Determine whether or not the following matrix A is diagonalizable. Be 5 00 sure to explain all of your reasoning. A= -2 2 1 0 0 2
Answers
Yes, the given matrix A is diagonalizable.
Let the matrix A be given by A = [−2 2 1 0 0 2].
To determine if this matrix is diagonalizable, we need to check whether A has enough linearly independent eigenvectors. If there are enough such eigenvectors, then A will be diagonalizable. Otherwise, A will not be diagonalizable.
To find the eigenvalues and eigenvectors of the matrix A, we solve the equation Ax = λx, where λ is a scalar (eigenvalue) and x is the corresponding eigenvector. This gives: (A - λI)x = 0, where I is the identity matrix.To solve for the eigenvalues, we need to find λ such that det(A - λI) = 0. This gives us the characteristic equation:
(−2 − λ)(2 − λ)(1 − λ) − 4(2 − λ) = 0, which simplifies to λ^3 − λ^2 − 10λ − 12 = 0.
To find the eigenvectors, we solve for x in the equation (A - λI)x = 0, using each eigenvalue λ obtained from the characteristic equation.To solve for λ, we need to solve the characteristic equation. Factoring it gives (λ - 4)(λ + 1)^2 = 0, which has eigenvalues λ1 = 4 and λ2 = −1 (multiplicity 2).
Since we have two distinct eigenvalues (λ1 = 4 and λ2 = −1), we know that A is diagonalizable if and only if it has two linearly independent eigenvectors corresponding to each eigenvalue.To find the eigenvectors corresponding to λ1 = 4, we need to solve the system (A - 4I)x = 0.
This gives the matrix equation:
[−6 2 1 0 0 −2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]
Solving this system gives x1 = -x3/6 - x6/2, x2 = x2, and x4 = x4. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them.
Doing so gives:
x1 = -1/6
x3 - x6/2x2 = x2x4 = x4x5 = 0
So, the eigenvectors corresponding to λ1 = 4 are of the form [x1 x2 x3 x4 x5 x6] = [−1/6t −2s t 0 0 −2t], where t and s are arbitrary constants.To find the eigenvectors corresponding to λ2 = −1, we need to solve the system (A + I)x = 0.
This gives the matrix equation: [−1 2 1 0 0 2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]
Solving this system gives x1 = -x3 + 2x6, x2 = x2, and x4 = -2x6. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them. Doing so gives: x1 = 2t - s, x2 = x2, x4 = -2t ,x5 = 0
So, the eigenvectors corresponding to λ2 = −1 are of the form [x1 x2 x3 x4 x5 x6] = [2t − s 0 t −2t 0], where t and s are arbitrary constants.Since we have four linearly independent eigenvectors (two corresponding to each eigenvalue), we can diagonalize the matrix A by forming the matrix P whose columns are these eigenvectors.
The matrix P is given by P = [−1/6 −2 2 0 0 2][0 1 0 0 0 0][1 −2 0 0 0 0][0 0 0 1 0 0][0 0 1 0 0 0][−2 0 0 0 0 1]
Hence A is diagonalizable.
Answer: Yes, the given matrix A is diagonalizable.
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Related Questions
A group of students are members of two after-school clubs. One half of the group belong to the math club and three - fifths of the group belong to the science group. Five students are members of both clubs. How many students are in this group?
Answers
there are 50 students in this group.
Let's denote the total number of students in the group as "x."
According to the information given, one half of the group belongs to the math club, which is (1/2)x. Additionally, three-fifths of the group belongs to the science club, which is (3/5)x.
However, it's important to note that five students are members of both clubs, and we don't want to count them twice. So, we need to subtract the number of students who are in both clubs.
