What is the value of x, if 32x+11x=172

a) If the confidence level had been 90% instead of 98%, the new confidence interval would be (0.325, 0.475).

b) If the sample size had been 255 instead of 170, the new confidence interval would be (0.292, 0.508).

c) If the confidence level had been 99% instead of 98%, the new confidence interval would be (0.304, 0.496).

a) First, we find the mean of the original confidence interval:

Mean = (Lower Limit + Upper Limit) / 2 = (0.313 + 0.487) / 2 = 0.4

Margin of Error = (Upper Limit - Mean) = (0.487 - 0.4) / 2 = 0.0435

New Margin of Error = Margin of Error * \((Z_{90} / Z_{98})\)

where \(Z_{90}\) is the critical value for a 90% confidence level, and \(Z_{98}\) is the critical value for a 98% confidence level.

From the standard normal distribution table, we find:

\(Z_{90}\) ≈ 1.645

\(Z_{98}\) ≈ 2.326

New Margin of Error = 0.0435 * (1.645 / 2.326) ≈ 0.0306

Finally, we construct the new confidence interval using the adjusted margin of error:

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0306, 0.4 + 0.0306)

                     ≈ (0.3694, 0.4306)

Therefore, the new confidence interval at a 90% confidence level would be approximately (0.369, 0.431) when rounded to three decimal places.

b) Standard Error = \(\sqrt{(p_{hat} * (1 - p_{hat})) / n}\)

where \(p_{hat}\) is the sample proportion and n is the sample size.

Given that the sample size increases to 255 while the sample proportion remains the same, the new sample proportion is:

\(p_{hat}\) = 68 / 255 ≈ 0.267

Standard Error = sqrt((0.267 * (1 - 0.267)) / 255) ≈ 0.028

For a 98% confidence level, the critical value is \(Z_{98}\) ≈ 2.326.

New Margin of Error = \(Z_{98}\) * Standard Error = 2.326 * 0.028 ≈ 0.065

New Confidence Interval = (\(p_{hat}\) - New Margin of Error, \(p_{hat}\) + New Margin of Error)

                     = (0.267 - 0.065, 0.267 + 0.065)

                     ≈ (0.202, 0.332)

Therefore, the new confidence interval with a sample size of 255 would be approximately (0.202, 0.332) when rounded to three decimal places.

c) From the standard normal distribution table, we find:

\(Z_{99}\) ≈ 2.576

New Margin of Error = Margin of Error * (\(Z_{99}\) / \(Z_{98}\)) = 0.0435 * (2.576 / 2.326) ≈ 0.0482

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0482, 0.4 + 0.0482)

                     ≈ (0.3518, 0.4482)

Therefore, the new confidence interval at a 99% confidence level would be approximately (0.352, 0.448) when rounded to three decimal places.

To know more about confidence level, refer here:

https://brainly.com/question/9386257

#SPJ4

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of phones produced abroad and y represent the number of phones produced locally.

The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:

30x + 20y = 6000            (1)

Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:

20x + 60y = 12000           (2)

Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:

70x = 6000

x = 600/7 ≈ 86

Put x = 86 in equation 1:

30(86) + 20 y = 6000

20y = 3420

y = 171

86 phones should be produced abroad and 171 phones locally

Answer:

.05

Step-by-step explanation:

y is increasing by 0.05 as x is increasing by 1.

The probability of randomly selecting a person whose bhirtday is in the month of december is P =  0.0859

We want to find the probability of randomly selecting a person whose birthday is in december, that probabilty will just be equal to the quotient between the number of days in a year that are in december (31 days) and the total number of days in a year (365).

So the probability will be:

P = 31/365 = 0.0859

We conclude that the probability of randomly selecting a person that wll have a birthday in december is 0.0859.

Learn more about probability:

https://brainly.com/question/25870256

#SPJ1

Missing side length of the given measures of the triangle is equal to           x = 1/2 units (approximately).

As given,

Given measures of the triangle ABC are

Angle A=(18 +18)°

             =36°

Consider side opposite to ∠A=a ,∠B=b ,∠C=c

Given side length

AC=b

     =20

AB=c

    =12

BC=c

    =x+12

Using cosine law

cos A= (b²+c²-a²)/2bc

⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)

⇒(1+√5)/4=(544-x²-24x-144)/480

⇒x²+24x-280+120√5=0

⇒x²+24x-11.7=0

Now, x = [-24±√24²-4(1)(-11.7)]/2(1)

           = (-24±24.955)/2

           ≈ (-24 ±25)/2

Hence, x = (-24+25) /2

               = 1/2

or x = -24.5 side length cannot be negative.

Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).

Learn more about side length here

brainly.com/question/18725640

#SPJ1

Answer:

54 can be divided by both 2 and 3. And yes there is more than one answer.

Step-by-step explanation:

54 is less than 60 but greater than 50, and it can also be divided by 2 and 3 without there being a remainder. All the other answers could be: 52, 54, 56, and 58 (all of which could be divided by 2) and 51, 54, and 57 (all of which could be divided by 3).

Hope this helps!!! :)

To compute the total number of teams enrolled for each club in alphabetical order, you need to gather the information of all the clubs and count the number of teams enrolled for each club.

