The solution of above equation is
[ 0 81/3 ]
To find the matrix A, we need to compute the inverse of C times D times C:
C^(-1) = [-2 1]
[ 1 0]
CDC^(-1) = [1 2][-2 1][4 0] = [4 -4]
[0 1]
Now we need to diagonalize A^4. First, let's find the eigenvalues of A:
|A - lambda*I| = 0
|4-lambda -4 | |lambda 0 |
|0 1-lambda| * |-4 1-lambda| = 0
Expanding the determinant, we get:
(4 - lambda)(1 - lambda) - 4*0 = 0
=> lambda^2 - 5*lambda + 4 = 0
=> (lambda - 4)*(lambda - 1) = 0
Therefore, the eigenvalues of A are λ1 = 4 and λ2 = 1. Now, let's find the eigenvectors associated with each eigenvalue:
For λ1 = 4:
(A - 4*I)x = 0
[(4 - 4) -4 ] [x1] [0]
[ 0 (1-4) ] [x2] = [0]
=> -4*x2 = 0
=> x2 = 0
Any value of x1 will satisfy the equation, so we can choose x1 = 1:
eigenvector v1 = [1 0]'
For λ2 = 1:
(A - I)x = 0
[(4 - 1) -4 ] [x1] [0]
[ 0 (1-1) ] [x2] = [0]
=> 3*x1 - 4*x2 = 0
=> x1 = (4/3)*x2
We can choose x2 = 3:
eigenvector v2 = [4 3]'
Now we can construct the diagonal matrix Λ with the eigenvalues on the diagonal:
Λ = [4 0]
[0 1]
And the matrix P with the eigenvectors as columns:
P = [1 4]
[0 3]
To compute A^4, we use the formula A^4 = P*Λ^4*P^(-1):
P^(-1) = (1/(13 - 40)) [ 3 -4]
[ 0 1]
Λ^4 = [4^4 0 ]
[0 1^4]
P^(-1) = (1/3) [ 3 -4]
[ 0 1]
A^4 = PΛ^4P^(-1) = [1 4][256/3 0 ][ 3 -4] = [4096/3 - 16384/3]
[0 3][ 0 1] [ 0 1] [ 0 81/3 ]
Therefore, the answer is:
[4096/3 -16384/3]
[ 0 81/3 ]
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Pls help will give brainlyist
Answer:
B. symmetric property
k/3 +3=18 ..................
Answer:
k=45
Step-by-step explanation:
k
3
+3=18
Step 1: Simplify both sides of the equation.
1
3
k+3=18
Step 2: Subtract 3 from both sides.
1
3
k+3−3=18−3
1
3
k=15
Step 3: Multiply both sides by 3.
3*(
1
3
k)=(3)*(15)
k=45
Answer:
k=45
Help me please asap please
Answer:
the first one is D. {3/2}
second one is C. {-10}
Step-by-step explanation:
hope this helps
please solve for x, and give me an explanation on how you did so? 1/2x-1/3=5/6
=======================================================
Explanation:
Fractions are a pain to deal with, so whenever possible I recommend you eliminate them. With equations like this, you can multiply both sides by the same number to do so. The question is: which number would that be?
If you pick on the LCD, then you'll be able to clear out the fractions. The LCD of 1/2, 1/3, and 5/6 is 6 since the LCM of the denominators is 6.
Multiply both sides by 6 to get
(1/2)x - 1/3 = 5/6
6*[ (1/2)x - 1/3 ] = 6(5/6)
6*(1/2)x - 6*(1/3) = 6(5/6)
3x - 2 = 5
------------
At this point, the fractions are gone. We can now solve like so
3x-2 = 5
3x-2+2 = 5+2 ... adding 2 to both sides
3x = 7
3x/3 = 7/3 .... dividing both sides by 3
x = 7/3
Answer:
x=5/6
Step-by-step explanation:
12x−13=5612x-13=56
Combine 1212 and xx.
x2−13=56x2-13=56
Move all terms not containing xx to the right side of the equation.
Add 1313 to both sides of the equation.
x2=56+13x2=56+13
To write 1313 as a fraction with a common denominator, multiply by 2222.
x2=56+13⋅22x2=56+13⋅22
Write each expression with a common denominator of 66, by multiplying each by an appropriate factor of 11.
Multiply 1313 and 2222.
x2=56+23⋅2x2=56+23⋅2
Multiply 33 by 22.
x2=56+26x2=56+26
Combine the numerators over the common denominator.
x2=5+26x2=5+26
Add 55 and 22.
x2=76x2=76
Multiply both sides of the equation by 22.
2⋅x2=2⋅
a survey among tenants of shared apartments asked each tenant what percentage of the cleaning around the apartment he or she does. the survey found that aggregating the percentages for each apartment produces an average of much more than 100%. this result may be due to what bias?
