The Least-squares problem that has minimal norm can be given using factorization.
The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.
It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.
When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.
The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.
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what is the height of the flag pole?
Answer:
x = 135
Step-by-step explanation:
the 2 situations are similar with ratios of corresponding sides in proportion , that is
[tex]\frac{x}{54}[/tex] = [tex]\frac{90}{36}[/tex] ( cross- multiply )
36x = 54 × 90 = 4860 ( divide both sides by 36 )
x = 135
if sin(x y)=3x−2y, then dydx=
The derivative of the given function sin(xy)=3x−2y is obtained as;
dy/dx = 3sec(xy)/x - y/x
Explain the term differentiation?Differentiation is the process of separating something or someone from others. When you distinguish between two toothpaste brands, you draw attention to their differences. The word different is evident in differentiation.The given equation is-
sin(xy) = 3x − 2y
Be sure to account for both sides of this argument.
d/dx(sin(xy)) = d/dx(3x − 2y)
Differentiate the equation's left side.
Set the left side equal to a right side to reform the equation.
x.cos(xy).y' + y.cos(xy) = 3
Solve for y'.
y' = 3sec(xy)/x - y/x
Thus, replace y' with dy/dx
dy/dx = 3sec(xy)/x - y/x
Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;
dy/dx = 3sec(xy)/x - y/x
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What is the variable? -7+4x=5
Answer: x =3
Step-by-step explanation:
-7+4x=5
4x = 12
x =3
Answer:x=3 good luck You got this one
Step-by-step explanation:
-7+4x=5
Move the constant to the right-hand side and change its sign
4x=5+7
Add the numbers
4x=12
Divide both sides of the equation by 4
x=3
Which of the following functions is represented in the graph?
cosine graph with points at 0 comma 3, pi comma negative 5, and 2 times pi comma 3
f(x) = 4cos(2x) + 3
f(x) = 8cos(2x) + 3
f(x) = 4cos(x) − 1
f(x) = 8cos(x) − 1
The function represented in graph is f(x) = 4cos(x) - 1. We can find it by putting given points in following options and checking whether it is matching to graph or not (hit and trial method)
What are trigonometric functions?
6 trigonometric functions are Sine, Cosine, Tangent, Cotangent, Secant, Cosecant .
Cosine ranges from (-1 to 1) for x.
Given points are 0, pi, and 2pi
For 0 , cos(0)= 1
For pi, cos(pi) = -1
For 2pi, cos(2pi) = 1
In f(x) = 4cos(x)-1
For x = 0,
f(0)=4cos(0)-1
3 = 3 i.e. correct.
For x = pi
f(pi) = 4cos(pi)-1
-5 = -5 i.e. correct
also correct for 2pi.
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The drama club is selling tickets to their play to raise money for the shows expenses. Each student ticker sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations hat could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
The number of students is 30 while the number of adults will be 37.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Suppose the number of students ticker is x and the number of adults is y.
7x + 9y = total revenute
7x + 9y = 543
Total tickets = x + y
x + y = 67
Multiply the above equation by 9
9x + 9y = 603
Subtract equations as
7x + 9y - 9x - 9y = 543 - 603
-2x = -60
x = 30
And, y = 67 - 30 = 37
Hence "The number of students is 30 while the number of adults will be 37".
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PLEASE HELP!
The number of miles y varies directly with the number of hours x as shown in the graph. write a direct variation equation to represent this relationship. then identify the constant of variation and interpret it's meaning.
Answer:rise over rub
Step-by-step explanation:
Help me aspp please before 11:59
1. In the first and third tables, there is no direct relationship, in the third table, there is a direct relationship.
2. y = 5x,b = (1/2)a and m = 5n are direct variation.
3. The constant of proportion is 5 and x when y is 49 will be 8.8
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
1.
(a) In the table x/y = -4/-8 = 1/2 is not maintained in 6/18 so it will not direct variation.
(b) In the table x/y = -5/-4 = is not maintained in 2/10 so it will not direct variation.
(c) In the table x/y = -3/-12 = 1/4 maintained so it will direct variation.
2.
A variation in the form of x ∝ y will be a direct variation so y = 5x,b = (1/2)a, and m = 5n are direct variations.
3.
As per the given y ∝ x then y/x = 35/7 = 5 so the constant of proportionality is 5.
When y = 49
x = 49/5 = 9.8
Hence "1. In the first and third tables, there is no direct relationship, in the third table, there is a direct relationship.
