Yes. The matrix A-2I is invertible because 2 is an eigenvalue for matrix A.
When the matrix (transformation) is applied to some vectors (eigenvectors), the eigenvalues of the matrix are scalars. In other words, if A is a square matrix of order n x n and v is a non-zero column vector of order n x 1, and Av = v (the product of A and v is just a scalar multiple of v), then the scalar (real number) is called an eigenvalue of the matrix A that corresponds to the eigenvector v.
The eigenvalues can be determined by formula,
[tex]|A-\lambda I|=0[/tex]
Where, [tex]\lambda[/tex] = eigenvalues.A square matrix with an inverse is known as an invertible matrix. A square matrix is said to be invertible if and only if the determinant is not equal to zero. In other words, a 2 x 2 matrix is only invertible if its determinant is not zero.
Given,
A is a 4x4 matrix whose eigen values are λ=1,2,3,4
we need to determine that A-2I is invertible or not.
We know that 2 is an eigen value of matrix A, so, if we substitute 2 to find determinant of A-2I, then we will get zero as answer.
So, when determinant of A-2I is zero then the matrix is invertible.
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help pls answer as soon as possible look at picture to answer
Answer:
Step-by-step explanation:
1/5y+3/20
plug in 1/4 for y
1/5(1/4)+3/20
1/20+3/20
4/20
1/5
Is the slope 1 /- 3 perpendicular to the slope 3?
No, the slopes are not perpendicular. The slope of 3 is three times larger than the slope of 1/-3, so the two slopes form an angle that is less than 90 degrees.
1. The slope of a line is the ratio of the vertical change to the horizontal change in the line, this is also known as the rise over run.
2. The slope of the first line is 1/-3 and the slope of the second line is 3.
3. To determine if the two slopes are perpendicular, we need to calculate the angle between them.
4. The angle between two slopes is equal to the arctan(slope1/slope2).
5. Using the formula, we can calculate the angle between the two slopes to be 63.43 degrees.
6. Since this angle is less than 90 degrees, the two slopes are not perpendicular.
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Write the sentence as an inequality.
Three is no less than a number z.
Write the sentence as an inequality. Three is no less than a number z.
3 ≥ z
How do you get the solution 2+2
Lets see how smart you people are
Answer:(1x2)+(4divided by 2)
Step-by-step explanation:
family music your family has an ipod filled with music. it has many thousands of songs. you figure that roughly 60% of the songs are music you like, 25% of the music is annoying songs from your little sister, and the rest is stuff from the 80s that only your parents still think is cool. driving across town, your mom puts the ipod on shuffle and you all listen to whatever randomness produces. what is the probability that the first song is a) an 80s song? b) a song picked by one of the kids? c) not one of your songs?
Step-by-step explanation:
If the iPod has many thousands of songs, it's safe to assume that the number of 80s songs, songs picked by one of the kids, and songs that you like are all significant. Therefore, the probabilities that the first song will be an 80s song, a song picked by one of the kids, or not one of your songs are roughly equal to the percentage of each type of song on the iPod.
For example, the probability that the first song will be an 80s song is roughly 15%, since only 15% of the songs on the iPod are 80s songs (80s songs make up 100% - 60% - 25% = 15% of the iPod's music). Similarly, the probability that the first song will be a song picked by one of the kids is roughly 25%, and the probability that the first song will not be one of your songs is roughly 40% (100% - 60% = 40%).
Note that these probabilities are only approximate, since the songs on the iPod are chosen randomly and the actual probabilities may vary slightly.
Please help !!!!!!!
Answer: he gives them 2 balls each and there are 2 balls remaining
Step-by-step explanation: 10 balls divided by 4 teams would be 2.5 though you cannot split a ball in half therefore you would just keep the two spare balls
The amount M (in trillions of dollars) of mortgage debt outstanding in the United States from 1990 through 2009 can be approximated by the function M = f(t) = 0.0037(t + 14.979)2, where t = 0 represents the year 1990.
a) Describe the transformation of the common function f(x) = x2. Then sketch the graph over the interval 0 ≤ t ≤ 19.
b) Predict the mortgage debt in the year 2014.
Answer:
The function f(t) = 0.0037(t + 14.979)^2 can be rewritten as f(t) = 0.0037(t^2 + 29.958t + 222.126). This is a quadratic function that has been stretched vertically by a factor of 0.0037 and shifted 14.979 units to the right and 222.126 units up.
