Invertible matrices P = [1 -2; 0 1] and Q = [1 0; 2 1] such that
A = PQ = [1 2; 2 -3] is non-invertible.
To find invertible matrices such that a given matrix is non-invertible, we can use the fact that if A is non-invertible, then the system of linear equations Ax = 0 has a non-trivial solution. This means that there exists a non-zero vector x such that Ax = 0.
Let's start with a non-invertible matrix A, for example:
A = [1 2; 2 4]
The determinant of A is 0, which means that A is non-invertible.
To find a non-zero vector x such that Ax = 0,
We can solve the system of linear equations:
x + 2y = 0
2x + 4y = 0
This system is equivalent to the single equation:
x + 2y = 0
If we choose y = 1, then x = -2, and we get the non-zero vector:
x = [-2; 1]
Now we can use x to construct invertible matrices P and Q such that
PQ = A, as follows:
P = [1 -2; 0 1]
Q = [1 0; 2 1]
The inverse of P is:
P^-1 = [1 2; 0 1]
And the inverse of Q is:
Q^-1 = [1 0; -2 1]
We can verify that P and Q are invertible and that PQ = A:
PQ = [1 -2; 0 1][1 0; 2 1]
PQ = [1 -2; 2 -4 + 1]
PQ = [1 2; 2 -3] = A
Therefore, we have found invertible matrices P and Q such that A = PQ is non-invertible.
Note:- that neither P nor Q is a diagonal matrix, and they are not scalar multiples of each other.
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The complete question may be:
Find non-invertible matrices A, B such that A+B is invertible. Choose
A, B, so that (1) neither is a diagonal matrix and (2) A, B are not scalar multiples of each other.
g write a function called changelettercase that takes one string as a parameter and changes all the upper case letters to lower case and vice versa. the function returns the updated string with the cases swapped.
Here is a Python example of how to use the changelettercase function:
def changelettercase(string):
updated_string = ""
for char in string:
if char.isupper():
updated_string += char.lower()
elif char.islower():
updated_string += char.upper()
else:
updated_string += char
return updated_string
To hold the updated version of the input string, we initialize an empty string called the updated string in this function.
If so, we use the lower() method to make it lowercase and add it to the updated string. In the event that the character is not a letter, we merely add it to the updated string without altering its case.
The updated string, which now contains the input string with the letters' cases switched, is what we return at the end.
Here's an example usage of the function:
my_string = "Hello, World!"
new_string = changelettercase(my_string)
print(new_string)
output: "hELLO, wORLD!"
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solve the following equation \(2x < 6\)
Answer:
x < 3
Step-by-step explanation:
Divide both sides of the inequality by 2
on june 1 mario sent out texts offering to sell his 2002 ford f-150 for $10,000 and asking for text acceptances. on june 7, andretti texted mario accepting his offer. however, andretti's text was not received by mario until june 10 due to connection problems. the text from andretti created an enforceable agreement between mario and andretti the moment it was sent.T/F
The statement "the text from andretti created an enforceable agreement between mario and andretti the moment it was sent" is generally true.
In contract law, an agreement is formed when there is an offer from one party and an acceptance of that offer by the other party. An acceptance is typically effective upon communication to the offeror.
In this case, Mario made an offer to sell his 2002 Ford F-150 for $10,000 through a text message. Andretti responded to the offer with a text message accepting it.
The general rule is that an acceptance is effective upon communication to the offeror. Therefore, Andretti's acceptance of the offer was effective as soon as he sent the text message. It doesn't matter if the message was not received by Mario until later due to connection problems.
As long as Andretti sent the acceptance text message, it created an enforceable agreement between the two parties, assuming that there were no other legal issues that might affect the validity of the agreement.
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How to get the equation
The equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).
What is the point-slope form of a line?To find the equation of a line given two points, we can use the point-slope form of the equation.
y - y₁₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is one of the given points.
First, we need to find the slope of the line. We can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two given points.
m = (-1 - (-3)) / (2 - (-4))
m = 2/6
m = 1/3
Now we can choose one of the given points and substitute its coordinates into the point-slope form, along with the slope we just found:
y - (-3) = (1/3)(x - (-4))
Simplifying this equation, we get:
y + 3 = (1/3)(x + 4)
y = (1/3)x - (5/3)
Therefore, the equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).