The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.
The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.
In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.
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Someone please answer for me thank you it’s geometry btw
The surface area of the prism is 462.55 in².
We have,
Slant height = 20.7 in
The perimeter of the base.
= 11 + 11 + 11 + 11
= 44 in
And,
The lateral surface area of the prism.
= Area of all sides except the base area
So,
= 3 x ( 1/2 x 11 x 20.7)
There are same three triangles.
So we add up all the 3 triangles.
= 341.55 in²
And,
Area of the base.
= 11²
= 121 in²
And,
The surface area of the prism.
= Lateral surface area + base area
= 341.55 + 121
= 462.55 in²
Thus,
The surface area of the prism is 462.55 in².
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I serious help. a ton
Answer:
Since BD bisects Angle ABC, Angle ABD = Angle DBC
\(3x+6=7x-18\)
Subtract 6 from both sides:
\(3x+6-6=7x-18-6\)
\(3x=7x-24\)
Subtract 7x from both sides:
\(3x-7x=7x-24-7x\)
\(-4x=-24\)
Divide both sides by -4:
\(\frac{-4x}{-4}=\frac{-24}{-4}\)
\(x=6\)
Angle \(ABD=3x+6=3(6)+6=18+6=24\)
Angle \(CBD=7x-18=7(6)-18=42-18=24\)
Angle \(ABC=ABD+CBD=24+24=48\)
Answer:
m<ABD= 6
m<CBD= -18
m<ABC= -108
Step-by-step explanation:
A shop is having a sale.all items are reduced by 25%. Work out the sale price of an item normally priced at £90 ?
Answer:
E67.5
Step-by-step explanation:
when we calculate 27%of E90 it result in 22.5then we subtract E22.5 from E90 which is equal to E67.5the ideal way to organize electronically the raw data for a study is to:____.
The ideal way to organize electronically the raw data for a study is to use a database management system (DBMS). A DBMS allows the researcher to store, manipulate, and retrieve data in a structured and organized manner. This enables the researcher to easily analyze the data and draw meaningful conclusions from it.
Additionally, a DBMS ensures data accuracy, consistency, and security. Overall, using a DBMS is the most efficient and effective way to manage raw data for a study.
This allows for efficient organization, storage, and retrieval of the data, making it easier to analyze and interpret the results. Additionally, employing proper data cleaning techniques and establishing a clear metadata structure can enhance the overall organization and accessibility of the study's raw data.
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which of the following statements are correct? multiple select question. research suggests that only statistical methods of sampling are common in practice. steps and techniques for both statistical and nonstatistical sampling are more similar than different. auditing standards recognize and permit both statistical and nonstatistical methods of audit sampling. auditing standards indicate that sample sizes for nonstatistical sampling should be larger than sample sizes for statistical sampling.
The correct statements are:
Auditing standards recognize and permit both statistical and nonstatistical methods of audit sampling.Steps and techniques for both statistical and nonstatistical sampling are more similar than different.Research suggests that only statistical methods of sampling are common in practice. (This is not true, as nonstatistical methods such as haphazard sampling and judgmental sampling are also commonly used in practice.)
Auditing standards indicate that sample sizes for nonstatistical sampling should be larger than sample sizes for statistical sampling. (Auditing standards do not prescribe a specific sample size for either type of sampling. Sample size should be determined based on factors such as the risk of material misstatement, the tolerable error, and the expected error.)
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A tea set was bought for Rs 336 after getting a discount of 16 % on its marked price. Find the marked price of the tea set.
Step-by-step explanation:
53.76
it helpful for you plrase give me like
\(\large \mathfrak{Solution : }\)
let the marked price of the tea set be n
According to the above problem,
\(n - ( \dfrac{16}{100} \times n) = 336\)\(n - \dfrac{4n}{25} = 336\)\( \dfrac{25n - 4n}{25} = 336\)\(21n = 8400\)\(n = \dfrac{8400}{21} \)\(n = 400\)Therefore the Marked price of the Tea set was ₹ 400
Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle Not a Right Triangle 10.5 cm, 20.8 cm, 23.3 cm6 cm, 22.9 cm, 20.1 cm
Answer:
Right Triangle-10.5 cm, 20.8 cm, 23.3 cmNot a Right Triangle-6 cm, 22.9 cm, 20.1 cmStep-by-step explanation:
Given the sets of side lengths of a triangle:
10.5 cm, 20.8 cm, 23.3 cm6 cm, 22.9 cm, 20.1 cmTo verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.
Pythagoras Theorem: \(Hypotenuse^2=Opposite^2+Adjacent^2\)In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm
\(23.3^2=20.8^2+10.5^2\\542.89=432.64+110.25\\542.89=542.89\)
Clearly these satisfies the required theorem and thus are side lengths of a right triangle.
