Your best submission for each question part is used for your score. 1. [-/2 Points] DETAILS TEAFM2 4.6.010. Let P(E) = 0.4, P(F) = 0.55, and P(F n E) = 0.25. Draw a Venn diagram and find the condition
Answers
The condition is P(F' ∩ E) = 0.15. We have given: P(E) = 0.4P(F) = 0.55P(F ∩ E) = 0.25. To draw a Venn diagram, we can use the following formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where A and B are any two events, let A = F and B = E
So, P(F ∪ E) = P(F) + P(E) - P(F ∩ E)
P(F ∪ E) = 0.55 + 0.4 - 0.25
P(F ∪ E) = 0.7
Now, we know that
P(A') = 1 - P(A) Where A' complements event A.
So
P(E') = 1 - P(E)
= 1 - 0.4
= 0.6
P(F') = 1 - P(F)
= 1 - 0.55
= 0.45
Now, we can use the above values to draw a Venn diagram as shown below: Venn diagram for the given probability values. Using the Venn diagram, we can conclude the following: As per the Venn diagram, the shaded region represents the event (F' ∩ E). We can find the probability of the event (F' ∩ E) as
P(F' ∩ E) = P(E) - P(F ∩ E)
P(F' ∩ E) = 0.4 - 0.25
P(F' ∩ E) = 0.15
The given probabilities can be used to draw a Venn diagram as shown below: Venn diagram for the given probability values in the Venn diagram, we can conclude that the shaded region represents the event (F' ∩ E). We can find the probability of the event (F' ∩ E) as:
P(F' ∩ E) = P(E) - P(F ∩ E)
P(F' ∩ E) = 0.4 - 0.25
P(F' ∩ E) = 0.15
Hence, the condition is P(F' ∩ E) = 0.15.
In the given question, we are given the probabilities of the events E and F and their intersection E ∩ F. We are asked to draw a Venn diagram and find the condition for the event F' ∩ E. We can use the formula
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) to find the probability of the union of two events, A and B. We can apply this formula to the events E and F as follows:
P(F ∪ E) = P(F) + P(E) - P(F ∩ E)
We can substitute the given probabilities to find the probability of the union of the events F and E.
We get:
P(F ∪ E) = 0.55 + 0.4 - 0.25
P(F ∪ E) = 0.7
Now, we can find the complements of events E and F. We know that:
P(A') = 1 - P(A)
Using this formula, we can find:
P(E') = 1 - P(E)
= 1 - 0.4
= 0.6
P(F') = 1 - P(F)
= 1 - 0.55
= 0.45
We can use these probabilities to draw the Venn diagram as shown above. The shaded region represents the event F' ∩ E. We can find the probability of this event as follows:
P(F' ∩ E) = P(E) - P(F ∩ E)
P(F' ∩ E) = 0.4 - 0.25
P(F' ∩ E) = 0.15
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The given probabilities are P(E) = 0.4, P(F) = 0.55, and P(F ∩ E) = 0.25. We need to draw a Venn diagram and find the condition. Venn diagram:
Let A denote the region inside the rectangle but outside both circles. Let B denote the region inside the rectangle and inside the circle F but outside E. Let C denote the region inside the rectangle and inside the circle E but outside F. Let D denote the region inside both circles E and F.
Now we know that, P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
In this case, P(E ∪ F) = P(A ∪ B ∪ C ∪ D) = 1.
P(E) = P(B ∪ D) = P(B) + P(D).
P(F) = P(C ∪ D) = P(C) + P(D).
P(E ∩ F) = P(D).
Then,
P(E ∪ F) = P(E) + P(F) - P(E ∩ F) ⇒ 1
= P(B) + P(C) + 2P(D) - 0.25 ⇒ 1
= P(B) + P(C) + 2(0.25) - 0.25 ⇒ 1
= P(B) + P(C) + 0.25. ⇒ P(B) + P(C)
= 0.75
Therefore, the required condition is P(B) + P(C) = 0.75.