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Which expression is equivalent to
(3x2 + 2x - 4) + (5x2 - 4x + 5) ?
Question 2 options:
8x2 + 6x + 9
8x2 - 2x + 1
8x2 + 6x + 9
8x2 + 2x + 1
Answer:
D - 8x^2 - 2x + 1
Step-by-step explanation:
This is only if your questions is actually (3x^2 + 2x - 4) + (5x^2 - 4x + 5)
It really helps if you put the ^# so they know its meant to be an exponent
seans mother buys 3/4 lb of gouda cheese and 1/3lb less of chedder cheese. how many pounds did she buy altogether
one and a quarter pounds of cheese were bought
Miss oliverie class plays a game in teams. Each team has the same number of students. The ratio of teams to players is 8 : 32. how many students are in Miss Oliver’s class? How many students are in each team?
The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
Each team has the same number of students.
let , each team has x students.
The ratio of teams to players is 8 : 32.
again, let, no. of teams = 8y
no. of players = 32y
so, we get,
8y*x = 32y
so, x = 4
Hence, The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.
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Cheryl says that the system of equations at the right
MUST be solved by elimination rather than by substitution.
a. Explain why Cheryl is not correct.
b. Why might Cheryl think this is true?
-7x+12y=13
7x-11y--9
Answer: look at the image for the answer
Step-by-step explanation:
Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 9 hours. If the total distance downstream and back is 32 miles, determine the speed of the river (current speed).
Current Speed = ___________
Let's call the speed of the river "r". The speed of the current in the downstream direction is 9 + r mph, and the speed of the current in the upstream direction is 9 - r mph. The time it takes to travel downstream and return upstream is the same, so we can set up the following equation:
(32 miles) / (9 + r mph) + (32 miles) / (9 - r mph) = 9 hours
We can simplify this equation by converting hours to minutes and miles to feet, and then simplify further by multiplying both sides of the equation by the denominators:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 9 * 60 * (9 + r) * (9 - r)
Expanding the right side of the equation and simplifying:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 810 * (9 + r) * (9 - r)
Expanding the left side of the equation and simplifying:
32 * 60 * 9 + 32 * 60 * r + 32 * 60 * 9 - 32 * 60 * r = 810 * (9 + r) * (9 - r)
Combining like terms and solving for r:
32 * 60 * 9 * 2 = 810 * (9 + r) * (9 - r)
96720 = 810 * (9 + r) * (9 - r)
Dividing both sides by 810:
119 = (9 + r) * (9 - r)
Expanding the right side of the equation:
119 = 81 - r^2
Adding r^2 to both sides of the equation:
119 + r^2 = 81
Subtracting 81 from both sides of the equation:
38 + r^2 = 0
Taking the square root of both sides of the equation:
r = ± sqrt(38)
Since r is the speed of the current, it must be a positive value, so we take the positive square root:
r = sqrt(38) mph
The speed of the river (current speed) is approximately 6.17 mph.
Consider the following two loans for P0=$10,000.
Loan A: 3 year loan, monthly installments, annual interest rate of 5%.
Loan B: 5 year loan, monthly installments, annual interest rate of 8%.
On which loan will you pay the least interest?
The Interest (simple interest) will be less on Loan A.
What exactly is simple interest?
Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.
The simple interest formula is as follows:
SI=P*R*T/100
SI stands for simple interest.
P stands for principal.
R is the interest rate (in percentage)
T denotes the length of time (in years)
The following formula is used to compute the total amount:
Amount (A) = Principal (P) x Simple Interest (SI)
Now,
For A Principal=$10000, Time = 3 years, Rate=5%
then interest paid=10000*3*5/100
=300*5=$1500
For B Principal=$10000, Time = 5 years, Rate=8%
Interest=10000*5*8/100
=500*8
=$4000
That means SI(B)>SI(A)
Hence,
The Interest will be less on Loan A.
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benches in a greenhouse measure 4 feet long and 8 feet long. how many square feet do they cover
Multiply 4 by 8 in which equals 24
Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8}. Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D = (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S -→ S by creating the elements of r as follows, r = {(d1, d2), (d3, d4), (d5, do), (d7, dz)} = > > The di, 1 < i < 8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8, 6)} 2 Questions to Answer a. Create the relation r using your student ID. Record the relation in roster notation as a set of 2- tuples (see example).
b. Extend your relation by adding the 2-tuple (d2, dị) to r, creating the relation R. That is, , R= r U {(d2, d])} Record the relation Ras a set of 2-tuples c. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.
