The linear system Ax = b, (a) the least squares solutions are x = A⁺b, (b) the orthogonal projection is projcol(A) b = A(AᵀA)⁻¹Aᵀb, and (c) the least squares error is || b - projcol(A) b ||.
(a) The least squares solutions of the linear system Ax = b are the values of x that minimize the squared difference between Ax and b. To find these solutions, we can compute the pseudoinverse of A, denoted A⁺, and then calculate x = A⁺b.
(b) The orthogonal projection projcol(A) b of b onto the column space of A is the vector that represents the closest approximation of b using the column vectors of A. It can be calculated as projcol(A) b = A(AᵀA)⁻¹Aᵀb.
(c) The least squares error || b - projcol(A) b || measures the difference between the vector b and its projection onto the column space of A. It can be computed as the norm (magnitude) of the difference vector b - projcol(A) b.
To find the solutions, projection, and least squares error, we can perform the necessary matrix operations using the given values of A and b. Since the given values are not provided, I am unable to show the detailed calculations. However, by following the described procedures, you can evaluate the solutions and obtain the desired results.
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Which angles are congruent to each other
Answer:
∠9 and ∠11
Step-by-step explanation:
Vertical angles are congruent, and angles 9 and 11 are vertical.
write an expression for the sequence of operations described below.
g fewer than the sum of f and 8
Do not simplify any part of the experssion.
Step-by-step explanation:
f + 8 > g this can be written in other ways but this sums it up
List down 5 values of x that makes it TRUE to the equation x - 5 < 35
Answer:
5,4,3,2,1
Step-by-step explanation:
an ice cream parlor has 31 different flavors. a super sundae allows a person to select 3 different flavors. how many different selections are possible?
How are cells and organs related?
Cells are made from tissues found in organ systems.
Cells reproduce with tissues to made organ systems.
Cells join together to form tissues, which form organs.
Cells go through binary fission to make new organs.
in the given image AB and CD are parallel with the transversal DB Which of the following angles are congruent to DBA select the two correct answers
Answer:
∠EDC and ∠FDB
Step-by-step explanation:
I just took test
Also please make me Brainliest
Probit coefficients are typically estimatedâ using:
A.
the method of maximum likelihood.
B.
the OLS method.
C.
by transforming the estimates from the linear probability model.
D.
nonlinear least squaresâ (NLLS).
Probit coefficients are typically estimated using:
A. the method of maximum likelihood.
The method of maximum likelihood is used to estimate the probit coefficients. This method aims to find the coefficients that maximize the likelihood of observing the given sample data. It involves an iterative process to identify the most likely parameter values for the model, making it suitable for nonlinear models like the probit model. Maximum likelihood estimation is a widely used method in econometric analysis due to its desirable properties, such as consistency and asymptotic efficiency.
In summary, probit coefficients are estimated using the method of maximum likelihood, which provides the most accurate and efficient estimates for this type of model.
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Awarding 15 points for best answer!
Answer:
Step-by-step explanation:
First
solveeee pleaseeee . thanks xoxo
t-4>-7
Answer:
t>-3 is the answer. hope this helped!
Step-by-step explanation:
Its simple you add 4 to both sides. t-4+4 > -7+4= t > -3
determine if the given set is a subspace of ℙ2. justify your answer. the set of all polynomials of the form p(t)=at2, where a is in ℝ.
The given subset satisfies all three conditions of a subspace, we can conclude that it is a subspace of ℙ2.
To prove this, we need to show that the set satisfies the three conditions of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.
Let p(t) and q(t) be two polynomials of the form \(p(t) = at²\)and \(q(t) = bt²\), where a and b are real numbers. Then, the sum of these two polynomials is:
\(p(t) + q(t) = at² + bt²\)
\(= (a+b)t²\)
Since a+b is a real number, the sum of p(t) and q(t) is still of the form at² and thus belongs to the given set. Therefore, the set is closed under addition.
Now, let p(t) be a polynomial of the form \(p(t) = at²\) and c be a real number. Then, the scalar multiple of p(t) by c is:
\(c p(t) = c(at²) = (ca)t²\)
Since ca is a real number, the scalar multiple of p(t) by c is still of the form at² and thus belongs to the given set. Therefore, the set is closed under scalar multiplication.