2. y = 5x,b = (1/2)a and m = 5n are direct variation.
3. The constant of proportion is 5 and x when y is 49 will be 8.8".
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say we had |v|-1 edges picked from a connected, weighted, and undirected graph. are we guaranteed that these edges form a mst? why or why not?
No, we can't guaranteed that these edges form a MST.
Since the edge (u, v) has the lowest weight in the graph, we begin by supposing that there is no MST of the graph that contains it. The contradiction that results from this is as follows. The graph must have at least one MST if it is connected because we know it has at least one spanning tree.
Think about such an MST T. Keep in mind that, based on our first hypothesis, it does not contain the edge (u, v). Therefore, by adding (u, v) and eliminating one other edge, let's say (x, y), from the cycle that the new edge creates, we can transform it into another spanning tree, denoted T'. Because (u, v) is the edge with the lowest weight, (x, y) has a weight larger than or equal to (u, v), and as a result, T's total weight is less than or equal to T.
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Suppose triangle GHJ cong triangle CVB.; CV=8.GJ=11 , and VB = 9 What is GH ?
Answer:
b
Step-by-step explanation:
3) Find the slope of each line. Tell whether the slop is Positive, Negative, Undefined or Zero
Answer: slope = -1
Step-by-step explanation:
count number down vs number it takes to get back to the line.
For example, 1 down, 1 across
Overview
Question Progress
Here is a list of numbers.
-45 -21
-16
12 33 40
11
a) Write down two numbers from the list that add up to -9.
c) Work out the sum of all the numbers in the list.
12 13 14
b) Write down two numbers from the list that have a difference of 29.
-21 + 12
Answer:
Step-by-step explanation:
fly
If you were asked to estimate 11% of 40, which one of these choices is best practice from what was taught above in the videos and examples in the lesson:
Group of answer choices
I would multiply .11 times 40 and get my estimate.
I would round 11% up to 20%, and find 20% of 40 for my estimate.
I would round 11% to 10%, and find 10% of 40 for my estimate.
The number 11% of 40 can solve by .11 times 40. Option A is the correct option.
What is percentage of a number?
A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
The value of a% is equal to a/100.
Thus the value of 11% is 11/100 = 0.11.
Given that 11% of 40.
Now putting 11% = 0.11 in above expression:
= 0.11 of 40.
Of means times:
= 0.11 times 40.
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A Birr 1,000 deposits is made at a bank that pays 12% interest compounded monthly. How much will be in the account at the end of 10 years?
Answer:
$15400
Step-by-step explanation:
1 year = 12 month
10 years = 120 months
12% = month
1440% = 120 months
1440% = 14.4
Take 1000 times 14.4 = $14400
So, we add the two numbers
1000 + 14400 = $15400
So, $15400 will be in the account at the end of 10 years.
braulio has $15 less than adam. together they have $153. write the system of equations that could be used to determine the amount of money braulio, b, and the amount of money adam, a, has each. how much does braulio make?
The amount of money with Adam and Braulio as per given system of equations is equal to $84 and $69.
As given in the question,
Let 'a' be the amount of money with Adam
And 'b' be the amount of money with Braulio
System of equations as per given given data:
b = a - 15___(1)
a + b = 153 ___(2)
Substitute the value of 'b' in (2) we get,
a + a -15 = 153
⇒2a = 153 + 15
⇒2a = 168
⇒ a = $84
Amount of money with Adam is $84
Amount of money with Braulio is b = 84 - 15
= $69
Therefore, the amount of money with Adam and Braulio is equal to $84 and $69.
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It will cost $7 per person to hold a birthday party at the recreation center. number of guests: 6,7,8.9,10
The completed table of values is
Number of guests 6 7 8 9 10
Cost 42 49 56 63 70
How to complete the table of values?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Rate per person = $7
Also from the question, we have the following table of values
Number of guests = 6,7,8.9,10
This means that the cost for x people at the party is
Cost = Number of guests x Rate per person
Substitute Number of guests = 6,7,8.9,10 in the above equation, so, we have the following representation
Cost (6) = 7 * 6 = 42
Cost (7) = 7 * 7 = 49
Cost (8) = 7 * 8 = 56
Cost (9) = 7 * 9 = 63
Cost (10) = 7 * 10 = 70
When represented as a table, we have
Number of guests 6 7 8 9 10
Cost 42 49 56 63 70
The above represents the table of values
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Complete question
PARTY PLANNING It will cost $7 per person to hold a birthday party at the recreation center.
Number of guests 6 7 8 9 10
Cost
Complete the table of values
5(2x-3) < 35, the solution set is {x|x <(blank) }
Answer:
x<5
Step-by-step explanation:
5(2x-3) < 35
_____ ___
5 5
2x-3<7
2x<10
_ _
2x 2x
x < 5
James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.
The system of equations below represents the scenario.
x + 4y = 265
2x + 6y = 470
Define the variables for x and y.
Determine the cost for one dining room table.
Using the system of equation, the cost of one dinning table is 145 dollars.
How to find the cost of one dinning table?James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.
The system of equation that represent the situation is as follows:
let
x = cost of one dinning room table
y = cost of one chair
Therefore,
x + 4y = 265
2x + 6y = 470
using substitution method,
x = 265 - 4y
2(265 - 4y) + 6y = 470
530 - 8y + 6y = 470
-2y = 470 - 530
-2y = -60
y = -60 / -2
y = 30
Hence,
x = 265 - 4(30)
x = 265 - 120
x = 145
Therefore,
cost of one dinning table = 145 dollars
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Nth Term of a Geometric Sequence
Dec 05, 4:44:35 PM
► Watch help video
Find the 12th term of the geometric sequence 9, -18, 36, ..
Answer:
Submit Answer
Answer:
Step-by-step explanation:
x^2+6x+1=0
solve using quadratic formula
The values of the x of the given equation [tex]x^{2} + 6x + 1 = 0[/tex] using quadratic formula is -10 and -2.
What is quadratic formula of a equation ?
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:
(-b±√(b²-4ac))/(2a)
Given equation;
[tex]x^{2} + 6x + 1 = 0[/tex]
Using quadratic formula
x = [tex]-b[/tex] ± [tex]\frac{\sqrt{(b^{2} - 4 (ac) } }{4a}[/tex]
Substitute the values a = 1, b = 6, c = 1, we get;
x = [tex]-6[/tex] ± [tex]\frac{\sqrt{( (6) ^{2} - 4. 1.1)} }{2*1}[/tex]
x = -6 ± 4
x = -6 - 4 & x = -6 + 4
= -10 = -2
x = -10, -2
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Lawson planted a tree when it was 14 inches tall and it will grow 3 inches per year. Ezra planted a tree when it was 8 inches tall and it will grow 5 inches per year. Determine how many years it will take for the trees to be the same height.
Answer:
3 years
Step-by-step explanation:
we can use the equation 14+3x=8+5x to determine when they will be they same height. X I'd
13. a prospector thinks there is an even (50-50) chance that his property contains oil. any property suspected to have oil can go through two independent tests. the first test is 80% reliable; if there is oil on the property, it reports positive 80% of the time, and it reports negative 80% of the time whenever there is no oil. for the second test, it reports positive 75% of the time when there is oil, as well as reporting positive 50% of the time when there is no oil. what is the probability the property has oil, given that both tests report positive? assume event a: first test reports positive; event b: second test reports positive; event o: the property has oil.
The probability the property has oil, given that both tests report positive.
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)
P(A∩B|O) = 0.8 * 0.75 = 0.6
P(O) = 0.5
P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)
P(A|O) = 0.8, P(¬O) = 0.5
P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8
P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375
The probability theory is defined.The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.
How does probability work?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.
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2) Ratio of basketballs to soccer balls
1)
2:1
OPEN ENDED QUESTION
In example #2, which quantity will you write first:
basketballs or soccer balls? Why?
The ratio of basketballs to soccer balls is 2 : 1
The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball
What is ratio?This refers to a number representing a comparison between two or more named things.
If the ratio of basketballs to soccer balls = 2 : 1
This means,
Basketball : soccer ball = 2 : 1
Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.
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b(x) = 6x², when x = 16
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra ISubstitution
Functions
Function NotationApplicationStep 1: DefineLet's see what the problem as given us.
[tex]\displaystyle\begin{aligned}& b(x) = 6x^2 \\& x = 16\end{aligned}[/tex]
Step 2: WorkWe can easily see that we can substitute in x as 16.
[Equation] Define given:∴ our final answer to the question is b(16) = 1536.
___
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___
Topic: Algebra I
Unit: Functions
Kevin ate 2/5 of a pie. Su yung ate 3/10 of the pie. how much of the pie did Kevin and Su Yang eat together
The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of pie Kevin and Su Yung ate be = A
Now , the equation will be
The amount of pie Kevin ate = 2/5 of the total pie
And ,
The amount of pie Su Yung ate = 3/10 of the total pie
So , the equation is
Total amount of pie Kevin and Su Yung ate = amount of pie Kevin ate + amount of pie Su Yung ate
Substituting the values in the equation , we get
Total amount of pie Kevin and Su Yung ate A = 2/5 + 3/10
Total amount of pie Kevin and Su Yung ate A = ( 4 + 3 ) / 10
Total amount of pie Kevin and Su Yung ate A = 7 / 10 of the total pie
Therefore , the value of A is 7/10
Hence ,
The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie
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Estimate 64.5 divided by 12.3 using rounding 60 divided by 10
64.5 divided by 12.3 using rounding 60 divided by 10 gives 5.33.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given numbers are,
64.5 and 12.3.
When 64.5 is divided by 12.3.
The 64.5 can be rounded as 64
And 12.3 can be written after rounded as 12
Now divide 64 by 12.
64 / 12 = 5.333
The value of 64.5 divided by 12.3 is 5.33.
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what expression is equivalent to 3/4a + 2/3 - 1/2a - 1/3 + 1/2a
Answer:
(3/4)a + 1/3
Step-by-step explanation:
3/4a + 2/3 - 1/2a - 1/3 + 1/2a
(3/4)a + (2/3) - (1/2)a - (1/3) + (1/2)a [added () to clarify. Is "3/4a" (3/4)a or 3/(4a)?
(3/4)a + (2/3) - (1/2)a - (1/3) + (1/2)a
(3/4)a - (1/2)a - (1/3) + (1/2)a + (2/3)
(3/4)a - (1/2)a + (1/2)a - (1/3) + (2/3) [Rearrange: like terms together]
a[(3/4) - (1/2) + (1/2)] - (1/3) + (2/3) [bring out the "a"]
a[(3/4)] + (1/3) [simplify]
(3/4)a + 1/3
Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes. If a supersonic jet were to travel from the sun at the speed of 1000 km per hour, approximately how long would it take to travel the same distance?
please tell anyone of you very fast
options are
A)3 months B)5 years
C)17 YEARS D)221 YEARS
The time taken by the jet to reach the earth form sun is 3 months
The correct option is option A)
What is speed?
Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
We are given that
Light travels at the speed of 3,00,000 km per second. Light from the sun reaches us in 8 minutes
We first find the distance between sun and earth
to do that we multiply speed of light and time taken by light to reach earth
D = 300000*8
D= 2400000km
Now we are given the speed of the jet which is 1000km/hr
We have to find the time taken by the jet to reach the earth
To do that we divide the distance by speed we get
t = 2400000/1000
t =2400 hr.
3 months
The time taken by the jet to reach the earth form sun is 3 months
The correct option is option A)
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There are 17 houses on 1 block. How many houses are on 23 blocks?
By using multiplication, it can be calculated that
There are 391 houses in 23 blocks
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.
This is a word problem on multiplication
Number of houses in one block = 17
Assuming there are equal number of houses in each block,
Number of houses in 23 blocks = 23 [tex]\times[/tex] 17 = 391
There are 391 houses in 23 blocks
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the amount of time it takes hugo to solve a rubik's cube is continuous and uniformly distributed between 4.5 minutes and 12.5 minutes. what is the probability that it takes hugo less than 8 minutes to solve a rubik's cube?
The probability that hugo will solve rubik's cube in less than 8 minutes is 0.4375.
We have given that,
the amount of time it takes hugo to solve a rubik's cube is continuous and uniformly distributed between 4.5 minutes and 12.5 minutes.
i.e. a = 4.5 and b = 12.5
The probability that we find a value of X lower than x is given by the f
P(X < x) = [tex]\frac{x-a}{b-a}[/tex]
We have to find probability that it takes hugo less than 8 minutes to solve rubik's cube.
Therefore
P(X < 8) = [tex]\frac{8-4.5}{12.5-4.5}[/tex]
= [tex]\frac{3.5}{8}[/tex]
P(X < 8) = 0.4375
Hence the probability that it takes hugo less than 8 minutes to solve a rubik's cube is 0.4375%.
The uniform continuous distribution is one of the simplest probability distributions in statistics. Is is a continuous distribution, this means that it takes values within a specified range. A continuous uniform distribution takes values in a range [a,b].
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Please help me with this problem
Answer:
the answer is number three
Step-by-step explanation:
820×10 = 8200
