The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8
Determining the values in the matrix equation.To determine the values of a, b, and c in the matrix equation:
4 a + 3 0 = 7 3
3 4 5 b c 5
By addition operation, we have
a + 0 = 3
3 + 5 = c
4 + b = 5
When the equations evaluated, we have
a = 3
c = 8
b = 1
The above are the values of a b and c
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Complete question
Determine the values of a, b, and c in the following matrix equation.
4 a + 3 0 = 7 3
3 4 5 b c 5
Help Mr. Johnson has a swimming pool in the shape of a rectangular prism. The dimensions of the pool are 2. 5 meters by 4. 5 meters. He fills the pool with 1. 2 meters of water. What is the volume of water in Mr. Johnson's pool?
There are 13.5 cubic meters of water in Mr. Johnson's pool.
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
To find the volume of water in Mr. Johnson's pool, we need to multiply the length, width, and depth of the pool. The length is 2.5 meters, the width is 4.5 meters, and the depth of water is 1.2 meters.
So, the volume of water in Mr. Johnson's pool is:
2.5 meters x 4.5 meters x 1.2 meters = 13.5 cubic meters
Therefore, there are 13.5 cubic meters of water in Mr. Johnson's pool.
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Suppose an amusement park is being built in a city with a population of 100. Voluntary contributions are being solicited to cover the cost. Each citizen is being ask to give $100. The more people contribute, the larger the park will be and the greater the benefit to each citizen. But it is not possible to keep out the noncontributors; they get their share of this benefits anyway. Suppose that when there are n contributors in the population, where n can be any whole number between 0 and 100. The benefit to each citizen in monetary unit equivalents in n 2 dollars.
Required:
a. Suppose that initially no one is contributing. You are the mayor of the city. You would like everyone to contribute and can use persuasion on some people. What is the minimum number whom you need to persuade before everyone else will join voluntarily?
b. Find the Nash equilibria of the game where each citizen is deciding whether to contribute
The minimum number of people that need to be persuaded is two. When there are 0 contributor, 1 contributor, 2 or more contributor this is a the Nash equilibria.
a. Let's first calculate the benefit to each citizen when there are n contributors. According to the problem, the benefit is n^2 dollars. So when there are 0 contributors, the benefit to each citizen is 0 dollars. When there is 1 contributor, the benefit to each citizen is 1 dollar. When there are 2 contributors, the benefit to each citizen is 4 dollars. And so on, up to 10,000 dollars per citizen when all 100 citizens contribute.
Now let's think about the incentives of each citizen to contribute. If no one contributes, everyone gets 0 dollars of benefit. If one person contributes, that person gets 1 dollar of benefit, and everyone else gets 0 dollars. So each person has an incentive to free-ride, hoping that someone else will contribute.
But if two people contribute, each person gets 4 dollars of benefit, which is more than the 1 dollar cost of contributing. So once there are at least two contributors, it becomes rational for everyone else to contribute as well.
Therefore, the minimum number of people that need to be persuaded is two. Once two people contribute, it becomes rational for everyone else to contribute as well.
b. Let's consider the Nash equilibria of the game where each citizen is deciding whether to contribute. A Nash equilibrium is a situation where no one has an incentive to change their strategy, given the strategies of all the other players.
In this case, each citizen has two strategies: contribute or free-ride. Let's consider the case where n citizens are contributing. If everyone else is contributing, then it is rational to contribute as well, since the benefit of contributing is greater than the cost.
If everyone else is free-riding, then it is rational to free-ride as well, since the cost of contributing is greater than the benefit. However, if some people are contributing and some people are free-riding, then it may be rational to contribute, since the benefit of contributing may outweigh the cost, depending on the number of contributors.
Therefore, there are multiple Nash equilibria in this game, depending on the number of contributors. When there are 0 contributors, everyone is free-riding and this is a Nash equilibrium. When there is 1 contributor, that person is contributing and everyone else is free-riding, and this is a Nash equilibrium. When there are 2 or more contributors, everyone is contributing, and this is a Nash equilibrium.