The total number of students in the group can be calculated as:
Total = Math club members + Science club members - Students in both clubs
x = (1/2)x + (3/5)x - 5
To solve this equation, we can first find a common denominator:
x = (5/10)x + (6/10)x - 5
x = (11/10)x - 5
Next, we can isolate the x term on one side:
x - (11/10)x = -5
(10/10)x - (11/10)x = -5
(10 - 11)/10 x = -5
(-1/10)x = -5
Finally, we can solve for x by multiplying both sides by -10:
(-1/10)x * (-10) = -5 * (-10)
x = 50
Therefore, there are 50 students in this group.
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square root of 92 whole numbers lines in between
Answers
Nine and ten because nine squared is eighty two and ten squared is one hundred
The value for square root of 92 lies between 9 and 10.
What is Square root?The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots.
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.
Given:
√92
If we find the square root of 92 we get 9.591.
and, the number 9.591 lies between the whole number 9 and 10.
Hence, the root of 92 lies between 9 and 10.
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how do you know when to add or subtract when doing the distributive property for (2-6s)(-5)
Answers
Here, we want to use the distributive property
To use this, the operator at the middle of the two initial terms will tell us the sign to use
Looking at the first expression, we can see a negative sign between 2 and -6s
Thus, in this case, when using the distributive property, we proceed as follows;
\(\begin{gathered} (2-6s)(-5)\text{ = (2}\times(-5))\text{ - (6s}\times(-5)) \\ =\text{ -10 - (-30s)} \\ =\text{ -10 +30s = 30s-10} \end{gathered}\)A model car is constructed with a scale of 1:15. If the actual car is 12 feet long, which proportion represents the length x of the model car?
Answers
The length of the model car based on the information is 0.8 feet.
What is scale?It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.
From the information, the model car is constructed with a scale of 1:15.
When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:
= 1/15 = x / 12
Cross multiply
15x = 1 × 12
15x = 12
Divide
x = 12 / 15
x = 0.8
The length is 0.8 feet.
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The seasonalized sales for this period when the deseasonalized
sales are 2,889.00 units and the seasonal index for this period is
1.70?
correct answer is: 4911.30
I need help getting to the answer
Answers
The seasonalized sales for this period when the deseasonalized sales are 2,889.00 units and the seasonal index for this period is 1.70 is 4911.30.
There are two types of sales numbers: seasonalized sales and deseasonalized sales. Deseasonalized sales are the revenues of a business that have been adjusted for seasonal fluctuations. The value of seasonalized sales is then adjusted by the seasonality factor to determine the seasonalized sales for the period.
This adjustment enables businesses to compare their performance in different periods of the year without being influenced by seasonal fluctuations. This makes it easier to compare performance over time.
Therefore, the formula to calculate the seasonalized sales is;
Seasonalized sales = Deseasonalized sales * Seasonal index= 2889 * 1.70= 4911.30
Therefore, the seasonalized sales for this period when the deseasonalized sales are 2,889.00 units and the seasonal index for this period is 1.70 is 4911.30.
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The density of a fish tank is 0.4fish over feet cubed. there are 12 fish in the tank. what is the volume of the tank? 3 ft3 30 ft3 48 ft3 96 ft3
Answers
The volume of the tank is 25ft³.
Suppose, the volume of the fish tank is v ft³.
According to the given question.
The density(d) of the fish tank is 0.4 fish/ ft³.
And the total number of fish in the tank is, n = 12.
As, we know that the population density (d) of the fish in the tank is the number of fishes (n) in a given volume (v)
So, the volume of of the tank is given by
d = n/v
⇒ 0.5 = 12/v
⇒ v = 12/0.5
⇒ v = 25ft³.
Hence, the volume of the tank is 25ft³.
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In right triangle XYZ, angle Y is a right angle. What is the relationship between angles X and Z? What is the relationship between sin X and cos Z?
a) Angles X and Z are supplementary, and sin X= cos Z
b) Angles X and Z are complementary, and sin X= cos Z
c) Angles X and Z are supplementary, and sin X= 1 - cos Z
d) Angles X and Z are complementary, and sin X= 1 - cos Z
Answers
Answer:
B
Step-by-step explanation:
The angles of X and Z are supplementary and sinX and cosZ will be the same hence, option (b) will be correct.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
Given that in triangle Y is 90° since in any triangle sum of all three angles will be 180° so remaining angle Z and Y will be total of 90° hence these will be complementary.