Finally, the zero vector is the polynomial of the form \(p(t) = 0t² = 0\), which clearly belongs to the given set. Therefore, the set contains the zero vector.
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How is 1.2×10−4 written in standard decimal notation?
Which quadratic expression is written in standard form? -X2 - 5x + 7 0 ) (x + 3)x (x + 4)2 x² + 2(x+3)
Because the general expression for a quadratic equation is
\(ax^2\text{ + bx + c }\)PLS SOMEONE ILL MARK YOU BRILLIANT AND GIVE YOU EXTRA POINTS!!!! Write the Linear Equation given:
1. Slope = 4; y-intercept = -5
2. Slope = 5; y-intercept = 3
3. Slope = -2; y-int; y-intercept = -8 4. Slope = 2⁄3; y- intercept = 2
5. Slope = -3⁄4; y-intercept = -2
6. Slope = 1⁄4; y-intercept = 7
7. Slope = -3; y-intercept = 2⁄3
8. Slope = 2⁄3; y-intercept = 10
9. Slope = -2; y-intercept = -1⁄2
10.Slope = -3⁄4; y-intercept = -3 Answers:
1.
2. 3. 4. 5. 6. 7. 8. 9.
Answer:
1. y=4x-5 2. y=5x+3 3. y=-2x-8 4. 2/3x+2 5. y=-3/4x-2 6. 1/4x+7 7. -3x+2/3 8. 2/3x+10 9. -2x-1/2 10. -3/4x-3
Step-by-step explanation:
the slope always goes in front of the x and then the y-intercept goes after.
3.2. Why, do you think, do banks and other financial institutions offer cash loans to people that did not apply for it?
An error from the bank would be a reason financial institutions offer cash loans to people that did not apply for it
Why, do you think, do banks and other financial institutions offer cash loans to people that did not apply for it?Banks and other financial institutions may offer cash loans to people who did not apply for them for a variety of reasons, but it is important to note that this practice is generally not common or accepted.
One possibility is that the financial institution may have made an error or mistake, such as sending loan offer letters or pre-approved offers to the wrong people. In some cases, this can be due to data entry errors, incorrect addresses, or other administrative issues.
Another possibility is that the financial institution may be engaging in predatory lending practices, where they target vulnerable or low-income individuals with high-interest loans or other financial products. This can be unethical
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If the mean of a population is 250 and its standard deviation is 20, approximately what proportion of observations is in the interval between each pair of values? a. 190 and 310 b. 210 and 290
As per the standard deviation the proportion of observations is in the interval between each pair of values is 190 and 310
The term in math known as standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Here we have know that the mean of a population is 250 and its standard deviation is 20.
Then the proportion of observations is in the interval between each pair of values is calculated as,
We have interval (190,310) and we can express this interval as:
=> (190,310) = (250−3⋅20, 250+3⋅20)
According to this interval , we have that k=3.
Based on the value of the constant the required percent of observations in interval(190,310) is at least 88.9%
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A small box holds 60 hats. A large box holds 180% as many hats in the small box. How many hats does the large box hold.
Answer:
108
Step-by-step explanation:
Answer:108
Step-by-step:180/100×6=180080180×6=
The number of sides of a regular polygon is 20,
a) Find each external angles of the polygon?
b) Find each internal angles of the above polygon ?
Answer:
Sum of all the exterior angles in any polygon is always 360º
Find the number of sides:
One exterior angles = 20º
Number of sides = 360 ÷ 20
Number of sides = 18
Step-by-step explanation:
Answer:
Step-by-step explanation:
a) external angles is also known as exterior angles
exterior angle = 360
we have n=20
360/n=360/20=18
the external angles of a regular polygon of 20 is 18 degree
b) internal angles is also known as interior angles
interior angle = 180
exterior angle = 18
interior angle - exterior angle
180-18=162 degree
the internal angles of 20 is 162 degree
HELP ASAP! WILL GIVE A LOT OF POINTS AND BRAINLY
The line of best fit for the following data is represented by y = 1.46x − 0.76.