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h(x)=|2x|-8 domain and range
For the function "h(x) = |2x| - 8", the domain is (-∞, ∞) and the range is [-8, ∞).
The function h(x) = |2x| - 8 is defined for all real numbers x, so the domain of h(x) is the set of all real-numbers, or (-∞, ∞).
To find the range of the function, we determine set of all possible output values of function. Since the function involves the absolute value of 2x, the output can never be less than -8.
When "2x" is positive, |2x| = 2x. When 2x is negative, |2x| = -2x. This means that the function h(x) will have two branches depending on whether 2x is positive or negative.
⇒ When 2x is positive, h(x) = |2x| - 8 = 2x - 8. This branch of the function will have all non-negative values.
⇒ When 2x is negative, h(x) = |2x| - 8 = -2x - 8. This branch of the function will have all non-positive values.
Combining the two , we get the range of the function h(x) as [-8, ∞).
Therefore, the domain of h(x) is (-∞, ∞) and the range of h(x) is [-8, ∞).
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Solve the equation. 2 = \dfrac{f}{8}2= 8
f
2, equals, start fraction, f, divided by, 8, end fraction
f =\,f=f, equals
The solution to the equation is f = 16. The value of f can be found by multiplying both sides of the equation by 8.
How we solve the equation: 2 = f/8 for f?To solve the equation 2 = f/8 for f, we aim to isolate f on one side of the equation.
To do so, we can multiply both sides of the equation by 8, as this will cancel out the denominator of f/8.
By multiplying 2 by 8, we obtain 16 on the left side of the equation.
On the right side, the 8 in the denominator cancels out with the 8 we multiplied, leaving us with just f.
we find that f = 16 is the solution to the equation.
This means that if we substitute f with 16 in the equation, we will have a true statement: 2 = 16/8, which simplifies to 2 = 2.
f = 16 satisfies the original equation and is the solution.
It's important to note that when solving equations, we perform the same operation on both sides to maintain equality.
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A cross section of the cylinder with the cone removed is a ring. To find the area of the ring, find the area of the outer circle and of the inner circle. Then subtract the area of the inner circle from the outer circle.
The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
Here, we have,
Given:
Let the radius of outer circle i.e CA be r
Let the radius of inner circle i.e CB be x
The diagram is given below as attachment.
We know that,
area of circle = πR²
Then subtract the area of the inner circle from the outer circle is:
The area of the outer circle - area of the inner circle
= πr² - πx²
= π (r² - x²)
=π (r - x) (r+x)
So, we get
Then subtract the area of the inner circle from the outer circle is:
π (r - x) (r+x)
Hence, The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
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HELP NEEDED ASAP!!!!
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
New York 14 1 4.5 8.5 4 5.5 6.1 3.2
Which of the choices below best describes how to measure the center of these data?
a.Both centers are best described by the mean.
b.Both centers are best described by the median.
c.The Rome data center is best described by the mean. The New York data center is best described by the median.
d.The Rome data center is best described by the median. The New York data center is best described by the mean.
The choice which best describes the measure of center of these data is (d) Rome data center is "best-described" by median and data center of "New-York" is "best-described" by mean.
In the table provided below, we see that the "IQR" for Rome is relatively large compared to the IQR for New York, which suggests that that there may be some skewness in the distribution of the Rome data. So, the median would be a better-measure of center than the mean.
On the other hand, the IQR for "New-York" is relatively small, which indicates that the data is more symmetric and the mean would be a better measure of center.
Therefore, the correct answer is (d).
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The given question is incomplete, the complete question is
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
New York 14 1 4.5 8.5 4 5.5 6.1 3.2
Which of the choices below best describes how to measure the center of these data?
(a) Both centers are best described by the mean.
(b) Both centers are best described by the median.
(c) The Rome data center is best described by the mean. The New York data center is best described by the median.
(d) The Rome data center is best described by the median. The New York data center is best described by the mean.