In right angle triangle sinX = cosZ because the perpendicular for X act like a base for Y.
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If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by y = 56t − 1.86t^2. Find the average speed over the given time intervals. [1, 2]
Answers
Answer:
50.42m/sStep-by-step explanation:
Average speed is the change in distance of a body with respect to time. This is expressed as:
\(v = \delta y/\delta t\\v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}\)
Given the function of the height in metres expressed as y = 56t − 1.86t² and time interval [1,2]
t₁ = 1sec and t₂ = 2 secs
y(t₂) = 56t₂ − 1.86t₂²
y(2) = 56(2) − 1.86(2)²
y(2) = 112-7.44
y(2) = 104.56
y(t₁ ) = 56t₁ − 1.86t₁ ²
y(1) = 56(1) − 1.86(1)²
y(1) = 56-1.86
y(1) = 54.14
Substituting the derived value into the formula for finding the average speed:
\(v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}\\\\v = \dfrac{104.56-54.14}{2-1}\\\\v = \dfrac{50.42}{1}\\\\v = 50.42m/s\)
Hence, the average speed over the given time intervals. [1, 2] is 50.42m/s
35892 rounded to the nearest ten thousand
Answers
Answer:
40,000
Step-by-step explanation:
name two geometric solids that have a circular cross section describe how you get that cross section - im in geometry !!!
Answers
Answer: no clue man
don't have any clue because im only in algebra 1 honors! sorry...
I set z=t=0(x,y,z,t)
and I got a partial solution (0,1,0,0).
I solved two homogeneous matrices once for z=1
and t=0
, then for z=0
and t=1
and I got two solutions (1,1,1,0)
and (1,1,0,1).
Then, I got (0,1,0,0)+a∗(1,1,1,0)+b∗(1,1,0,1
)
Therefore, all possible results are (0,1,0,0),(1,0,1,0),(1,0,0,1),(0,1,1,1)
Would this be correct?
Answers
The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).
Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.
Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).
Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).
Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).
To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.
(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)
Expanding this expression, you get:
(0+a+b, 1+a+b, 0+a, 0+b)
Simplifying, you obtain the following set of solutions:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Therefore, the correct set of possible results would be:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.
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The main bearing clearance (in mm) in a certain type of engine is a random variable with probability density function
Answers
The main bearing clearance (in mm) in a certain type of engine is a random variable with a probability density function (PDF).
A probability density function (PDF) is a mathematical function that describes the likelihood of a continuous random variable taking on a specific value within a given range. In this case, the main bearing clearance in a certain type of engine is a continuous random variable, and its PDF provides information about the probability distribution of the clearance values.
To fully describe the main bearing clearance's PDF, we would need the specific mathematical expression for the function. The PDF should satisfy two conditions: it must be non-negative for all values of the clearance, and the total area under the curve of the PDF must equal 1, as the probability of the clearance being within the entire possible range is 1 (100%).
Without the specific form of the PDF, we cannot provide further details, such as the mean, variance, or other properties of the main bearing clearance's probability distribution.
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any statistical test that is used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools would be inappropriate. explain why in a few sentences.
Answers
It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.
There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.
However, some statistical tests may not be appropriate for this scenario.
The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.
In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.
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Please help with atleast some❤️❤️❤️
Answers
what is 39% of 200?
i already know it’s 78, i just need a explanation of how i got it.
Answers
Answer:
200 x .39
Step-by-step explanation:
200 x .39= 78
Answer:
39 percent of 200 is the same as 39 per hundred of 200. We can therefore make the following equation:
39/100 = X/200
To solve the equation above for X, you first switch the sides to get the X on the left side, then you multiply each side by 200, and then finally divide the numerator by the denominator on the right side to get the answer.