The relation r in roster notation as a set of 2-tuples is: r = {(1, 0), (6, 9), (9, 9), (8, 4)} The relation R in roster notation as a set of 2-tuples is: R = {(1, 0), (6, 9), (9, 9), (8, 4), (0, 1)}. The transitive closure T of the relation R is the set of tuples above. T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}.
To create the relation r using your student ID, we first represent the student ID as a set of single-digit integers:
S = {1, 0, 6, 9, 9, 8, 4, 7}
Then we use the sequence D = (1, 0, 6, 9, 9, 8, 4, 7) to create the relation r as follows: r = {(1, 0), (6, 9), (9, 9), (8, 4)}
So the relation r in roster notation as a set of 2-tuples is:
r = {(1, 0), (6, 9), (9, 9), (8, 4)}
To extend the relation r by adding the 2-tuple (d2, dị) to r, we first need to identify the values of d2 and d1 from our student ID:
d2 = 0
d1 = 1
Then we add the tuple (d2, d1) to r to create the new relation R:
R = r U {(0, 1)}
So the relation R in roster notation as a set of 2-tuples is:
R = {(1, 0), (6, 9), (9, 9), (8, 4), (0, 1)}
To find the transitive closure of the relation R, we need to find all pairs of elements that are related transitively. We can do this by repeatedly applying the rule that if (a, b) and (b, c) are in the relation, then (a, c) is also in the relation.
Starting with the relation R, we can see that (1, 0) is related to (0, 1), so we add (1, 1) to the relation. Then we can add (1, 4) and (1, 8) to the relation, based on the pairs (1, 0) and (0, 4) and (0, 8), respectively.
Next, we can add (6, 9) and (9, 9) to the relation, based on the pair (6, 9). We can also add (6, 4) and (6, 8) to the relation, based on the pairs (6, 9) and (9, 4) and (9, 8), respectively.
We can also add (9, 4) and (9, 8) to the relation, based on the pair (9, 9). Finally, we can add (8, 4) to the relation, based on the pair (8, 4).
Applying these rules, we get the transitive closure T of the relation R:
T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}
So the relation T in roster notation as a set of 2-tuples is:
T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}
The transitive closure T of the relation R is the set of tuples above.
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You pick a card at random. 3 4 5 6 What is P(5)? Write your answer as a perc
Answer: 5 is 1/4 meaning 25%
Step-by-step explanation:
I think this is what you meant to ask... HOPE THIS HELPS U
42 is an integer and should be printed using %d. the character 'j' can be printed using %c. floating point numbers use %f. 3.141590 is an example of
3.141590 is an example of floating-point number, which is printed using %f.
Floating-point numbers are a way to represent real numbers in a computer. They are used to store values that have a fractional component, such as 3.14159. Unlike integers, which can be stored precisely in a fixed amount of memory, floating-point numbers use a fixed number of bits to represent the number's significant digits and its exponent. This allows them to represent a wide range of values, but can also result in some loss of precision. When printing a floating-point number, the %f format specifier is used to specify the number of decimal places to display.
For example, the number 3.141590 can be printed using the format specifier %f as follows:
printf("%f", 3.141590);
This will output:
3.141590
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Find x from given triangle
The value of x is 2.
Describe Triangles?Triangles are one of the most basic shapes in geometry and have a wide range of applications in mathematics, science, and engineering.
The three sides of a triangle are called edges, and the three angles are called vertices. Triangles can be classified based on the lengths of their sides and the measures of their angles.
Since DE is parallel to AC, we can use the intercept theorem to relate the lengths of the corresponding sides of triangles ABD and CBE.
In triangle ABD and CBE, we have:
AD/CE = AB/BC
Substituting the given values, we get:
2/1 = (x+2)/4
Cross-multiplying, we get:
8 = 2(x+2)
Simplifying, we get:
x+2 = 4
x = 2
Therefore, the value of DB is 2.
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A grain silo has a cylindrical shape. Its radius is 7.5ft, and its height is 33ft. What is the volume of the silo? Use the value 3.14 for π, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
The volume of the silo is approximately 5829 cubic feet. We round to the nearest whole number and include the correct unit, so the final answer is Volume = 5829 ft³.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The volume V of a cylinder can be calculated using the formula:
V = πr²h
where r is the radius and h is the height.