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Related Questions
Let B and C be two ordered bases of R^3, and consider a linear transformation T : R^3 -> R^3. Suppose that the change of base matrix Ic, B is given by [-3 -1 1] [-1 2 -1] [-1 -3 -2] and the coordinate matrix Tc,c of T with respect to C is given by [2 -2 -2][-1 -3 -1] [2 0 -1] Use this to determine coordinate matrix TB,B of T with respect to B! [ __ __ __ ]TB,B = [ __ __ __ ][ __ __ __ ]
Answers
The coordinate matrix of T with respect to the base B is [-9 -11 -8].
What is coordinate?Coordinate in math is a pair of numbers that represent a specific point in a two-dimensional space or a three-dimensional space. In two-dimensional space, it is written in the form (x, y) where x is the horizontal coordinate and y is the vertical coordinate. In three-dimensional space, it is written in the form (x, y, z) where x is the horizontal coordinate, y is the vertical coordinate, and z is the depth coordinate. Coordinates are used to plot points on a graph, calculate the distance between points, and to identify the location of a point.
Solution:
To determine the coordinate matrix of T with respect to the base B, we need to multiply the change of base matrix Ic,B with the coordinate matrix Tc,c of T with respect to C.
Multiplying the two matrices, we get:
TB,B = Ic,B × Tc,c
= [-3 -1 1][2 -2 -2] + [-1 2 -1][-1 -3 -1] + [-1 -3 -2][2 0 -1]
= [-9 -9 -7] + [-2 -2 4] + [2 -3 -5]
= [-9 -11 -8]
Therefore, the coordinate matrix of T with respect to the base B is [-9 -11 -8].
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Explain why angle “a” must be 135
Answers
In a fourth grade class, three-sixths of the students are girls. If there are 15 girls, what is the total number of students in the class
Answers
Answer:
30
Step-by-step explanation:
3/6 students are girls, 1/2 the students are girls.
So 15 + 15 = 30
13 points if someone gets it right.
You spin this spinner twice.
1 polka-dot section, 2 white sections, 1 shaded section
Whta is the probability of the spinner stopping at a polka- dot section and then say stopping a solid white section? Write your answer as a fraction
Answers
The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.
The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.
When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.
Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.
Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).
To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8
Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.
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A block measure 22 cm by 11 cm by 7 cm.
How many of these blocks will be needed to
build a wall 5 1/2m long, 22 cm thick and 3 1/2
m high?
Answers
Answer: 2,500 blocks
Step-by-step explanation:
Hi, to answer this question we have to calculate both volumes:
Volume of a rectangular prism= length x width x height
Volume of the block = 22 x 11 x 7 = 1,694 cm3
Before calculating the volume of the wall, we have to convert the measures in m to cm:
Since:
1m = 100 cm
5 1/2 m x 100 = 550 cm (length)
3 1/2 m x 100 =350 cm (height)
Volume of the wall = 550 x 22 x 350= 4,235,000 cm3
Finally:
Volume of the wall /Volume of the block = 4,235,000 / 1,694 = 2,500 blocks.
Feel free to ask for more if needed or if you did not understand something.
Validation of the model and answering the question "what are my options" occur in the ___ phase of the IDC.
A. choice
B. design
C. intelligence
D. implantation
Answers
Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.
The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.
In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.
In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.
Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.
The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.
Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.
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Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4. Show work.
I NEED THIS FAST LIKE PLEASEE HELP
Answers
Answer:
y = -1/6x - 1/2
Step-by-step explanation:
y = -1/6x + b
-1 = -1/6(3) + b
-1 = -1/2 + b
-1/2 = b
Help me out pls it's due today
Answers
1) 2/5 = .4
2) 32%
3) 300 Total Employees, 36 Female Employees
4) 70 minutes
5) 10 eggs
6) 14,000
7) 2000
8) 625 liters
9) .75 kg
10) I have no idea about this one sry
what is the exact length of third side
Answers
Answer:
Step-by-step explanation:
The sum of the squares of the shorter sides is equal to the square of hypotenuse!