Un terreno de forma rectangular tiene un perímetro de 105 metros. Si el ancho es la mitad del largo, ¿Cuáles son las medidas del terreno? *
Sea "l" la medida del largo del terreno y "a" la medida del ancho del terreno.
De acuerdo con el problema, el ancho es la mitad del largo, es decir, a = l/2.
El perímetro de un rectángulo se calcula sumando las longitudes de sus cuatro lados, por lo que en este caso:
Perímetro = 2l + 2a = 2l + 2(l/2) = 3l
Sabemos que el perímetro es de 105 metros, entonces:
3l = 105
l = 105/3 = 35
Por lo tanto, el largo del terreno es 35 metros. Y, como el ancho es la mitad del largo, entonces:
a = l/2 = 35/2 = 17.5
Por lo tanto, el ancho del terreno es de 17.5 metros.
En resumen, las medidas del terreno son 35 metros de largo y 17.5 metros de ancho.
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Peter picks one bill at a time from a bag and replaces it,
He repeats this process 100 times and records the results in
the table.
Peter's Experiment
Value Frequency
$1 28
14
$10 56
$20 2
Based on the table, which bill has an experimental
probability of 3 for being drawn from the bag next?
None of the bills have an experimental probability of 3, as all probabilities are between 0 and 1.
Based on the table, the experimental probability for each bill being drawn from the bag next can be calculated by dividing the frequency of each bill by the total number of draws (100). Using this formula, we can calculate the experimental probabilities for each bill:
1. For the $1 bill: Experimental probability = [tex]\frac{(Frequency of $1 bill)}{Total draws} = \frac{8}{100} = 0.28[/tex]
2. For the $10 bill: Experimental probability =[tex]\frac{(Frequency of $10 bill)}{Total draws} = \frac{56}{100} = 0.56[/tex]
3. For the $20 bill: Experimental probability =[tex]\frac{(Frequency of $20 bill)}{Total draws} = \frac{2}{100} = 0.02[/tex]
None of the bills have an experimental probability of 3, as all probabilities are between 0 and 1.
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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.\
The statement that is true is: "The range of the function is all real numbers less than or equal to 9
What is the function about?This quadratic function is indicated by a downward-opening parabola due to the negative coefficient of the squared term.
Found at coordinates (-2, 9), the vertex will be the highest point on this curved graph
Located on the x-axis at points (-5, 0) and (1, 0), each one serves as an intersection. Because of these intersections the following statement can be confidently said: "The range of the function consists of all actual numbers that are lesser or equal to 9."
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In the last hour, Ellie observed 32 monarchs, 56 gulf fritillaries and 8 giant swallowtails visit her butterfly garden. If 48 butterflies visit her garden, how many can we expect be giant swallowtails
We can expect 4 giant swallowtails to visit Ellie's garden.
In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).
Now, we can calculate the probability of a giant swallowtail visit:
Probability
= (number of giant swallowtails) / (total butterfly visits)
= 8/96
= 1/12
Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails
= (total butterflies) × (probability of giant swallowtails)
= 48 × (1/12)
= 4
So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.
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The note below depict a triangle prism. What is the total surface area of the prism?
How do you set it up and solve?
The total surface area of the prism is 282
What is the total surface area of the prism?From the question, we have the following parameters that can be used in our computation:
The net of a triangle prism.
The total surface area of the prism is the sum of the individual shapes
So, we have
Surface area = 2 * 1/2 * 6 * 5 + 3 * 6 * 14
Evaluate
Surface area = 282
Hence. the total surface area of the prism is 282
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Answer:
The total surface area is 282
What is the perimeter of the triangle?
?? units.
Answer:
36 units
Step-by-step explanation:
You want to know the perimeter of the right triangle with leg lengths 9 units and 12 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides. We can count squares to find the lengths of the horizontal and vertical legs. The length of the hypotenuse can be found using the Pythagorean theorem:
c² = a² +b²
c² = 9² +12² = 81 +144 = 225
c = √225 = 15 . . . . length of the hypotenuse
Then the perimeter is ...
P = a +b +c = 9 +12 +15 = 36 . . . units
The perimeter of the triangle is 36 units.