In the set of side lengths 6 cm, 22.9 cm, 20.1 cm
\(22.9^2=20.1^2+6^2\\524.41\neq 440.01\)
Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.
What value of x is in the solution set of 8x - 6> 12 + 2x?
O -1
O0
O3
O5
Answer:
5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Inequality
8x - 6 > 12 + 2x
Step 2: Solve for x
Subtract 2x on both sides: 6x - 6 > 12Add 6 on both sides: 6x > 18Divide 6 on both sides: x > 3Here we see that any value x greater than 3 would work as a solution to the inequality.
∴ our answer is 5.
The U.S. Senate consists of 100 senators, with 2 from each of the 50 states. There are 50 Democrats in the Senate. A committee of size 10 is formed, by picking a random set of senators such that all sets of size 10 are equally likely. a) Find the expected number of Democrats on the committee. b) Find the expected number of states represented on the committee (by at least one senator) c) Find the expected number of states such that both of the state's senators are on the committee.
Note that based on probabilities,
The expected number of Democrats on the committee is 5.
The expected number of states represented on the committee is 26.
The expected number of states such that both of the state's senators are on the committee is 9.09.
How is this so ?a) The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.
So, the expected number of Democrats on a committee of size 10 is
1/2 * 10 = 5.
b) The minimum number of states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.
The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/ 2 = 26.
c) There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.
The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99
= 1/11.
The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.
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A rectangular solid with a square base has a volume of 4096 cubic inches - determine the dimensions that yield the minimum surface area
Answer:
side of base, a = 10.1 inches, height, h = 40.1 inches
Step-by-step explanation:
Volume of rectangular solid, V = 4096 cubic inches
Let the side of base is a and the height is h.
\(V = a^2h\\\\4096 = a^2 h ..... (1)\)
surface area of the solid
\(S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches\)
So, h = 40.2 inches
Kelsey walked 1.7 miles to the park. Then she walked another 1.3 miles to a cafe. How far did Kelsey walk in all?
Answer:
3 miles
Step-by-step explanation:
1.7 carry a one because 3+7 is 10
+ 1.3
--------
3.0
Answer:
3 miles
Step-by-step explanation:
Kelsey first walked to the park which took 1.7 miles. Then she walked an additional 1.3 miles to get to the cafe.
If we are only counting the amount of miles that she walked without going back home then we can do this simply by doing
1.7+1.3
0.7+0.3 = 1.0 so we carry the one and in total we get 1.0+1.0+1.0 to get 3.0 miles or in other words 3 miles!
{3, 5, 7, 9, 11)
Determine the mean and the mean absolute deviation (MAD).
(PLEASE HELPPP!!!!!!)
Answer:
Mean Absolute Deviation = 2.4
Step-by-step explanation:
Find you have to find the mean (average):
3 + 5 + 7 + 9 + 11 = 35
35 / 5 = 7
Mean = 7
The mean absolute deviation is the mean (average) of the distance from the other numbers (absolute means that if the number is negative it turns into a positive):
3 - 7 = 4
5 - 7 = 2
7 - 7 = 0
9 - 7 = 2
11 - 7 = 4
Now we have to find the mean of this numbers:
4 + 2 + 0 + 2 + 4 = 12
12 / 5 = 2.4
Mean Absolute Deviation = 2.4
Answer:
2.4
Step-by-step explanation:
Hope I helped :)
If f(1)=6 and f(n)=f(n−1)−3 then find the value of f(5).
The value of f(5) for the given function is -6.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
A heuristic, on the other hand, is an approach to problem-solving that seeks to come up with a workable answer quickly rather than promising an ideal or even accurate solution.
When an algorithmic solution is not viable, useful, or effective, heuristics are frequently applied.
Given that, f(1)=6 and f(n)=f(n−1)−3 thus we have:
f(2) = f(1) - 3 = 6 - 3 = 3
f(3) = f(2) - 3 = 3 - 3 = 0
f(4) = f(3) - 3 = 0 - 3 = -3
f(5) = f(4) - 3 = -3 - 3 = -6
Hence, the value of f(5) for the given function is -6.
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The formula below gives the sum of the degrees, S, of the interior angles of a polygon. If n represents the number of sides, which equation solves for n?
S = (n-2) x 180
F. n = s/180 + 2
G. n = 180s + 2
H. n = s+2/180
J. n = (s+2) x 180
Answer: F. n = s/180 + 2
Step-by-step explanation:
To find the equation that solves for n, we will isolate the n variable.