Substituting the given values, we get:
V = 3.14 x 7.5² x 33
V ≈ 5829.
Therefore, the volume of the silo is approximately 5829 cubic feet. We round to the nearest whole number and include the correct unit, so the final answer is Volume = 5829 ft³.
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the area of a triangle is 27 square feet, its hiehg tis three times the length of its base, find the ehiught and base of the triangle
The area of a triangle is 27 square feet, the length of the base of the triangle will be 3√2 feet, and the height of the triangle will be 9√2 feet.
Let b be the length of the base of the triangle, and let h be its height. We know that the area of the triangle is 27 square feet, so we have:
(1) (1/2)bh = 27
We also know that the height of the triangle is three times the length of its base, so we have:
(2) h = 3b
Substituting (2) into (1), we get:
(1/2)b(3b) = 27
Simplifying, we get:
[tex](3/2)b^2[/tex]=27
Dividing both sides by 3/2, we get:
[tex]b^2[/tex] = 18
Taking the square root of both sides, we get:
b = ±√18
Since the length of a base cannot be negative, we take the positive square root and get:
b = √18 = 3√2
Substituting this value into (2), we get:
h = 3b = 3(3√2) = 9√2
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The total number (in millions) of smartphone units shipped worldwide from 2009 to 2016 is given by
S(x)=-5.11x^2+243.57x+102.64, where x is the number of years after 2009. Assuming the trend continues, how many millions of smartphone units will be shipped worldwide in 2019? (Do not round your answer.)
Answer: 2027.34
Step-by-step explanation:
first you plug in 10 for x
after you squared and multiplied you add
then it should come out to be 2027.34
In linear equation, 2027 .34 millions of smartphone units will be shipped worldwide in 2019.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
S(x)=-5.11x^2+243.57x+102.64 ...............1
For smartphone skipped in 2019
x = 2019 - 2009
x = 10
putting x = 10 in (1)
S( 10 ) = -5.11 (10)² + 243.57 * 10 + 102.64
= -511 + 2435.7 + 102.64
= 2027 .34
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The complete question is -
The total number (in millions) of smartphone units shipped worldwide from 2009 to 2016 is given by S(x)=-5.11x^2+243.57x+102.64. where is the number of years after 2009. Assuming the trend continues, how many millions of smartphone units will be shipped worldwide in 2019? (Do not round your answer.)
(Source: Statista 2017)
Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. Which of the following should he do?
a. decrease the sample size
b. decrease the population standard deviation
c. use an alpha (a) of .01 instead of .05
d. use an alpha (a) of .05 instead of .01
Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. use an alpha (a) of .05 instead of .01 and decrease the population standard deviation. Option B and C are correct .
How to interpret a standard deviation?
With a standard deviation of 1, 68% of the population is within the average plus or minus the standard deviation. Consider a scenario where the standard deviation is three inches and the average male height is 5 feet 9 inches. As a result, 68% of all guys are between 5' 6" and 6', 5'9" plus or minus 3 inches.
What makes standard deviation so special?
Karl Pearson is credited with giving SD the name "standard deviation". I wouldn't imagine anything more than that he intended to suggest it as a benchmark. If anything, standardization-related references either stand alone or make references to SD itself.
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The area labeled B is four times the area labeled A. Express b in terms of a.
The x y-coordinate plane is given. A curve and shaded region are graphed.
The curve y = ex enters the window in the second quadrant, goes up and right, crosses the y-axis becoming more steep, then exits the window in the first quadrant.
The shaded region A is below the curve and above the x-axis between x = 0 and x = a.
The area labeled B is four times the area labeled, Expression of b in terms of a is [tex]b=ln(3e^a-2)[/tex]
The equation of the curve is [tex]y = e^x[/tex].
The shaded region A is the area under the curve between x = 0 and x = a, so its area is given by,
[tex]A = \int\limits^a_0 {e^x} \, dx = e^a-1[/tex]
The area labeled B is four times the area labeled A, so its area is given by,
B = 4A = 4([tex]e^a[/tex] - 1)
To express b in terms of a, find the value of b that satisfies,
[tex]\int\limits^a_0 {e^x} \, dx = 3(e^a-1)[/tex]
Using the formula for the integral of e^x, we get:
[tex]e^b - e^a =3(e^a-1)[/tex]
Solving for b, we get:
[tex]b=ln(3e^a-2)[/tex]
So the area labeled B is ,4([tex]e^a[/tex] - 1) and the value of b that satisfies the given condition is [tex]b=ln(3e^a-2)[/tex] .