An electrician estimates 2,500 feet of number 12 NM cable is needed to wire a house. Each coil of cable holds 250 feet. The amounts used in different rooms are as follows: 335.4 feet, 293.7 feet, 1,205.1 feet, and 337.5 feet. How many coils of wire are used
Answers
The electrician will need to use 9 coils of cable to wire the house. An electrician estimates that 2,500 feet of number 12 NM cable is required to wire a house.
The cable is distributed across different rooms with the following amounts: 335.4 feet, 293.7 feet, 1,205.1 feet, and 337.5 feet. To determine the total cable needed, we add up the amounts used in each room:
335.4 + 293.7 + 1,205.1 + 337.5 = 2,171.7 feet
The total cable needed is 2,171.7 feet, which is less than the initial estimate of 2,500 feet. Each coil of cable holds 250 feet. To calculate how many coils of wire are used, we divide the total cable needed by the length of each coil:
2,171.7 ÷ 250 ≈ 8.69 coils
Since a partial coil cannot be used, the electrician will need to use 9 coils of cable to wire the house.'
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Write f(x)=|x-2| as a piecewise function.
Answers
Answer:
Hi! A piecewise function is a function defined by multiple sub-functions, or pieces of different functions over different intervals. Piecewise definition is a way of expressing the function and is not actually integral to the function itself.
f(x) = |x - 2| is an absolute value function. As a piecewise function, it's written like this:
f(x) = {x - 2, x ≥ 2
{-x + 2, x < 2
Hope this helps! Have a great day.
Study the scenario described below and answer all questions that follow. Firms achieve their missions in three conceptual ways: (1) differentiation, (2) costs leadership, and (3) response. In this regard, operations managers are called on to deliver goods and services that are (1) better, or at least different, (2) cheaper, and (3) more responsive. Operations managers translate these strategic concepts into tangible tasks to be accomplished. Any one or combination of the three strategy options can generate a system that has a unique advantage over competitors (Heizer, Render and Munson, 2017:74). P\&B Inc., a medium-sized manufacturing family-owned firm operates in a market characterised by quick delivery and reliability of scheduling as well as frequent dramatic changes in design innovation and customer demand. As the operations analysts at P\&B Inc., discuss how you would prioritise for implementation the following FOUR (4) critical and strategic decision areas of operations management as part of P\&B's 'input-transformation-output' process to achieve competitive advantage: 1. Goods and service design 2. Human resources and job design 3. Inventory, and 4. Scheduling In addition to the above, your discussion should include an introduction in which the strategy option implicated by the market requirements is comprehensively described
Answers
The prioritized critical decision areas for P&B Inc. to achieve competitive advantage are goods and service design, human resources and job design, inventory management, and scheduling, aligned with a response strategy.
To achieve a competitive advantage in a market characterized by quick delivery, reliability of scheduling, and frequent design innovation and customer demand changes, P&B Inc. needs to prioritize critical decision areas.
Goods and service design should focus on creating innovative and differentiated products/services that meet customer needs. Human resources and job design should ensure a skilled and motivated workforce capable of delivering high-quality outputs.
Inventory management is crucial to balance stock levels, minimize costs, and meet customer demands promptly. Scheduling should prioritize efficient resource allocation and sequencing of tasks to optimize production and meet customer deadlines.
By effectively managing these decision areas, P&B Inc. can align its operations with a response strategy, delivering quick and reliable outcomes while adapting to market dynamics.
This strategic approach allows the company to differentiate itself, attract customers, and maintain a competitive edge in the industry.
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find the distance in exact form between the point p ( − 4 , 3 , − 2 ) and the point q ( 4 , 1 , − 4 ) .