Given:
S = (n - 2) x 180
Divide both sides of the equation by 180:
\(\frac{S}{180}\) = n - 2
Add 2 to both sides of the equation:
\(\frac{S}{180}\) + 2 = n
Reflexive property:
n = \(\frac{S}{180}\) + 2
F. n = s/180 + 2
researchers observed 50 random people brush their teeth and recorded the number of seconds each person spent brushing. from the sample, they found a mean time of 41.5 seconds. further, their calculations revealed that this estimate is within a margin of error of 2.45 from the true average time that all people spend brushing their teeth. write the interval estimate that will estimate the true average time that people spend brushing their teeth. write your answer using inequality notation:
Answer:
The interval estimate is:
41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45
or
38.05 ≤ true average time ≤ 44.95
Inequality notation:
[38.05, 44.95]
The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.
Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:
(sample mean) ± (margin of error)
Substituting the given values, we get:
41.5 ± 2.45
Simplifying, we get:
[39.05, 43.95]
Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.
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Jack Talon rolled 82 barrels onto the ship's
deck. 50% of those barrels were empty. How
many empty barrels did Jack roll onto the
ship's deck?
Answer:
41
Step-by-step explanation:
You do 50% of 82 which is 41.
Answer: 41 empty barrels
Step-by-step explanation:
if Jack rolled 82 total barrels and 50% of them were empty, that is the same as taking 82 times .5, which gives us 41. This is how we know he rolled 41 empty barrels onto the ships deck.
What is the value of m?
Answer:
23
Step-by-step explanation:
400 - 8m = 216
move 8m to the other side
400 = 216 + 8m
subtract 216 from both sides
8m = 184
divide both sides by 8
m = 23
Answer:
23
Step-by-step explanation:
400 - 216 = 184
184/8 = 23
Check
400 - 8m = 216
400 - 8(23) =
400 - 184 =
216 = 216 :)
Need to know asap!!
Expand and simplify:
6(3j – 2) - 4(2j + 4)
write an equation of the line with the given slope and y-intercept,(4,3) and (0,1)
Answer:
y=1/2x+1
Step-by-step explanation:
First use slope formula.
\(\frac{y2-y1}{x2-x1}\)
Plug in the information needed.
\(\frac{1-3}{0-4}=\frac{-2}{-4}=\frac{1}{2}\)
The slope is \(\frac{1}{2}\).
Now, use point-slope formula.
y-y1=m(x-x1)
Plug in the information needed.
y-3=1/2(x-4)
y-3=1/2x-2
y=1/2x+1
The equation of the line in slope-intercept form is y=1/2x+1.
Hope this helps!
If not, I am sorry.
Below are two parallel line intersecting them
Answer:
x = 53°
Step-by-step explanation:
alternate exterior angles are equal
Answer:
Step-by-step explanation:
Two lines are parallel.
x = 53
Alternate exterior angles are equal
find the area of a cicle
with Radius 7cm using pie
Answer: 153.94cm
Step-by-step explanation:
Answer:
A = 49 cm ²
Step-by-step explanation:
A = πr²
= 22/7 * 7 *7
= 49 cm²
Explain how to find the value of y in the equation 6ly + 4) = 12.
Please help
Answer:
6y + 4 = 12 is simple. 6 times y + 4 to equal 12. 6 + 4 = 10. 12-10=2. To get 2 more than 6 is Y=4/3
Step-by-step explanation:
Use the Distributive Property to expand 6(−4x+3y) .
Answer:
-24x + 18y
Step-by-step explanation:
Probability of an uncertain outcome is a number between 0 and +1, exclusively. True False
True. Probability of an uncertain outcome is a number between 0 and +1, exclusively.
The probability of an uncertain outcome is a measure of the likelihood that the outcome will occur, and it is always a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain. Probabilities between 0 and 1 indicate the degree of uncertainty about whether the event will occur or not.
Probabilities cannot be negative or greater than 1, as they represent a proportion of the total possible outcomes. If the probability of an event were negative or greater than 1, it would imply that the event is impossible or certain to occur, respectively, and violate the fundamental laws of probability theory.
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Select all equations that represent this question:
Diego has run 2/3 of a race""s distance. He has run 8 1/2 kilometers. How long is the whole race
The whole race is 12 3/4 kilometers.
The correct equations that represent this question are:
(8 1/2) ÷ 2/3 = ?
2/3 × ? = 8 1/2
(8 1/2) × 3/2 = ?
In this question we have been given Diego has run 2/3 of a race""s distance. He has run 8 1/2 kilometers.
We need to find the length of the whole race.
Let the whole race be x.
Since Diego has run 2/3 of a race's distance which is 8 1/2 kilometers. The length of the whole race will be given by an equation:
2/3 × x = 8 1/2
x = (8 1/2) ÷ 2/3
x = (8 1/2) × 3/2
x = 17/2 × 3/2
x = 51/4
x = 12 3/4 kilometers.
Therefore, the length of the whole race= 12 3/4 kilometers.
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The choices for given question are given below.