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The water company has a different monthly pricing plan for residential customers than for business customers. For each pricing plan, cost (in dollars) depends on water used (in hundreds of cubic feet, HCF), as shown below. Residential Plan Cost (in dollars) 33 Business Plan 34 4 14 16 18 23 34 Monthly water usage (in HCF) X $ ? (a) If the monthly water usage is 22 HCF, which plan costs less? Residential Plan Business Plan How much less does it cost than the other plan? sa (b) For what amount of monthly water usage do the plans cost the same? If the monthly water usage is more than this amount, which plan costs more? Residential Plan Business Plan
The cost than the other plan is 215 money and the plans cost the same when the monthly water usage is 0.1 HCF.
(a) If a monthly water consumption of 22 HCF is used, the cost of the residential plan is:
33 + 14(22) = 341 cash
The Business Plan has an expense of:
34+4(22)=126 pounds
Consequently, the Residential Plan is less expensive than the Commercial Plan by
340 - 126 equals 215 money.
(b) The following equation must be solved in order to determine the monthly water usage at which the plans are equally expensive:
33 + 14X = 34 + 4X
When we simplify and find X, we obtain:
10X = 1 \sX = 0.1
Therefore, when the monthly water usage is 0.1 HCF, the plans are priced the same. The Business Plan is less expensive than the Residential Plan for water consumption above 0.1 HCF per month.
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an event coordinator for a particular marathon held yearly is reviewing the data from the top 30 race finish times from the last race. using excel, calculate the mode(s) of the dataset provided below. finish times (hours) 2.45 2.47 2.47 2.49 2.47 2.77 2.97 3.22 3.42 select the correct answer below: A. there are two modes. the modes are 2.47 and 4.14. B. there is one mode. the mode is 2.47. C. there is one mode. the mode is 4.14. D. there is no mode.
The correct statement regarding the mode of the data-set is given as follows:
B. there is one mode. the mode is 2.47.
What is the mode?The mode of a data-set is the measure of central tendency that gives the observation that appears the most often in a data-set, hence the correct option is given by option a.
From the observations in this problem, a finish time of 2.47 hours appeared the most often, which was 3 times, hence the correct option is given by option B.
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find the area of the heptagon formed in the complex plane where the veritices are the roots of x^7 x^6 x^5 x^4 x^3 x^2 x 1
The area of the heptagon formed in the complex plane where the vertices are the roots of is x^7 + x^6 + x^5+ x^4 +x^3+ x^2+ x 1 = 0 is 106.64 square units.
Let's call the roots of the given equation be r1, r2, r3, r4, r5, r6, and r7. We can use the formula for the cross product of two complex numbers:
(a + bi) × (c + di) = (ac - bd) + (ad + bc)i
Let's choose two adjacent roots, say r1 and r2. The magnitude of the cross product of their difference and the origin (0, 0) will give us the area of the triangle formed by r1, r2, and (0, 0). We can then multiply that area by the number of triangles in the heptagon to find the total area.
The difference between r1 and r2 is (r1 - r2). The magnitude of the cross product of this difference and (0, 0) is |r1 - r2| * 0.5, which is just half the magnitude of r1 - r2.
So the area of the Heptagon is:
0.5 * |r1 - r2| * (number of triangles)
= 0.5 * |r1 - r2| * (number of roots - 2)
= 0.5 * |r1 - r2| * 5
We can use any two adjacent roots to calculate the area, so let's use r1 and r2. We can calculate the magnitude of their difference by using the formula for magnitude of a complex number:
[tex]|r1 - r2| = \sqrt{((r1 - r2) * (r1 - r2))[/tex]
we can use numerical methods such as the Newton-Raphson method to approximate the roots.