__
Additional comment
The leg lengths have the ratio 9:12 = 3:4, telling you this is a 3:4:5 right triangle. This means you know the side lengths are 3:4:5 = 9:12:15, and their sum is 9+12+15 = 36.
It is handy to memorize a few of the Pythagorean triples that often show up in algebra, trig, and geometry problems: {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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if f' * (x) = 2x - 1 and g(x) - x + 3 prove that f g(x) is a linear function
The composite function fg(x) is a linear function by the proof shown below
Proving that the function fg(x) is a linear functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x - 1
g(x) = -x + 3
The above functions are linear functions
This means that the function fg(x) will also be a linear function
To prove this, we have
f(g(x)) = 2(g(x)) - 1
substitute the known values in the above equation, so, we have the following representation
f(g(x)) = 2(-x + 3) - 1
So, we have
f(g(x)) = -2x - 7
Hence, the function is a linear function
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A community center charges x dollars for a summer activity if individuals are signed up before the day of the activity. Individuals who sign up the day of the activity are charged a fee of x plus 0. 20 x dollars. Which expression also represents the fee for signing up the day of the activity, and what does it mean about the fee?.
The expression that represents the fee for signing up the day of the activity is x + 0.20x. This means that fee for signing up the day of the activity is original fee (x) plus an additional 20% of original fee (0.20x).
For example, if the community center charges $50 for signing up before the day of the activity, then the fee for signing up the day of the activity would be:
$50 + ($50 x 0.20) = $50 + $10 = $60
So, individuals who sign up the day of the activity are charged a higher fee than those who sign up before the day of the activity, because they are charged the original fee plus an extra 20% of the original fee. This is often used as an incentive for individuals to sign up early and to help the community center plan and prepare for the activity accordingly.
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A person standing on the ground throws a rock upward with an initial velocity of 16 feet per second. The person’s hand is 12 feet above the ground when the rock is released. This is modeled by the equation h = -16^2 + 16t + 12. How long does it take for the rock to hit the ground?
It will take the rock 1.5 seconds to hit the ground
How to determine how long it take for the rock to hit the ground?Since the situation is modeled by the equation h = -16t² + 16t + 12
The rock will hit the ground when height is zero i.e. h = 0. Thus, we have:
-16t² + 16t + 12 = 0 and we can then solve for the time (t) .
-16t² + 16t + 12 = 0 (divide through by -16)
t² - t - 3/4 = 0
Using factorization method:
(t + 1/2) (t - 3/2) = 0
t = -1/2 or 3/2
Since t cannot be negative. Thus, t = 3/2 = 1.5.
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Jessica records the number of winners at the dunk-a-teacher booth at the town fair as shown in the table. if there are 750 contestants on monday, how many should jessica expect to dunk a teacher? enter your answer in the box.
If there are 750 contestants on Monday, Jessica should expect around 75 of them to dunk a teacher.
Based on the table provided, we can see that the percentage of winners at the dunk-a-teacher booth varies from day to day.
On Monday, 10% of contestants were able to dunk a teacher.
Therefore, if there are 750 contestants on Monday, Jessica should expect around 75 of them to dunk a teacher.
This is calculated by multiplying 750 by 0.10, which gives us 75. It's important to note that this is just an estimation, as the actual number of winners may be slightly higher or lower than 75.
However, this gives Jessica a rough idea of what to expect at the booth on Monday.