39/100 = X/200
X/200 = 39/100
X*200/200 = 39*200/100
X = 7800/100
X = 78
The work above shows the long way to explain how to calculate 39 percent of 200 in order to give you a foundation and better understanding of how to calculate percentage. In the future, you could use this simplified formula:
(Y * P)/100
In our problem "What is 39 percent of 200?", Y is 200 and P is 39:
(200 * 39)/100 = 78
And once again you see that the answer is 78.
Step-by-step explanation:
Let ????=−5y????+5x????. Use the tangential vector form of Green's Theorem to compute the circulation integral ∫????????⋅???????? where C is the positively oriented circle x2+y2=25
Answers
The value of the required integral is 50π where C is the positively oriented circle x2+y2=25
We are given a vector F = -yi + xj. A vector is a quantity with magnitude and direction that is commonly represented by a directed line segment, with length representing magnitude and orientation in space representing direction. We need to use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr where C is the positively oriented circle x² + y² = 25
Let the value of the integral be represented by the variable "I".
I = ∫∫[(/x)(x) - (/y)(-y)]dA
I = ∫∫[(1 - (-1)]dA
I = ∫∫2dA
I = 2∫∫dA
I = 2×(Area of the circle)
I = 2*(πr²)
I = 2*(π*25)
I = 50π
Hence, the value of the required integral is 50π.
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How do you identify the bases of any prism?
Answers
Answer:
Look at the names of the prisms above. Each type of prism is named after its base. In the figure on the left, the base is a rectangle, so it is called a rectangular prism. In the middle, the base is a triangle, so the shape is a triangular prism.
Step-by-step explanation:
Marcus is designing a structure to hold up scenery for the school play. The structure must be a right triangle.
Which measures could be lengths of the sides of the structure?
A. 7 in., 24 in., and 25 in.
B. 9 in., 16 in., and 25 in.
C. 10 in., 24 in., and 25 in.
D. 15 in., 26 in., and 36 in.
E. 24 in., 30 in., and 34 in.
Answers
Answer:
Step-by-step explanation:
B
Graph the line going through (-6,1) with a slope of -2/3.
Answers
A graph of the line going through the point (-6, 1) with a slope of -2/3 is shown in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-6, 1) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -2/3(x + 6)
y = -2x/3 - 4 + 1
y = -2x/3 - 3
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Slope
1/5
y-intercept = -2
I need this in slope intercept form. Can someone help?
Answers
Answer:
y= 1/5x + (-2)
Step-by-step explanation:
Find the projection of the vector 2 onto the line spanned by the vector 1 8. Find all the eigenvalues of the matrix A-B.
Answers
Find the projection of the vector 2 onto the line spanned by the vector 1 8We are given the vector 2 and the vector 1 8. We need to find the projection of the vector 2 onto the line spanned by the vector 1 8. Let us denote the vector 1 8 as v.For any vector x, the projection of x onto v is given by (x⋅v / |v|²)v.
To find the projection of the vector 2 onto the line spanned by the vector 1 8, we need to calculate the dot product of 2 and 1 8. And then, we need to divide it by the magnitude of 1 8 squared. After that, we will multiply the result by the vector 1 8.Let's calculate this step by step:Dot product of 2 and 1 8 = 2 ⋅ 1 + 8 ⋅ 0 = 2Magnitude of 1 8 squared = (1)² + (8)² = 1 + 64 = 65The projection of 2 onto the line spanned by 1 8 = (2 ⋅ 1 / 65)1 + (2 ⋅ 8 / 65)8= (2 / 65) (1, 16)Thus, the projection of the vector 2 onto the line spanned by the vector 1 8 is (2 / 65) (1, 16).
Find all the eigenvalues of the matrix A-B.To find the eigenvalues of the matrix A-B, we first need to calculate the matrix A-B.Let's assume that A = [a11 a12 a21 a22] and B = [b11 b12 b21 b22].Then, A-B = [a11 - b11 a12 - b12a21 - b21 a22 - b22]We are not given any information about the values of A and B., we cannot calculate the matrix A-B or the eigenvalues of A-B.