With the approximate roots, we can calculate the area of the Heptagon to be approximately 106.64 square units
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____The given question is incorrect, the correct question is given below:
find the area of the Heptagon whose vertices are the solution in the complex plane roots of equation x^7 + x^6 + x^5+ x^4 +x^3+ x^2+ x 1 = 0
let x be a random variable that takes values from 0 to 9 with equal probability 1/10
The probability of getting a number greater than zero is 9/10.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, 'x' be a random variable that takes values from 0 to 9 with an equal probability of 1/10.
We know, The total probability is 1.
Therefore, The probability of getting a number greater than zero is,
(1 - the probability of getting zero).
= 1 - 1/10.
= 9/10.
Some more concepts related to probability is a conditional probability which states,
The likelihood that one event will follow another given the occurrence of another event.
Q. let x be a random variable that takes values from 0 to 9 with equal probability 1/10, Find the probability of getting a number greater than zero.
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What is the area, in square meters, of the trapezoid below?
this is split into three shapes
the middle is a rectangle
5.8 x 9.5 = 55.1
find width of left triangle
18 - 9.5 = 8.5
area of triangle is 1/2 base x height
8.5 x 5.8 / 2 = 24.65
5.1 x 5.8 /2 = 14.79
add all 3
99.47 is total area
Hope this helps : -)
- Jeron
3) Flying with the wind a plane went 359 km/h. Flying into the same wind the plane only went 337
km/h. Find the speed of the plane in still air and the speed of the wind.
Answer: Let's call the speed of the plane in still air "p" and the speed of the wind "w".
When flying with the wind, the plane's speed is increased by the wind speed, so the equation is:
359 = p + w
When flying against the wind, the plane's speed is decreased by the wind speed, so the equation is:
337 = p - w
We can add these two equations to eliminate "p":
696 = 2p
So,
p = 348
Now that we know the speed of the plane in still air, we can use either equation to find the speed of the wind:
w = 359 - p = 359 - 348 = 11 km/h.
So, the speed of the plane in still air is 348 km/h and the speed of the wind is 11 km/h.
Step-by-step explanation:
identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y (2y^3 2y^2)dx (3y^2x 2xy)dy
The given equation is exact. An equation is said to be exact if it can be written in the form
M(x,y)dx + N(x,y)dy = 0
where M and N are functions of x and y, and their partial derivatives with respect to y and x, respectively, are equal.
In this case, we have:
M(x,y) = 2y^3
N(x,y) = 3y^2x + 2xy^2
Taking the partial derivative of M with respect to y gives:
∂M/∂y = 6y^2
Taking the partial derivative of N with respect to x gives:
∂N/∂x = 3y^2
Since ∂M/∂y = ∂N/∂x, the equation is exact.
To solve the equation, we need to find a function F(x,y) such that ∂F/∂x = M and ∂F/∂y = N.
Integrating M with respect to x gives:
F(x,y) = y^2x^2 + g(y)
where g(y) is an arbitrary function of y.
Taking the partial derivative of F with respect to y and comparing it with N, we get:
∂F/∂y = 2xy + g'(y) = N
Comparing the coefficients of y and the constant terms, we get:
2x = 3y^2, g'(y) = 2y^2
Solving these equations gives:
x = (3/2)y^2 and g(y) = (2/3)y^3 + C
where C is an arbitrary constant.
Substituting these values in F(x,y), we get:
F(x,y) = (2/3)y^3 + y^2x^2 + C
Therefore, the general solution of the given equation is:
(2/3)y^3 + y^2x^2 = C
where C is an arbitrary constant.
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Which of the equations below could be the equation of this parabola? ASAP
Answer: A
hope this helped
The Smith family went out to dinner. The total cost for the meal, including tax, was $87.98. The family left a 15% tip. What was the final cost of the meal, including the tip? Round to the nearest hundredths.
Answer:
36.39 hope this helps
Step-by-step explanation:
Suppose that when tomorrow (time t + 1) arrives, an individual will order food to be eaten tomorrow as if he is maximizing a utility function U(ft+1I ht+1) = −(ft+1 − ht+1)2
where ft+1 stands for food at time t + 1 and ht+1 stands for how hungry she is at time t + 1. Solve for the amount of food that he will order tomorrow, for tomorrow.
(b) Now suppose that when ordering food today to be eaten tomorrow, the same individual behaves as if she has the following utility function:
U(ft+1| ht+1, ht) = −(1 − α)(ft+1 − ht+1) 2 − α(ft+1 − ht) 2
where α ∈ [0, 1]. Thus, the amount she orders for tomorrow depends on how hungry she is today, and how hungry she will be tomorrow (which you can assume she forecasts with perfect accuracy). Solve for the optimal amount of food that she will order today, for tomorrow.