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In circle M with m \angle LMN= 66m∠LMN=66 and LM=19LM=19 units find area of sector LMN. Round to the nearest hundredth
We can use the formula for the area of a sector to find the area of sector $LMN$
How to find the area of a sector with central angle $\theta$ in a circle with radius $r$?The area of a sector with central angle $\theta$ in a circle with radius $r$ is given by:
$A = \frac{\theta}{360^\circ} \pi r^2$
In this case, we know that $m\angle LMN = 66^\circ$ and $LM = 19$ units, so the radius of circle M is half of the diagonal of the rectangle formed by $LM$ and $MN$. Using the Pythagorean theorem, we can find the length of $MN$:
$MN^2 = LM^2 + LN^2 = LM^2 + LM^2 = 2LM^2$
$MN = \sqrt{2} LM = \sqrt{2} \cdot 19$
So the radius of circle M is $r = \frac{1}{2}MN = \frac{1}{2}\sqrt{2} \cdot 19$
Now we can use the formula for the area of a sector to find the area of sector $LMN$:
$A = \frac{m\angle LMN}{360^\circ} \pi r^2 = \frac{66^\circ}{360^\circ} \pi \left(\frac{1}{2}\sqrt{2} \cdot 19\right)^2 \approx \boxed{90.89}$ square units (rounded to the nearest hundredth).
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In a regular tiling, if there are six polygons meeting at a vertex, then the angles at the vertex are _____ degrees
In a regular tiling, if there are six polygons meeting at a vertex, then the angles at the vertex are 120 degrees.
This is because each regular polygon has interior angles that are multiples of 180 degrees divided by the number of sides. For a regular hexagon, which has six sides, each interior angle measures 120 degrees. When six regular hexagons meet at a vertex in a regular tiling, the total angle sum at the vertex is 720 degrees (6 times 120 degrees).
Since the angles must be divided equally among the six hexagons, each angle at the vertex is 120 degrees.
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Solve the following diamond problem by finding the answers that would go in box 1 and box 2
20x?
sot
box2
-9x
box 1 =
box 2 =
Answer:
Step-by-step explanation:
The missing numbers are: box 1 = -5x and box 2 = 4sot, A diamond problem is a type of math puzzle that involves finding two missing values in a diamond-shaped diagram.
The top and bottom numbers of the diamond represent a product, and the left and right sides represent two numbers that add up to a middle value. The goal is to find the two missing values that fit into the diamond.
To solve a diamond problem, we need to factor the product of the top and bottom numbers and look for two factors whose sum is equal to the middle value. This is because the product of two numbers can only be made up of factors that multiply together to form the product. Once we find the two factors, we can insert them into the left and right sides of the diamond.
In the given diamond problem, we have 20x? as the top and sot as the bottom. The product of these two numbers is 20x^2sot. To find the factors, we can list all the possible factor pairs of this product and check which of them adds up to -9x, which is the middle value in the diamond. We found that -5x and 4sot are the factors that add up to -9x.
Solving diamond problems can help improve factoring skills and problem-solving abilities. It requires logical thinking and an understanding of how factors and multiples work. Additionally, diamond problems can be used to introduce algebraic concepts to students in a visual and intuitive way, making them a useful tool for teaching math to learners of all ages.
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Find the missing side lengths. leave your answers as radicals in simplest form. show your work to support your answer.
The value of the missing side lengths a and b of the right angles triangle are 2 and √2 respectively.
A right-angled triangle's other angle must be 45 degrees because the base angle is that number. The third angle in a triangle must be 90 degrees since the sum of the triangle's three angles is 180 degrees.
Using trigonometric ratios, we know that,
sin(45) = 2√2/a and,
cos(45) = b/a.
Simplifying, we get,
a = 2√2/sin(45)
= 2√2/√2
= 2 and,
b = a cos(45)
= 2 cos(45)
= √2.
Therefore, the value of a is 2 and the value of b is √2.
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The table shows the daily low temperature in Oymyakon for the first five days of
January, 2020.
Date:
January 1 January 2 January 3 January 4 January 5
Low temperature:
-42°F
-31°F
-40°F
-40°F
-44°F
What is the mean of the temperatures shown?
The mean of the temperatures shown is -39.4°F.
What is the mean temperature?
The average mean air temperature throughout a specific time period, typically a day, a month, or a year, as measured by a thermometer that has been properly exposed. The mean temperature is often calculated for the year and for each month in climatological tables.