Answers
The exact distance between point P(-4, 3, -2) and point Q(4, 1, -4) is √72 units.
To find the distance between two points in three-dimensional space, we can use the distance formula. The formula for the distance between two points P(x1, y1, z1) and Q(x2, y2, z2) is given by √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).
Using this formula, we can calculate the distance between point P(-4, 3, -2) and point Q(4, 1, -4).
Substituting the coordinates into the formula, we have:
Distance = √((4 - (-4))² + (1 - 3)² + (-4 - (-2))²)
= √(8² + (-2)² + (-2)²)
= √(64 + 4 + 4)
= √(72)
= √(36 * 2)
= √36 * √2
= 6√2.
Therefore, the exact distance between point P(-4, 3, -2) and point Q(4, 1, -4) is 6√2 units.
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. give three examples of groups of order 120, no two of which are isomophic. explain why they are not isomorphic
Answers
Three examples of groups of order 120 that are not isomorphic are the symmetric group S5, the direct product of Z2 and A5, and the semi-direct product of Z3 and S4.
The symmetric group S5 consists of all the permutations of five elements, which has order 5! = 120. This group is not isomorphic to the other two examples because it is non-abelian, meaning the order in which the elements are composed affects the result. The other two examples, on the other hand, are abelian.
The direct product of Z2 and A5, denoted Z2 × A5, is formed by taking the Cartesian product of the cyclic group Z2 (which has order 2) and the alternating group A5 (which has order 60). The resulting group has order 2 × 60 = 120. This group is not isomorphic to S5 because it contains an element of order 2, whereas S5 does not.
The semi-direct product of Z3 and S4, denoted Z3 ⋊ S4, is formed by taking the Cartesian product of the cyclic group Z3 (which has order 3) and the symmetric group S4 (which has order 24), and then introducing a non-trivial group homomorphism from Z3 to Aut(S4), the group of automorphisms of S4. The resulting group also has order 3 × 24 = 72. However, there are exactly five groups of order 120 that have a normal subgroup of order 3, and Z3 ⋊ S4 is one of them. These five groups can be distinguished by their non-isomorphic normal subgroups of order 3, making Z3 ⋊ S4 non-isomorphic to S5 and Z2 × A5.
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Arrange the following integers from largest (top) to smallest (bottom). The integers are: − 90 , 87 , − 21 , 56 , 95 and 65.
Answers
The Arrangement of the given integers from largest (top) to smallest (bottom), will be: 95, 87, 65, 56, -21, -90.
What are the integers?Integers is one that is made up of whole numbers, comprising both positive and negative values, along with zero. There are no fractional or decimal components in integers. Integers refer to complete numbers that comprise positive and negative values, along with zero.
To arrange integers from largest to smallest, one can look at the numbers, compare and place in descending order. A good examples of integers are -3, -2, -1, 0, 1, 2, 3, etc.
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Given that Y= 3x – 8, what is the sum of the gradient and intercept of the linear equation? *
Answers
Answer:
- 5
Step-by-step explanation:
The equation of a line in slope - intercept form is
y = mx + c ( m is the slope (gradient) and c the t- intercept )
y = 3x - 8 ← is in slope- intercept form
with gradient m = 3 and y- intercept c = - 8 , thus
m + c = 3 + (- 8) = 3 - 8 = - 5
_____ suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.
a. The Carnegie model
b. Prospect theory
c. The bounded rationality perspective
d. McGregor's Theory X
Answers
The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.
Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.
For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.
In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.
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Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
Answers
The area of a pool from the given situation is 816 ft².
Given that, the dimensions of plot is 50 ft and 40 ft.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, area of a plot = Length × Width
= 50 × 40
= 2000 ft²
Area of a pool = Area of a plot - Area of a grass
= 2000 - 1184
= 816 ft²
Therefore, the area of a pool from the given situation is 816 ft².