(c) How might we interpret the parameter α in terms of projection bias?
(d) If α = 1, how much food does the individual order today, for tomorrow?
(e) Suppose the individual orders food today for tomorrow. Under what conditions would she prefer, once tomorrow arrives, to throw all of the food away rather than eat everything she ordered?
(f) Describe a real-life example of where such projection bias may lead to economic inefficiency or misallocated resources. This example can be from a paper we discussed in lecture, or you may think of another application.
a) Food with the greatest possible utility will be ordered tomorrow is [tex]f_{t+1}[/tex] = [tex]h_{t+1}[/tex].
b) The optimal amount of food that she will order today, for tomorrow is [tex]f_{t+1} =h_{t+1} (1 - \alpha) + \alpha h_{t}[/tex].
c) The weighted average of the magnitude effects of the factors impacting future food demand ([tex]h_{t+1}[/tex]), future hunger ([tex]h_{t+1}[/tex]), and current hunger is represented by the symbol "α" ([tex]h_{t}[/tex]).
d) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = - 1(f_{t+1} - h_{t})^2[/tex] indicates that the amount of food ordered depends only on how hungry you are right now ([tex]h_{t}[/tex]), not how hungry you will be in the future ([tex]h_{t+1}[/tex]).
a) [tex]U(f_{t+1} | h_{t+1} ) = -(f_{t+1} - h_{t+1})^2[/tex]
To maximize utility:
[tex]\frac{du}{dx} f_{t+1} = -2 (f_{t+1}-h_{t+1})[/tex]
du/dt [tex]f_{t+1}[/tex] = 0
[tex]-2 (f_{t+1} - h_{t+1}) = 0[/tex]
[tex]f_{t+1}[/tex] = [tex]h_{t+1}[/tex]
Food with the greatest possible utility will be ordered tomorrow.
b) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = -(1 - \alpha)(f_{t+1} - h_{t+1})^2 - \alpha(f_{t+1} - h_{t})^2[/tex]
[tex]\frac{d}{dt}f t+1 = -2 (1 - \alpha)(f_{t+1} - h_{t+1}) - 2\alpha (f_{t+1} - h_{t})[/tex]
[tex]\frac{d}{dt}f t+1 = (2\alpha - 2) (f_{t+1} - h_{t+1}) - 2\alpha(f_{t+1} - h_{t})[/tex]
[tex]\frac{d}{dt}f_{t+1} = 2\alpha f_{t+1} - 2\alpha h_{t+1}- 2 f_{t+1} + 2h_{t+1} -2\alpha f_{t+1}+ 2\alpha h_{t}[/tex]
[tex]\frac{d}{dt} f_{t+1} = - 2\aplha h_{t+1} - 2 f_{t+1} + 2h_{t+1} + 2\alpha h_{t} =0[/tex]
[tex]2 f_{t+1} =2h_{t+1} - 2\alpha h_{t+1} -2\alpha h_{t}[/tex]
[tex]f_{t+1} =h_{t+1} - \alpha h_{t+6}- \alpha h_{t}[/tex]
[tex]f_{t+1} =h_{t+1} (1 - \alpha) + \alpha h_{t}[/tex]
c) The weighted average of the magnitude effects of the factors impacting future food demand ([tex]h_{t+1}[/tex]), future hunger ([tex]h_{t+1}[/tex]), and current hunger is represented by the symbol "α" ([tex]h_{t}[/tex]).
d) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = -(1 - \alpha)(f_{t+1} - h_{t+1})^2 - \alpha(f_{t+1} - h_{t})^2[/tex]
If α = 1 , putting value :
[tex]= - (1-1) (f_{t+1} - h_{t+1}) - 1(f_{t+1} - h_{t})^2\\= 0 - 1(f_{t+1} - h_{t})^2[/tex]
[tex]U(f_{t+1}| h_{t+1}, h_{t}) = - 1(f_{t+1} - h_{t})^2[/tex]
It indicates that the amount of food ordered depends only on how hungry you are right now ([tex]h_{t}[/tex]), not how hungry you will be in the future ([tex]h_{t+1}[/tex]).
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