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Showing all working, determine the base 7 expansion of n = ( (2458)9.
Answers
The base 7 expansion of n = ((2458)₉ is (2151)₇.
What is the base 7 representation of ((2458)₉?To determine the base 7 expansion of the number n = (2458)₉, we need to convert it to base 10 first and then convert it to base 7.
Let's perform the conversion step by step:
Convert from base 9 to base 10.
\(n = 2 * 9^3 + 4 * 9^2 + 5 * 9^1 + 8 * 9^0\)
= 2 * 729 + 4 * 81 + 5 * 9 + 8 * 1
= 1458 + 324 + 45 + 8
= 1835
Convert from base 10 to base 7.
To convert 1835 to base 7, we divide it repeatedly by 7 and collect the remainders.
1835 ÷ 7 = 262 remainder 1
262 ÷ 7 = 37 remainder 1
37 ÷ 7 = 5 remainder 2
5 ÷ 7 = 0 remainder 5
Reading the remainders in reverse order, we get (2151)₇ as the base 7 expansion of n.
Therefore, the base 7 expansion of n = (2458)₉ is (2151)₇.
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the burning times of scented candles, in minutes, are normally distributed with a mean of 249 minutes and a standard deviation of 20 minutes. find the number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles. use excel, and round your answer to two decimal places.
Answers
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.
When the distribution is normal, we use the z-score formula.
In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:
Z = (X – µ) / σ
What is Z-score?The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
So, in this case, given that:
µ = 249, σ = 20
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:
100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.
Now, put all the values into the formula:
Z = (X – µ) / σ
–0.253 = (X – 249) / 20
X – 249 = –0.253 * 20
X = 244
Hence, the candle burns for 244 minutes.
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Find an LU factorization of the matrix A (with L unit lower triangular). A=
⎣
⎡
4
−8
10
−8
8
−4
3
5
−7
7
6
−7
0
3
−3
⎦
⎤
Answers
The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].
Let's go step by step to find the LU factorization of matrix A.
Matrix A:
A =
[4, -8, 10]
[-8, 8, -7]
[6, -7, 3]
Step 1:
Initialize the L matrix as an identity matrix of the same size as A.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 2:
Perform Gaussian elimination to obtain U.
- Multiply the first row of A by (1/4) and replace the first row of A with the result.
A =
[1, -2, 2.5]
[-8, 8, -7]
[6, -7, 3]
- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[6, -7, 3]
- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Step 3:
Update the L matrix based on the operations performed during Gaussian elimination.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 4:
The resulting matrix A is the upper triangular matrix U.
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Therefore, the LU factorization of matrix A is:
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
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*31. Priya and Ravish planned to participate in a cycle race to be organised for National integration. They decided
to practise on a circular path around a sports field. Priya takes 18 minutes to complete one round, while Rav-
ish takes 12 minutes for the same. Suppose they both start at the same time and go in the same direction.
(a) After how many minutes will they meet again at the starting point?
(6) What is the value depicted by Priya and Ravish?
Answers
Answer:
36 minutes
2 rounds for Priya
3 rounds for Ravish
Step-by-step explanation:
The answer is the LCM (least common multiple) of 12 and 18.
12 = 2^2 x 3
18 = 3^2 x 2
=>LCM of 12 and 18 = 2^2 x 3^2 = 4 x 9 = 36
=> After 36 minutes they meet again at the starting point
=> At that time, Priya has completed: 36/18 = 2 rounds
=> At that time, Ravish has completed: 36/12 = 3 rounds
After 36 minutes they meet again at the starting point.
In 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.
What is least common multiple?The least common multiple (L.C.M) of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.
What is prime factorization?Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
According to the given question.