Date: Low temperature:
January 1 -42°F
January 2 -31°F
January 3 -40°F
January 4 -40°F
January 5 -44°F
Mean = Total sum of all 5 days temperature / total number of days
Mean = -42 - 31 - 40 - 40 - 44 / 5
= -197 / 5
= - 39.4°F
Hence, the mean of the temperatures shown is -39.4°F.
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HELP ON MATH ASAPPP I NEED TO PASS
I think it might be C
At a mountain village in papúa new guinea it rains on average 6 days a week. Determine the probability of rains on two successive days
Answer:
36/49.
Step-by-step explanation:
Probability if rains on one day = (6/7)
Probabiilty it rains the next day also
= 6/7 * 6/7
= 36/49.
Three vertices of parallelogram wxyz are w(-5,2), x(2,4), and z(-7, -3). find the coordinates of vertex y.
the coordinates of vertex y are
Coordinates of vertex y are (-12,-1).
How to find the coordinates of vertex Y?To find the coordinates of vertex y in parallelogram WXYZ, we can use the fact that opposite sides of a parallelogram are parallel. We can use this property to find the coordinates of y by first finding the vector between points X and Z, and then adding that vector to the coordinates of point W.
The vector between points X and Z is (-7-2,-3-4)=(-9,-7). Adding this vector to the coordinates of point W gives (-5-9, 2-7)=(-14,-5). Therefore, the coordinates of vertex Y are (-14,-5).
Hence, the coordinates of vertex Y in the parallelogram WXYZ are (-14, -5).
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Let w = 2xy + y2 - 4x2, += st, y=,= Compute Bu (1.-3) - 88 -(1, -3)
To compute Bu(1.-3) - 88 - (1, -3), we need to substitute the values of u and v into the expression for w.
First, we need to find the values of u and v. Since u = 1.-3 and v = (1, -3), we have:
u = 1.-3 = 1 - 0.3 = 0.7
v = (1, -3)
Next, we can substitute these values into the expression for w:
w = 2xy + y^2 - 4x^2
= 2(1)(-3) + (-3)^2 - 4(1)^2 (substituting x = 1 and y = -3)
= -6 + 9 - 4
= -1
Finally, we can compute Bu(1.-3) - 88 - (1, -3) by multiplying the gradient of w by the vector (1, -3) and subtracting 88:
Bu(1.-3) - 88 - (1, -3) = (-8x + 2y, 2x + 2y) (1, -3) - 88
= (-8(1) + 2(-3), 2(1) + 2(-3)) (1, -3) - 88
= (-14, -4) (1, -3) - 88
= (-14)(1) + (-4)(-3) - 88
= -14 + 12 - 88
= -90
Therefore, Bu(1.-3) - 88 - (1, -3) = -90.
Since the question seems to have some typos or missing information, I'll assume you want to find the partial derivatives of w with respect to x and y, and evaluate them at the point (1, -3).
Given w = 2xy + y² - 4x², let's compute the partial derivatives:
∂w/∂x = 2y - 8x
∂w/∂y = 2x + 2y
Now, let's evaluate these partial derivatives at the point (1, -3):
∂w/∂x(1, -3) = 2(-3) - 8(1) = -6 - 8 = -14
∂w/∂y(1, -3) = 2(1) + 2(-3) = 2 - 6 = -4
Thus, the evaluated partial derivatives are ∂w/∂x(1, -3) = -14 and ∂w/∂y(1, -3) = -4.
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How many outcomes are there in a 5 digit license plate if the first 2 digits must be letters and the last 3 digits are numbers?
The letters and numbers can be repeated.
100
B 260
676,000
D 1,757,600
I seriously need help with this please anyone.
1. Complete the Pythagorean triple. (24,143, ___)
2. Given the Pythagorean triple (5,12,13) find x and y
3. Given x=10 and y=6 find associated Pythagorean triple
4. Is the following a possible Pythagorean triple? (17,23,35)
Answer:
no it is not possible
Step-by-step explanation:
without the addition of fertiliser, the annual crop from a potato farm would only be 80% of the previous years crop. a farm produced 15 tonnes of potatoes in its first year of production. assume that no fertiliser is used. give answers correct to two decimal places where necessary. list the size of the potato crop for each of the first four years
The crop sizes for first 4 years without using fertilisers are:
15 tonnes12 tonnes9.6 tonnes7.68 tonnes.What is the size each of the first 4 years?The size of the potato crop for each of the first four years is computed as follows:
For Year 1:
= 15 tonnes * 1
= 15 tonnes
For Year 2:
= 15 tonnes x 0.8
= 12 tonnes
For Year 3:
= 12 tonnes x 0.8
= 9.6 tonnes
For Year 4:
= 9.6 tonnes x 0.8
= 7.68 tonnes
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Let and be two ordered bases of , and consider a linear transformation. Suppose that the change of base matrix is given by and the coordinate matrix of with respect to is given by use this to determine coordinate matrix of with respect to.
The coordinate matrix of the linear transformation with respect to the second ordered basis is found by multiplying the change of basis matrix by the coordinate matrix of the linear transformation with respect to the first ordered basis is [tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]
Let V be a vector space with two ordered bases B and B', and let T be a linear transformation from V to V. Suppose that the change of basis matrix from B to B' is P, and the coordinate matrix of T with respect to B is A.
To find the coordinate matrix of T with respect to B', we can use the formula
A' = P⁻¹AP
where A' is the coordinate matrix of T with respect to B'.
To use this formula, we need to find the inverse of P. If P is invertible, then we have
P⁻¹ = 1/det(P) * adj(P)
where det(P) is the determinant of P and adj(P) is the adjugate of P.
Assuming that P is invertible, we can compute its inverse as follows
det(P) = 1*(-2) - 2*2 = -5
adj(P) =[tex]\left[\begin{array}{cc}-2&2\\-2&1\end{array}\right][/tex]
So, P⁻¹ = (-1/5)*[tex]\left[\begin{array}{cc}-2&2\\-2&1\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}2/5&-2/5\\2/5&-1/5\end{array}\right][/tex]
Now, we can use the formula to find the coordinate matrix of T with respect to B'
A' = P⁻¹AP = *[tex]\left[\begin{array}{cc}-2&1\\-1&0\end{array}\right][/tex]*[tex]\left[\begin{array}{cc}-1&2\\2&1\end{array}\right][/tex]= [tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]
Therefore, the coordinate matrix of T with respect to B' is
[tex]\left[\begin{array}{cc}0&2/5\\1&-1/5\end{array}\right][/tex]
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--The given question is incomplete, the complete question is given
" Using change of base matrices to find coordinate matrices of linear transformations Let B and C be two ordered bases of R2, and consider a linear transformation T: R2 + R2. Suppose that the change of base matrix Ic, B is given by [0 -2 3 3] and the coordinate matrix Tc,c of T with respect to C is given by [ -1 -1 2 -1] Use this to determine coordinate matrix TB,B of T with respect to B. TB,B ? "--
How many dollars worth of food is wasted in America each day?
How many additional people could survive eating the food that is thrown away?
Around $441 million worth of food is wasted in the US each day.
How much food is wasted in the USA each day?According to the United States Department of Agriculture (USDA), about 30-40 percent of the food supply in the United States goes to waste. In terms of dollars, that translates to approximately $161 billion worth of food being wasted each year in the United States.
Dividing that number by 365, we can estimate that around $441 million worth of food is wasted in the US each day.
It's difficult to estimate how many people could be fed with the food that is thrown away, as food waste can take many forms, such as uneaten meals at restaurants, spoiled produce at grocery stores, and expired food in households. However, according to Feeding America, a national food bank network, approximately 42 million Americans, including 13 million children, are food insecure, which means they lack reliable access to affordable, nutritious food.
If we assume that all the food that is currently being wasted in the US could be redistributed to those who are food insecure, it could potentially feed a significant number of people. However, in reality, the logistics of collecting, storing, and distributing food waste can be complex, and some food waste may not be safe or nutritious to eat. Additionally, addressing food waste is just one piece of the puzzle in addressing food insecurity, which is a complex issue with many underlying factors.
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