(image below)
What is the sum of the residuals? What does this tell us about the line of best fit?
1.06; This indicates that the line of best fit is accurate and a good model for prediction.
−1.06; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
0; This indicates that the line of best fit is very accurate and a good model for prediction.
0; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
The sum of the residuals and what it tells us about the line of best fit is that: −1.06; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
How to calculate the sum of the residuals?Mathematically, the residual value of a data set can be calculated by using this formula:
Residual value = actual value - predicted value
Next, we would determine the predicted values as follows:
At point (4, 6), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(4) − 0.76.
Predicted value, y = 5.08
At point (6, 7), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(6) − 0.76.
Predicted value, y = 8.
At point (7, 8), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(7) − 0.76.
Predicted value, y = 9.46.
At point (9, 13), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(9) − 0.76.
Predicted value, y = 12.38.
At point (10, 14), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(10) − 0.76.
Predicted value, y = 13.84
At point (11, 15), we have;
Predicted value, y = 1.46x − 0.76.
Predicted value, y = 1.46(11) − 0.76.
Predicted value, y = 15.3.
Now, we can calculate the sum of the residuals as follows:
Sum of the residuals = Sum of actual values - Sum of predicted values
Sum of the residuals = (6 + 7 + 8 + 13 + 14 + 15) - (5.08 + 8 + 9.46 + 12.38 + 13.84 + 15.3)
Sum of the residuals = 63 - 64.06
Sum of the residuals = -1.06.
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Answer:
-1.06
Step-by-step explanation:
i took the test :)
anyone get this ? (geometry)
Can you solve this?
Solve this with a EXPLANATION to get a Brainliest!
Good luck! :D
Answer:
hope this helps
Step-by-step explanation:
Hope this helps!
Brainliest pls
Have a great day!
t Marie's Beading Boutique, 32 out of the 32 beads on clearance are plastic. What percentage of beads on clearance are plastic?
Write your answer using a percent sign (%).
Answer:
100%
Step-by-step explanation:
If all 32 the beads were plastic it would be 100%
The graph of a line passes through the two points below.
Which of these can be used to determine the slope of the line?
ㅇ
ㅇ
2-3
4-1
2+3
(2, 4); (3,-1)
2-3
4+1
401 20
An expression which can be used to determine the slope of the line include the following: A. \(\frac{-1 - 4}{3-2}\)
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 - 4)/(3 - 2) ⇒ (required expression).
Slope (m) = -5/1
Slope (m) = -5.
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Complete Question:
The graph of a line passes through the two points below.
(2, 4); (3,-1)
Which of these can be used to determine the slope of the line?
A. \(\frac{-1 - 4}{3-2}\)
B. \(\frac{-1 + 4}{3+2}\)
C. \(\frac{4 - 1}{3-2}\)
D. \(\frac{-1 - 3}{4-2}\)
use the ratio test to determine whether the series is convergent or divergent.[infinity]n4nn = 1 identify and. evaluate the following n → [infinity] an 1an
L < 1, the series is convergent according to the ratio test. The ratio test to determine if the given series is convergent or divergent.
The series we're analyzing is Σ(n^4)/(n^n) from n=1 to infinity. To use the ratio test, we need to evaluate the limit L as n approaches infinity for the absolute value of (a_(n+1))/a_n: L = lim (n→∞) |(a_(n+1))/a_n| = lim (n→∞) |((n+1)^4)/(n+1)^(n+1)) * (n^n)/(n^4)|
Now, we can simplify the expression: L = lim (n→∞) |(n^n * (n+1)^4) / (n^4 * (n+1)^(n+1))|
Notice that we can cancel out some terms: L = lim (n→∞) |((n+1)^4) / (n+1)^(n+1) * (n^n)/(n^4)|
Now, let's divide (n+1)^4 by (n+1)^(n+1): L = lim (n→∞) |(1 / (n+1)^n) * (n^n)/(n^4)|
Now, let's evaluate the limit: L = |(1 / (∞)^n) * (∞^n)/(∞^4)| = 0
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⚠️HELP PLS AND THANK U!! Will give brainliest if you give a good explanation! Have a good weekend! ⚠️The population of fish in a local bay is modeled by the equation P(t) = 2,500(1.025)', where t represents the
number of years since 2,500 fish were first measured. Based on this equation, which of the following
represents the percent the population will grow in a decade?
(1) 2.5%
(3) 28%
(2) 25%
(4) 32%
Answer:
Its 25%
Step-by-step explanation:
The percent population that will grow in a decade is 28% option (3) 28% is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have:
\(\rm P(t) = 2,500(1.025)^t\)
Plug t = 10
\(\rm P(10) = 2,500(1.025)^{10}\)
P(10) = 3200
Percent grow = [(3200 - 2500)/2500]×100
Percent grow = 28%
Thus, the percent population that will grow in a decade is 28% option (3) 28% is correct.
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which variety of nonrandom sampling takes proportions into consideration?
a) convenience
b) judgment
c) quota
d) purposive
The variety of nonrandom sampling that takes proportions into consideration is: c) quota
Quota sampling is the variety of nonrandom sampling that takes proportions into consideration. In quota sampling, the researcher selects a specific number of participants from each subgroup of the population based on their proportion in the overall population. This ensures that the sample represents the different subgroups in the population proportionately.
In quota sampling, the researcher selects participants based on specific characteristics or proportions to ensure that the sample represents the target population accurately. The researcher sets quotas for different groups or segments based on known proportions or desired representation in the population.
For example, if a population consists of 60% males and 40% females, a quota sample might be designed to include the same proportions of males and females. The researcher would continue to select participants from each group until the quotas are met.
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To determine her breathing rate, Miranda divides up her day into three parts: morning, afternoon, and evening. She then measures her breathing rate at 4 randomly selected times during each part of the day. What type of sampling is used? A. Simple random B, Stratified C. Systematic D. Convenience E. Cluster
The type of sampling used in this scenario is B. Stratified sampling. Stratified sampling involves dividing the population into distinct subgroups or strata and then selecting samples from each subgroup.
In this case, Miranda divides her day into three parts: morning, afternoon, and evening. Each part of the day represents a stratum or subgroup. Miranda measures her breathing rate at 4 randomly selected times during each part of the day. This means she is taking samples from each of the three strata (morning, afternoon, and evening) and collecting data from within those subgroups.
By using stratified sampling, Miranda ensures that her samples represent the different parts of her day in a proportional and systematic manner, allowing her to capture potential variations in her breathing rate throughout the day.
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Tua wanted to teach his pet raven to count because they are very smart birds. He used various fruits and nuts to represent numbers. A peanut = 1 A grape = 2 peanuts 14 is represented by an acorn and 3 grapes. An acorn is worth half a plum. What is the value in fruits and nuts, of two plums and a peanut, divided by a grape and a peanut?
The value of two plums and a peanut, divided by a grape and a peanut is 11
How to solve the expression?The given parameters are:
Peanut = 1Grape = 2 Acorn + 3 grapes = 14Acorn = 1/2 PlumSubstitute Grape = 2 in Acorn + 3 grapes = 14
Acorn + 3 *2 = 14
Acorn + 6 = 14
Subtract 6 from both sides
Acorn = 8
Substitute Acorn = 8 in Acorn = 1/2 Plum
8 = 1/2 Plum
Multiply both sides by 2
Plum = 16
So, we have:
Peanut = 1
Grape = 2
Acorn = 8
Plum = 16
The value of two plums and a peanut, divided by a grape and a peanut is:
(2 plums + peanut)/(grape + peanut)
This gives
(2 * 16 + 1)/(2+ 1)
Evaluate
11
Hence, the value of two plums and a peanut, divided by a grape and a peanut is 11
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l=8cm b=6cm h=5cm
find the total surface area and volume of cuboid
Type the correct answer in the box
The area of the figure units.
Answer:
i think its 23. ............
Find the largest six digits number which is divisible by 120 exactly.
Answer:
999,960
Step-by-step explanation:
let x be a multiple of 120
120x ≤ 999,999
999,999 / 120 = 8333.325
8333 ≤ x ≤ 8334
8333(120) = 999,960
8334(1200) = 1,000,080 this is a 7-digit number
Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960