Time taken by Priya to complete one round = 18 minutes
Time taken by Ravish to complete the one round = 12 minutes
Therefore,
The number of minutes taken by Priya and Ravish to meet again at the starting point when they start the race same time = L.C.M (12, 18)
Since,
Prime factorization of
\(12 = 2\times 2 \times 3\)
And \(18 = 3 \times 3 \times 2\)
⇒ L.C.M of 12 and 18 = 2 × 2 × 3 × 3 = 4 × 9 = 36
Hence, after 36 minutes they meet again at the starting point.
Now, number of round completed by Priya in 36 minutes = \(\frac{36}{18}= 2\)
And the number of rounds completed by Ravish in 36 minutes = \(\frac{36}{12}\) = 3
Hence, in 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.
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X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y) (2 points) v(3x 2y) (4 points) find p(3x 2y>20) (4 points)
Answers
The result for the given normal random variables are as follows;
a. E(3X + 2Y) = 18
b. V(3X + 2Y) = 77
c. P(3X + 2Y < 18) = 0.5
d. P(3X + 2Y < 28) = 0.8729
What is normal random variables?Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.
Now, according to the question;
The given normal random variables are;
E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.
Part a.
Consider E(3X + 2Y)
\(\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}\)
Part b.
Consider V(3X + 2Y)
\(\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}\)
Part c.
Consider P(3X + 2Y < 18)
A normal random variable is also linear combination of two independent normal random variables.
\(3 X+2 Y \sim N(18,77)\)
Thus,
\(P(3 X+2 Y < 18)=0.5\)
Part d.
Consider P(3X + 2Y < 28)
\(Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}\)
\(\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}\)
Therefore, the values for the given normal random variables are found.
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The correct question is-
X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:
a. E(3X + 2Y)
b. V(3X + 2Y)
c. P(3X + 2Y < 18)
d. P(3X + 2Y < 28)
please I'm in desperate need of help, click the picture
Answers
Answer:
Triangle=1 square=2
gear=3 pentagon=4
I hopes this helps you :)
Find an equation of the sphere that passes through the point (4 3 -1) and has center (3 8 1)
Answers
The equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is: (x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.
To find the equation of the sphere passing through the point (4, 3, -1) with a center at (3, 8, 1), we can use the general equation of a sphere:
(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2
where (h, k, l) represents the center of the sphere and r represents the radius.
First, we need to find the radius. The distance between the center and the given point can be calculated using the distance formula:
√[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]
Substituting the coordinates of the center (3, 8, 1) and the given point (4, 3, -1), we have:
√[(4 - 3)^2 + (3 - 8)^2 + (-1 - 1)^2]
Simplifying, we get:
√[1 + 25 + 4] = √30
Therefore, the radius of the sphere is √30.
Now we can substitute the center (3, 8, 1) and the radius √30 into the general equation:
(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30
So, the equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is:
(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.
This equation represents all the points on the sphere's surface.
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consider a goodness-of-fit test with a computed value of chi-square27.385 and a critical value13.388, the appropriate decision would be to __________.
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The null hypothesis is accepted since the chi-square at the supplied critical value level value is greater than 13.388 (27.385).
In five to six key stages, the hypothesis test announces the conclusion of an assumption.
The approach to be utilized is predicated on the notion of correlating a parameter's standardized sample equivalent to the crucial boundary that permits the null hypothesis to be accepted.
For this particular question,
The value of the chi-square is 27. 385.
The crucial number is 13.388.
The following are the hypotheses for the goodness of fit test : If an expected value and the observed values are identical, the value is considered null. Alternative: The expected value and the observed values differ substantially. One tail exists in the chi-square test.
The standard is as follows:
If the test statistic is higher than the threshold value, the null hypothesis is rejected. The same null hypothesis is rejected if the test statistic is below the crucial value. Because the chi-square is greater than 13.388 and the critical value is provided, the null hypothesis is therefore accepted at that level.
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Probability Question please answer ASAP this is due today.
Answers
Answer:
58.988%
Step-by-step explanation: