11pi/6
well, we know that π is 180°, so what's 11π/6?
[tex]\begin{array}{ccll} radians°rees\\ \cline{1-2} \pi &180\\\\ \frac{11\pi }{6}&x \end{array}\implies \cfrac{\pi }{ ~~ \frac{11\pi }{6} ~~ }~~ = ~~\cfrac{180}{x}\implies \cfrac{ ~~ \frac{\pi}{1} ~~ }{\frac{11\pi }{6}}~~ = ~~\cfrac{180}{x} \\\\\\ \cfrac{6\pi }{11\pi }=\cfrac{180}{x}\implies \cfrac{6 }{11 }=\cfrac{180}{x}\implies 6x=1980\implies x=\cfrac{1980}{6}\implies x=330[/tex]
Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Answer:
Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Step-by-step explanation:
You're welcome
Find the equation of the line that passes through (-3,1) and is parallel to y=4-3x
The equation of the line that passes through (-3,1) and is parallel to y=4-3x is y = -3x -8.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
An equation y = 4 - 3x
The slope of a line that is parallel to y = 4 - 3x is,
= -3
The equation of the line that passes through (-3,1) and is parallel to y=4-3x,
y - 1 = -3(x + 3)
y - 1 = -3x -9
y = -3x -8
Therefore, y = -3x -8 is the required equation.
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Which of the following measures of dispersion can attain a negative value?
Mean deviation
Range
Standard deviation
None of the above
Answer: Option D is correct (None of the above)
Step-by-step explanation:
None of the above.
A measure of dispersion is a statistical technique for extracting a particular value from a dispersed series in which the amount to which different values of the series tend to deviate from one another or from the average is quantified. All dispersion measurements, from range to standard deviation, are positive.
Problem 3: A city ballot includes a local initiative that would legalize gambling. The issue is hotly contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 53% of 1200 randomly selected voters plan to vote "yes," while a college Statistics class finds 54% of 450 randomly selected voters in support. Both groups will create 95% confidence intervals.
a) Without finding the confidence intervals, explain which one will have the larger margin of error.
b) Find both confidence intervals.
c) Which group concludes that the outcome is "too close to call"? Explain.
a. Without finding the confidence intervals, the larger margin of error will be the statistics class.
b. The confidence interval is (50.5%, 55.5%)
c. The group that concludes that the outcome is "too close to call is the statistics class.
.
How to calculate the interval?It should be noted that the Without finding the confidence intervals, the larger margin of error will be the statistics class. This is because of the smaller sample size.
The group that concludes that the outcome is "too close to call is the statistics class. This is because the intervals that are obtained contains 50%.
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Please answer this question for me
A counterexample to the statement given in this problem is:
Three colinear points.
How to obtain the counter example on this problem?The statement for this problem is given as follows:
You can connect any three points to form a triangle.
This statement is false, as for example, three points on a line do not form a function.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the first option is the correct option in the context of this problem.
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PLEASE HELP I NEED TO FINISH MY HW TODAY SO I WONT HAVE TO DO IT ON MY BDAY TOMORROW!!!
Michael took out a loan at an annual
compound interest rate of 30%.
After 2 years, he owes a total of £9126.
What was the original amount that Michael
borrowed?
Give your answer to the nearest £1.
Answer:
Start: 400
After 1 Year: 7020
Step-by-step explanation:
You will have a good b-day tmrw
HAPPY EARLY BIRTHDAY!!!!
enter a formula in cell b3 using the vlookup function to find the meaning for the medical abbreviation listed in cell a3. use the name abbreviation for the lookup table. the item names are located in column 2 of the lookup table. be sure to require an exact match.
The formula in cell B3 using the VLOOKUP function to find the meaning for the medical abbreviation listed in cell A3, using the "abbreviation" lookup table, would be: =VLOOKUP(A3, "abbreviation", 2, FALSE).
A3 is the cell that contains the medical abbreviation we want to find the meaning for.
"abbreviation" is the name of the lookup table that contains the item names and meanings.
2 is the column number of the lookup table where the meanings are located.
FALSE is used to require an exact match for the abbreviation in cell A3, so that the correct meaning is returned.
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The variables y and x have a proportional relationship, and y = 9 when X = 2.
What is the value of y when X = 3?
Enter
your answer as a decimal in the box.
y=
Answer:
13.5
Step-by-step explanation:
y=kx
k=y/x
k=9/2
k=4.5
y=kx
y=4.5*3
y=13.5
Situation:
An archaelogist in Turkey discovers a
spear head that contains 32% of its
original amount of C-14.
N = Noe
-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Find the age of the spear head to the nearest year
Answer:
13,093 years
Step-by-step explanation:
N = N0 e -kt . Here, N = 27 % of N0 = 27/100(N0 ) , k = 0.0001, then 27/100N0 = N0 e-0.001t .
Therefore, 0.27 = e-0.001t .On taking natural logarithms of both the sides, we get - 0.001t ln e = ln 0.27 ( log ab = b log a), or, - 0.001t = -1.30933332 ( as ln e = 1).
Therefore, t = 1.30933332/ 0.0001 = 13093.33 years = 13093 years on rounding off to the nearest year.
Distribute to create an equivalent expression with the fewest symbols possible.
\dfrac15(15+10k) =
5
1
(15+10k)=start fraction, 1, divided by, 5, end fraction, left parenthesis, 15, plus, 10, k, right parenthesis, equals
The expression when distributed is 3 + 2k
How to create an equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
1/5(15 + 10k)
The distribution property states that
a(b + c) = ab + ac
using the above as a guide, we have the following:
1/5(15 + 10k) = 1/5 * 15 + 1/5 * 10k
Evaluate the products
1/5(15 + 10k) = 3 + 2k
Hence, the equivalent expression is 3 + 2k
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Solve this right triangle. C = 90. (Round off the answer to the nearest whole number or degree.) a = 2, b = 3, A =
The triangle ΔABC is the right-angle triangle. Then the measure of angle ∠A is 33.7°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The triangle ΔABC is the right-angle triangle in which angle ∠C is the right angle.
Then the measure of the angle ∠A is given as,
tan ∠A = 2/3
∠A = tan⁻¹ (2/3)
∠A = 33.7°
Thus, the measure of angle ∠A is 33.7°.
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Área de la base
Segundo de secundaria
Los datos faltantes de los prismas rectos (áreas de base, longitudes)
A = 45 mm² A = 81 m², V = 729 m³ A = 21 cm² b = 8.696 m, A = 78.264 m²¿Cómo determinar los datos faltantes en prismas rectos?
El volumen de los prismas rectos (V), en unidades de longitud al cubo, es igual al producto de la área de la base (A), en unidades de longitud al cuadrado, y la altura (h), en unidades de longitud:
V = A · h
A continuación, determinamos los datos faltantes asociados a cada casa:
Caso 1 - Prisma recto de base hexagonal
A = V / h
A = 450 mm³ / 10 mm
A = 45 mm²
Caso 2 - Prisma recto de base cuadrada
A = l²
A = (9 m)²
A = 81 m²
V = A · l
V = (81 m²) · (9 m)
V = 729 m³
Caso 3 - Prisma recto de base trapezoidal
A = V / h
A = 147 cm³ / 7 cm
A = 21 cm²
Case 4 - Prisma recto de base rectangular
b = V / (h · a)
b = 900 m³ / [(11.5 m) · (9 m)]
b = 8.696 m
A = (9 m) · (8.696 m)
A = 78.264 m²
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James got a 75/100 and James teacher wants to convert that mark over 100 into ?/40 how much will James mark be now out of 40
n the figure below, m∠AED=88∘, m∠AEC=61∘, and m∠BEC=24∘. If m∠BED=x∘, then what is x?
Please and thank you!!
Check the picture below.
now, if we just add that shaded part of (x-24)° to the 61°, we'll end up with the whole AED angle or 88°.
[tex](x-24)~~ + ~~61~~ = ~~88\implies x+37=88\implies x=51[/tex]
not even sure where to start with this, all help is appreciated
[tex]\sqrt{tan^2y} + \sqrt{y^2}[/tex] for y ∈ ([tex]\frac{\pi }{2},\pi[/tex])
A function is what happens even if [tex]$f(-x)=f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] and A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] .
What do you mean parity?Parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}, \frac{\pi}{2} < y < \pi$[/tex] : Even .
Defining parity
A function is what happens even if. [tex]$f(-x)=f(x)$[/tex] [tex]for all $x \in \mathbb{R}$[/tex] A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex]
[tex]$$\begin{aligned}& f(-y): \quad \sqrt{y^2}+\sqrt{\tan ^2(y)} \\& -f(y): \quad-\sqrt{\tan ^2(y)}-\sqrt{y^2}\end{aligned}$$[/tex]
Check parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}$[/tex]
Equal or equivalentness, as a trait or state. Women have battled for equal pay to males in the workplace, or the equivalent of a commodity's price in one currency to that in another.
An integer's evenness or oddness is defined by its parity. In light of the fact that both 6 and 14 are even, it can be claimed that their parities are the same, but 7 and 12 have the opposite parity (since 7 is odd and 12 is even). the state of equality, particularly the state of equal pay or status Prison guards are want pay parity with the police. Women still lack balance in many occupations, especially at the top levels.
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The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H_0:p=0.08H0:p=0.08 versus H_a:p\ne0.08Ha:p=0.08 at the significance level of \alpha=0.08α=0.08 .The p-value of the test was 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion?
The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
Given information:
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.
The director tested the hypotheses H.
p=0.08
[tex]\alpha =\\[/tex]0.05
p-value of of the test is found to be 0.03 which is smaller than the significance level of [tex]\alpha =0.05\\[/tex]
Now, for smaller value of p-value, the null hypothesis is ignored.
Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
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The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
Given information:
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.
The director tested the hypotheses H.
p=0.08
α =0.05
p-value of of the test is found to be 0.03 which is smaller than the significance level of α =0.05
Now, for smaller value of p-value, the null hypothesis is ignored.
Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
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for the following proof (of equivalence of 2 formulae) provide the justifications at each step, using the following equivalences. use the following key:
The two formulas X and Y will be known as equivalence if and only if X ↔ Y is a tautology.
Consider there to be X and Y as the two formulas. In the event that X Y is a tautology, these formulas are referred to as equivalence. If the two formulas X Y are tautologies, we can also write them as X Y and read this relation as X is equivalent to Y.
Using a truth table, We will build the truth tables for any two-statement formula using this technique, and then we will determine whether the assertions are equivalent.
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The figure shows a rectangular box in three-dimensional space that contains several vectors. (The vector c is in the xz-plane, and the vector e is in the xy-plane.)
Are the following statements true or false?
1. e = a - b
2. g = f + a
3. a = d
4. d = g - c
5. c = f
6. a = -b
The statement 2( g = f + a) and 5(c = f) are true where as statement 3(a = d), 4(d = g - c), and 6(a = -b) are false.
The statement a = d is FALSE because they have opposite directions, a is in the direction of positive x, while d is in the direction of negative x axis.The statement c= f is TRUE because they have the same directions, in the direction of positive z axis and same length, the height of the rectangular box.The statement d=g−c is FALSE because by the triangle rule c=d+g=> d=−g+c≠g−cThe statement g=f+a is TRUE because the reference vector of f (given by the vector with the initial point at the origin and direction in the positive direction of z), added with the vector a satisfies the triangle rule to obtain the vector g:g=f+aThe statement a=− b is FALSE because their directions are not parallel, they are perpendicular.To learn more about the triangle, visit:
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A student is standing 20 ft away from the base of a tree. He looks up to the top of the tree at a 50° angle of elevation. His eyes are 5ft above the ground. What is the height of the tree to the nearest foot?
The height of the tree is 29 feet.
What is an angle of elevation?A measure of an angle formed which an object is viewed above the horizontal plane is termed angle of elevation.
Let the distance from the top of the tree to the student's eyes be represented by x. Thus, applying the required trigonometric function;
Tan θ = opposite/ adjacent
Tan 50 = x/ 20
x = 20*Tan 50
= 23.8351
x = 24 ft
So that;
the height of the tree = 24 + 5
= 29 feet
Therefore, the height of the tree is 29 feet.
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Help asap!
Will mark brainiest!
The net surface area of rectangular prism is 242.2 meters square.
What is the net surface area?A rectangular prism is a three-dimensional shape with two top and bottom faces and four lateral faces. A rectangular prism seems to be a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism seems to be a cuboid, and a cuboid and a rectangular prism both have the same cross-section.
This rectangular prism's surface area = l x b
We have provided
4 rectangular areas
A₁ = 4.3m x 10m
= 43 m²
2 rectangular areas
A₂ = 6.75m x 5.2m
= 35.1 m²
As a result, the rectangular prism's surface area is:
S.A. = 4A₁ + 2A₂
S.A. = 4(43) + 2(35.1)
= 172+ 70.2
= 242.2 meter square
As a result, the net surface area of the rectangular prism is 242.2 meters square.
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help me will mark BRAINLIEST
The measure of angle Y is given as follows:
m < Y = 90º.
How to obtain the measure of angle y?The sum of the measures of the internal angles of a triangle is of 180º.
For the larger triangle, the measures are given as follows:
2 x 25 = 50º.x = z.Hence the measures of angles x and z are given as follows:
x + z + 50 = 180º
2x = 130
x = 130/2
x = z = 65º.
Then for the smaller triangle, the measures are:
y.25.65.Meaning that the measure of angle y is given as follows:
y + 25 + 65 = 180
y + 90 = 180
y = 90º.
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Over what interval is the function increasing? x (x, y) −4 −8 (−4, −8) −2 −2 (−2, −2) 0 0 (0, 0) 2 −2 (2, −2) 4 −8 (4, −8)
The increasing and decreasing function is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the function f(x).
Increasing and decreasing functions are functions in calculus for which the value of f(x) increases and decreases respectively with the increase in the value of x. We can write -
Increasing Function - A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).Decreasing Function - A function f(x) is said to be decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≥ f(y).Strictly Increasing Function - A function f(x) is said to be strictly increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) < f(y).Strictly Decreasing Function - A function f(x) is said to be strictly decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) > f(y).Properties of increasing or decreasing functions If the functions f and g are increasing functions on an open interval I, then the sum of the functions f + g is also increasing on this interval.If the functions f and g are decreasing functions on an open interval I, then the sum of the functions f + g is also decreasing on this interval.If the function f is an increasing function on an open interval I, then the opposite function -f is decreasing on this interval.If the function f is a decreasing function on an open interval I, then the opposite function -f is increasing on this interval.If the function f is an increasing function on an open interval I, then the inverse function 1/f is decreasing on this interval.If the function f is a decreasing function on an open interval I, then the inverse function 1/f is increasing on this interval.If the functions f and g are increasing functions on an open interval I and f, g ≥ 0 on I, then the product of the functions fg is also increasing on this interval.If the functions f and g are decreasing functions on an open interval I and f, g ≥ 0 on I, then the product of the functions fg is also decreasing on this interval.Therefore, the increasing and decreasing function is discussed above.
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A firm is engaged in producing two products A and B each unit of product A require two kg of row material and 4 labour - hrs for procecing. wheras each unit of product B requres 3 kg of row material and 3 hrs labour. evrey unit of product A requires 4 hrs pakeging and whereas B needs 3.5 hrs. every week the firm has availablity of 60 kg of row material, labor 96 hrs and 105 hrs in pakeging department
1 unit of product A sold yields $40 profit and 1unit of B sold yildes $35 profit.
a.formulate this problame as a Lpp
b.find the optimal solution
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
a. Formulating this problem as a Linear Programming Problem (LPP):
Let x be the number of units of product A produced, and y be the number of units of product B produced.
The objective function is to maximize the total profit:
Maximize z = 40x + 35y
Subject to the following constraints:
The availability of raw material: 2x + 3y ≤ 60 (kg)
The availability of labor hours: 4x + 3y ≤ 96 (hrs)
The availability of packaging hours: 4x + 3.5y ≤ 105 (hrs)
Non-negativity constraints: x ≥ 0, y ≥ 0
b. To find the optimal solution, we can use a graphical method or simplex method.
We can use the simplex algorithm to find the optimal solution by iteratively moving from one feasible solution to another until we reach the optimal solution.
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
Note: The values and solution are obtained by solving the LPP problem and the availability of resources, hence the solution might be different for different values.
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