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Can yall help me with this
Answers
Answer:
B. $54
Step-by-step explanation:
PEMDAS: Do multiplication and division first
65 - (2*7=14) + (9/3=3)
65-14+3
Go from left to right and solve
51+3=54
(1 point) college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected student
Answers
Probability Theory
P (K) =\(\frac{n (K) }{n (S)}\)
P(K) : probability of selected K
n (K) : number of occurence of K
n (S) : number of all occurence
In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :
n (A) : the number of occurence of students who curry a gun
n (B) : the number of occurence of students who curry a knife
n (C) : the number of occurence of students who curry other weapon
and the number of all students is n ( A U B U C) -> union of sets
how many randomly selected student? in question, there is no specific about the student. so, we can answer with :
1) probability of students who curry a gun
P (A) = \(\frac{n (A) }{n (AUBUC)}\)
2) probability of students who curry a knife
P (B) = \(\frac{n (B) }{n (AUBUC)}\)
3) probability of students who curry other weapon
P (C) = \(\frac{n (C) }{n (AUBUC)}\)
and if question want to estimate with percentage, we can multiply with 100%. example :
1) percentage of probability of students who curry a gun
P (A) = \(\frac{n (A) }{n (AUBUC)}\) x 100%
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Max has a square piece of cloth. He cuts it in half from one corner to the opposite corner. How many sides does each of the cut pieces have?
Answers
Answer:
Step-by-step explanation:
You have a cloth:
____________
| |
| |
|___________|
and you cut it in half.
There are three sides
Answer:
Step-by-step explanation:
The cut pieces will each have three sides: two that are equal and one that is the hypotenuse.
If the original square had sides of length s, then the cut pieces would each have two of that length: s and s; the third side would have length h = √(s² + s²), or h = s√2.
assume that y varies inversely with x. if y = 8 when x = 1.55, find x when y = -0.62
Answers
Answer:
y varies inversely with x is written as
y = k /x
where k is the constant of variation
y = 8 x = 1.55
8 = k / 1.55
Multiply through by 1.55
k = 12.4
The formula is
y = 12.4 / x
when y = - 0.62
- 0.62 = 12.4/x
- 0.62x = 12.4
Divide both sides by - 0.62
x = 12.4/-0.62
x = - 20
When y = - 0.62 x = - 20
Hope this helps
A. Solve for x. B. Is the triangle equilateral?
Answers
Answer:
x=8
No it’s not an equilateral
Step-by-step explanation:
Since side AB is about the same length as BC we can set them equal to each other
x-1=7
+1 +1
x=8
This is not an equilateral because if you fill in X for the third side you will get 5
8-3=5
Please help me with this math problem!! It's due tonight!! :)
Answers
Answer:
x = 7
Step-by-step explanation:
5x - 1 + 8x + 5 = 95
13x + 4 = 95
13x = 91
x = 7
Triangle in 95° so x is
»8x + 5° + 5x - 1° = 95°
»13x + 4° = 95°
»13x = 91°
»x = 91°/13
»x = 7°✅
The number of trading cards varies directly as the number of packages. If there
are 84 cards in 7 packages, how many cards are in 12 packages?
Let x = the number of packages and y = the total number of cards.
y = mx
Direct variation equation
a
b
There are 91 cards in 12 packages.
There are 144 cards in 12 packages
Not enough information was given.
There 84 cards in 12 packages.
Answers
Answer:
There are 144 cards in 12 packages
Step-by-step explanation:
Direct Proportion
The number of trading cards is directly proportional to the number of packages. We are given there are 84 cards in 7 packages.
Let x= number of packages, y=total number of cards
The direct variation equation is:
y = m.x
Where m is a constant we need to find by using the given data: y=84 when x=7, thus
84 = 7m
Dividing by 7:
m = 84/7=12
The equation is:
y = 12x
For x = 12 packages:
y = 12*12 = 144 cards
The answer is:
There are 144 cards in 12 packages
11. The sum of proper subsets and subsets of a set is
127. How many elements are there in this set?
Answers
Elements in set A is 7.
How do you calculate the number of items in a correct subset?Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.
RECALL: The number of proper subsets of a set with nn elements is 2^n-12
N
−1.
Let n = number of elements of the set.$
Then,Then, 2^n-1 = 127
2^n = 127+1
2^n=128
2^n = 2^7
N=7
$The set has 7 elements.
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According to the given information in the question the element in set A is 7.
How do you calculate the number of items in a correct subset?Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.
RECALL: The number of proper subsets of a set with nn elements is 2^n-12
N
−1.
Let n = number of elements of the set.$
Then, Then, 2^n-1 = 127
2^n = 127+1
2^n=128
2^n = 2^7
N=7
$The set has 7 elements.
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What is the solution of the inequality sh
below?
9+b≤2
Answers
Answer:
b≤-7Step-by-step explanation:
b+9≤2
Subtract 9 from both sides:
b+9-9≤2-9b≤-79+b≤2
subtract 9 on each side which will be -7
the answer will be b≤-7
Hellllppp
Examine the rotation. Which best describes point D?
angle of rotation
center of rotation
image
pre-image
Answers
Answer:
center of rotation
Answer:
Center of rotation.
Step-by-step explanation:
The center of rotation is the point at which an image turns.
Point D is described as the center of rotation.
Which of the following below is a solution to y=4x-3
(2,5)
(5,5)
(4,5)
(3,5)
Answers
\( \fbox{(2,5)}\)
Step-by-step explanation:Hello, substitute all the given coordinates & see if RHS match with LHS
given equation,
y = 4x-3
First coordinate,
(x,y) = (2,5)
5= 4×2-3
5=5
Hence, first solution satisfies the given equation,
let's solve for rest other cordinates,
second coordinate,
(x,y) = (5,5)
5= 4×5-3
5 ≠ 17
does not satisfy,
third coordinate,
(x,y) = (4,5)
5= 4×4-3
5 ≠ 13
does not satisfy,
fourth coordinate,
(x,y) = (4,5)
5 = 4×3-3
5 ≠ 9
does not satisfy.
Hence the correct answer is (2,5)
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The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 730 homeless patients and no more than 1,100 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,400 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,900 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,900 per month How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients homeless patients profit $
Answers
Answer:
High income patient = 800
Homeless patient = 1,600
Step-by-step explanation:
Provided,
Profit per homeless patient = $9,900
Profit per high-income patient = $7,900
Maximum beds = 2,400
Since profit is more in case of homeless patients, maximum homeless patients shall be admitted.
Provided homeless patients can be maximum twice of high income patients
If high income patients = \(x\)
Then, homeless patients = \(2x\)
Total patients = 2,400
Now,
\(x + 2x = 2,400\)
\(3x = 2,400\\x = 800\)
This shall mean that high income patient = 800
Homeless patient = \(2 \times 800 = 1,600\)
Profit shall be maximum in this,
As maximum profit per patient is on homeless patient, and homeless patient cannot be more than 1,600 as because of the management decided ratio of high income patient and homeless patient.
Profit in this case,
Homeless patient = \(1,600 \times 9,900 = 15,840,000\)
High income patient = \(800 \times 7,900 = 6,320,000\)
Total profit = $22,160,000
High income patient = 800
Homeless patient = 1,600
The calculation is as follows:Here we assume high income patients be
So, homeless patients be 2x
And, Total patients = 2,400
Now,
x + 2x = 2,.400
3x = 2,400
x= 800
so, the homeless patient should be 2(800) = 1,600
Now
Profit in this case,
Homeless patient = 1,600 (9900) = 15,840,000
High income patient = 800 (7,900) = 6,320,000
Total profit = $22,160,000
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