To sketch the graph of this function, we can start with the graph of f(t) = t^2, which is a parabola that opens upwards. The transformation of this function stretches the parabola vertically by a factor of 0.0037, so its maximum and minimum values will be much smaller. The shift of 14.979 units to the right means that the vertex of the parabola will be located 14.979 units to the right of the vertex of the original parabola. The shift of 222.126 units up means that the minimum value of the function will be located 222.126 units above the minimum value of the original parabola.
On the interval 0 ≤ t ≤ 19, the graph of the function will be a parabola that stretches vertically by a factor of 0.0037 and is shifted 14.979 units to the right and 222.126 units up from the graph of f(t) = t^2.
To predict the mortgage debt in the year 2014, we can substitute t = 24 into the function f(t) = 0.0037(t + 14.979)^2. This gives us f(24) = 0.0037(24 + 14.979)^2 = 0.0037(39.979)^2 = 0.0037 * 1595.7441 = 5.90834 trillion dollars. This is the predicted mortgage debt in the year 2014.
I need this answer quickly :(
it is 31. i hope this helped you!
Answer:59
Step-by-step explanation:
does 4 equal to the fraction 8 over 4?
The comparison of the expressions 4 and fraction 8 over 4 is that they are not equal
How to compare the expression?From the question, we have the following parameters that can be used in our computation:
4 and fraction 8 over 4
Rewrite the above expression using mathematical operators and mathematical symbols
So, we have the following representation
4 and 8/4
The above expression are integers and fraction expressions
So, we express 8/4 as an integer
This gives
4 and 2
The number 2 is less than the number 4
This means that both numbers are not equal
Hence, the conclusion is not equal
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A researcher wants to test the claim that the proportion of juniors and seniors who exercise regularly is not the same. He finds that 42 of 65 randomly selected juniors and 34 of 52 randomly selected seniors report exercising regularly. Construct 90% confidence intervals for each population proportion. Which of the statements gives the correct outcome of the researcher's test of the claim?
The 90% confidence interval for juniors is (.530, .762), and the 90% confidence interval for seniors is (.525, .783). Since the intervals overlap, there is not enough evidence to say there is a difference between regular exercise rates among juniors and seniors.
The 90% confidence interval for juniors is (.549, .744), and the 90% confidence interval for seniors is (.545, .762). Since the intervals are not the same, there is enough evidence to say there is a difference between regular exercise rates among juniors and seniors.
The 90% confidence interval for juniors is (.530, .762), and the 90% confidence interval for seniors is (.525, .783). Since the intervals are not the same, there is enough evidence to say there is a difference between regular exercise rates among juniors and seniors.
The 90% confidence interval for juniors is (.549, .744), and the 90% confidence interval for seniors is (.545, .762). Since the intervals overlap, there is not enough evidence to say there is a difference between regular exercise rates among juniors and seniors.
The correct statements regarding the confidence intervals is given as follows:
The 90% confidence interval for juniors is (.549, .744), and the 90% confidence interval for seniors is (.545, .762). Since the intervals overlap, there is not enough evidence to say there is a difference between regular exercise rates among juniors and seniors.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
For juniors, the parameters are given as follows:
[tex]n = 65, \pi = \frac{42}{65} = 0.646[/tex]
Then the lower bound of the interval is of:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 - 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.549[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.646 + 1.645\sqrt{\frac{0.646(0.354)}{65}} = 0.744[/tex]
For seniors, the parameters are given as follows:
[tex]n = 52, \pi = \frac{34}{52} = 0.654[/tex]
Then the lower bound of the interval is of:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 - 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.545[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.654 + 1.645\sqrt{\frac{0.654(0.346)}{52}} = 0.762[/tex]
The intervals overlap, hence there is not enough evidence to conclude that there is a difference.
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Please help me raise my grade
Ashley is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 100100, find ashley's age.
From the information given, Ashley's age is 27
how to calculate the value:
Let the four siblings' ages be;
Ashley's age is x, x + 1, x + 2, x + 3.
If their combined ages equal 100
We possess
x + x + 1 + x + 2 + x + 3 = 100
assemble similar terms
4x + 6 = 100
4x = 100 - 6
4x = 96
Set the topic to "x"
x = 96/ 4
x = 24
But Ashely is x + 3 = 24 + 3 = 27 years old.
Thus, Ashley's age is 27
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Solve the following system of equations. Show your work.
−2x+5y=−2
4x−10y=4
Solution:
The system of equations - 2x + 5y = - 2 and 4x - 10y = 4 has infinitely many solutions.
What is the graphical solution of system of equations?Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, A system of equations - 2x + 5y = - 2...(i) and 4x - 10y = 4...(ii).
Now, multiplying eqn(i) by 2 it becomes - 4x + 10y = - 4...(iii).
Now, by Adding (ii) and (iii) we get,
0x + 0y = 0.
So, 0 = 0, and hence these are coinciding lines with infinitely many solutions.
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What is splitting and give an example?
Answer:
Splitting is where numbers in an equation are broken apart to make it easier to calculate.
Step-by-step explanation:
Splitting is where numbers in an equation are broken apart to make it easier to calculate. Ex:
21 * 7
20 * 7 + 1 * 7 =
140 + 7
147
) if the pile contains only 20 quarters but at least 40 of each other kind of coin, how many collections of 40 coins can be chosen?
the different collections than many (40+4-1)! / (40!)(43-40)! - (20+4-1)! / (20!)(23-20)!.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
if the pile contains only 20 quarters but at least 40 of each other kind of coin,
So the P (n k ) = (20+4-1)! / (20!)(23-20)! subtracted from (40+4-1)! / (40!)(43-40)!
Hence the different collections than many (40+4-1)! / (40!)(43-40)! - (20+4-1)! / (20!)(23-20)!
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Need help on these questions
a small electric bike speed is 24 miles in 2/3 hour At this rate how many miles can it drive in 1 hour
Answer: 36 miles
Step-by-step explanation:
2/3 hour = 40 minutes
We know that its speed is 24 miles in 40 minutes
So take 24 divided by 40 = 0.6 miles per minute
Then take 0.6 times 60 = 36 miles in 1 hour
So it can drives 36 miles in 1 hour
need help ASAP! please help
The missing angles in the triangle is as follows:
∠1 = 62.5°∠2 = 62.5°∠3 = 55°∠4 = 75°∠5 = 50°How to find the measure of angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
∠3 = 55 degrees (vertically opposite angles)
Vertically opposite angles are congruent to each other.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Using exterior angle theorem ,
105 = ∠5 + 55
∠5 = 105 - 55
∠5 = 50 degrees
∠4 = 180 - 50 - 55
∠4 = 75 degrees
Therefore, the other triangle is an isosceles triangle. This means the base angles are equal.
Hence,
∠1 = ∠2 = x
2x + 55 = 180
2x = 180 - 55
2x = 125
x = 125 / 2
x = 62.5 degrees.
Hence,
∠1 = ∠2 = 62.5 degrees.
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select all of the expressions that could be used to determine 60% of x.
80% of the picture frame is glass. What is the area of the moulding
Answer:
20
Step-by-step explanation:
If 80% of the picture frame is glass, then 100-80 = <<80=20>>20% of the frame is moulding.
If the total area of the frame is 100 square inches, then the area of the moulding is 20 square inches. Answer: 20.
What is a formula for the nth term of the given sequence? 144, 192, 256...
Answer:
An=144(3/4)1-n
Step-by-step explanation:
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what can you do to round a decimal
get trolled
Step-by-step explanation:
troll people make them get trolled
Answer:
Step-by-step explanation:
to round a decimal, well it depends if it asks you to round to tenths, thousandths or hundredths sometimes even cents..
If you were to be given 5.5567 and it says to round to the hundredth place then you would look at the two points so 5. 55 and then look at the number beside it which is 6 and because 6 is bigger it would round up so you'd get 5.56 hopefully you understood that even if it's just a little..
Select all the measurements that are equivalent to 48 centimeters.
0.48 m
4.8 mm
480 mm
4,800 m
48,000 km
Answer: 0.48 m, 480 mm
Step-by-step explanation:
1 m = 100 cm
So take 48 divided by 100 = 0.48m, so this is correct.
1 cm = 10 mm
So take 48 times 10 = 480 mm, so this is correct
Find the missing number in the number sentence below.
-86+ _____ = 0
Question 4 options:
A: 89
B: 0.86
C: 87
D: 86
Answer:
86
Step-by-step explanation:
f(4) = 10 and f(-4)= 14, find f(5)
Answer: f(5)=9.5
Step-by-step explanation:
If the graph displays f(x)=(-1/2)x+12, then the answer for f(5) would be 9.5.
However, if the graph/line varies from this, (and is not just a straight line or y=mx+b,) the answer will be different as well.
Given the information you gave me though, this is the best I can do. Please check the given graph/equation before inputting the above answer.
Manipulate the equation for s
S/r+m=v
Answer choice
Add M
Multiply by r
Multiply by v
Subtract m
Divide by r
Step-by-step explanation:
rearrange the equation so that the unknown you are r trying to calculate is on its own on one side of the equation
There are 4,500 cities on planet Purple. The planetary government takes a random sample of 350 cities and finds that the average number of complaints about feral cats from the sample was 3.4 ± 0.49. Which of the following is an estimate of the total number of feral cat complaints for planet Purple?
Between 1018.5 and 1361.5 complaints
Between 171.5 and 1190 complaints
Between 13,095 and 17,505 complaints
Between 2,205 and 15,300 complaints
Based on the margin of error, an estimate of the total number of feral cat complaints for planet Purple is A. Between 1018.5 and 1361.5 complaints.
What is the margin of error?The margin of error shows the statistical difference between the actual and projected or estimated results.
The margin of error gives the difference between the upper limit and the lower limit of the sample estimate.
With the margin of error, one establishes a level of confidence or the confidence interval in the sample results.
The total number of cities on planet Purple = 4,500
Random sample size = 350 cities
Average complaints = 3.4
Margin or error = ± 0.49
Upper limit = 1,361.5 [350 x (3.4 + 0.49)]
Lower limit = 1,081.5 [350 x (3.4 - 0.49)]
Thus, using the margin of error, an estimate of feral cat complaints hovers over Option A.
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A line has a slope of negative one-fourth and passes through point (negative five-fourths, 1). What is the equation of the line?.
The equation of the line is y - 1 = -1/4( x + 5/4).
Here we have to find the equation of the line.
Data given:
Point on the line= (-5/4, 1)
slope(m) = -1/4
The formula of the equation of the line:
y - y1 = m(x - x1)
where m = slope of the line
(x1, y1) = point on the line
Now putting the values in the equation we have:
y - 1 = -1/4( x- (-5/4))
y - 1 = -1/4( x + 5/4)
Therefore the equation of the line is y-1 = -1/4( x + 5/4).
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a gum manufacturer wants to determine whether blue packaging or red packaging is preferred. the company performs a sales test by introducing red packages into a random sample of ten stores, and blue packages are introduced in an independent, random sample of ten stores. the technique most appropriate for analyzing the data is
The technique most appropriate in introducing red packages into a random sample of ten stores, and blue packages are introduced in an independent, for analyzing the data is the Independent Samples T-test for means.
The test examines the means of two independent groups to see if there is statistical evidence that the related population means differ considerably. A parametric test is the Independent Samples t Test.
The Independent Samples t Test is frequently used to test the following variables: Statistical disparities between two groups' means, statistical differences between two interventions' means, and statistical differences between the means of two change scores. When comparing the means of exactly two groups—no more and no less—use an independent samples t-test.
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the number of miles that a particular type of car can run before its battery wears out is exponentially distributed with an average of 20,000 miles. what is the probability that the car batery will die somewhere between 25000 and 30000 miles ? ( round to three decimal places )
So the probability that the car will die between 25000 and 30000 miles is P(X > 25000) = 0.286
How does probability work?Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, generally speaking, 0 indicates the event's impossibility and 1 indicates its certainty.
Here,
Exponential distribution is memory less.
Let be the event of car number of miles car travels before dying out.
So mean
m = 20000
Now P(X > t) = [tex]e^{\frac{-t}{m} }[/tex]
Since P( X > [tex]\frac{(x+y)}{X > x}[/tex]) = P(X > y)
=> P(X > 25000) = [tex]e^{\frac{-25000}{20000} }[/tex]
=> P(X > 25000) = [tex]e^{\frac{-5}{4} }[/tex]
=> P(X > 25000) = 0.286
So the probability that the car will die between 25000 and 30000 miles is P(X > 25000) = 0.286
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