1. Create a list of all the clubs in alphabetical order.
2. Iterate through the list of clubs.
3. For each club, gather the information about the teams enrolled.
4. Count the number of teams enrolled for each club.
5. Repeat this process for all the clubs.
6. Once you have the total number of teams enrolled for each club, you can organize the results in alphabetical order.

To compute the total number of teams playing in each division in the current season, you need to gather the information of all the divisions and count the number of teams playing in each division.

1. Create a list of all the divisions in the current season.
2. Iterate through the list of divisions.
3. For each division, gather the information about the teams playing.
4. Count the number of teams playing in each division.
5. Repeat this process for all the divisions.
6. Once you have the total number of teams playing in each division, you can organize the results.

To compute the total number of games for each coach in alphabetical order, you need to gather the information of all the coaches and count the number of games for each coach.

1. Create a list of all the coaches in alphabetical order.
2. Iterate through the list of coaches.
3. For each coach, gather the information about the number of games they have coached.
4. Count the number of games for each coach.
5. Repeat this process for all the coaches.
6. Once you have the total number of games for each coach, you can organize the results in alphabetical order.

To compute the number of games for each location in alphabetical order, you need to gather the information of all the locations and count the number of games played at each location.

1. Create a list of all the locations in alphabetical order.
2. Iterate through the list of locations.
3. For each location, gather the information about the games played at that location.
4. Count the number of games played at each location.
5. Repeat this process for all the locations.
6. Once you have the number of games for each location, you can organize the results in alphabetical order.

In conclusion, to compute the total number of teams enrolled for each club, the total number of teams playing in each division, the total number of games for each coach, and the number of games for each location, you need to gather the relevant information and count accordingly.

To know more about number   visit

https://brainly.com/question/3589540

#SPJ11

The total price of the land would increase by $2020 if you measured the parcel with a steel tape measure on a day when the temperature was 17°C above normal.

The coefficient of thermal expansion for steel is 0.0000116 m/m°C. This means that for every 1°C increase in temperature, a steel tape measure will expand by 0.0000116 m. On a day when the temperature is 17°C above normal, the steel tape measure will expand by 0.0000116 * 17 = 0.0002072 m.

The land title says the dimensions of the parcel are 30 m x 40 m. If the steel tape measure expands by 0.0002072 m, then the actual dimensions of the parcel are 30.0002072 m x 40.0002072 m. This means that the actual area of the parcel is 30.0002072 * 40.0002072 = 12000.8288 square meters.

The land title says the price of the land is $60,000 per square meter. So, the actual price of the land is 12000.8288 * 60,000 = $7200492.8. This is $2020 more than the price listed on the land title.

The coefficient of thermal expansion is a measure of how much a material expands when its temperature increases. The coefficient of thermal expansion for steel is very small,

but it is still significant enough to cause a measurable change in the length of a steel tape measure when the temperature changes.

In this case, the temperature is 17°C above normal, which is a significant change in temperature. The steel tape measure will expand by 0.0002072 m, which is a small change, but it is still enough to cause a measurable change in the area of the parcel.

The actual area of the parcel is 0.0002072 m larger than the area listed on the land title. This means that the actual price of the land is $2020 more than the price listed on the land title.

To know more about length click here

brainly.com/question/30625256

#SPJ11

\(6 \times (w + 5) = 7\)

Answer:

6 x w (+2)<4+3i>

Step-by-step explanation:

Answer:greater

Step-by-step explanation: .03 is greater than .02, think about it is 3 less or greater than 2?

Answer:

Step-by-step explanation:

the y intercept is 3 and the slope is 3/2

so you go up 3 from the y intercept and 2 to the right

a) There will always be a specific time t,1 at which the object reaches a particular height.

b) The object hits the ground after approximately 12.5 seconds.

c) The average rate of change in s over the interval [24,25] is approximately -239.1 meters per second.

(a) The existence of a time t,1 can be explained by the fact that the object is falling from a certain height and will eventually reach the ground.

Since time is a continuous variable, the object's height, represented by the position function s(t), will change continuously as time progresses.

Therefore, there will always be a specific time t,1 at which the object reaches a particular height.

(b) To find the time it takes for the object to hit the ground, we need to determine when the height is zero. Set s(t) = 0 and solve for t:

-4.9t² + 3062.5 = 0

t₁ = 122.55 / (-9.8) ≈ -12.5

t₂ = -122.55 / (-9.8) ≈ 12.5

Therefore, the object hits the ground after approximately 12.5 seconds.

(c) The average rate of change in s over the interval [24,25] can be found by calculating the difference in position divided by the difference in time:

Average rate of change = (s(25) - s(24)) / (25 - 24)

Substituting the position function into the equation:

Average rate of change = (−4.9(25)² + 3062.5) - (−4.9(24)² + 3062.5) / (25 - 24)

Simplifying the equation:

Average rate of change = (−4.9(625) + 3062.5) - (−4.9(576) + 3062.5)

Average rate of change = (-3062.5 + 3062.5) - (-2822.4 + 3062.5)

Average rate of change = 0 - (-2822.4 + 3062.5)

Average rate of change = 0 - 239.1

Average rate of change ≈ -239.1 meters per second

The average rate of change in s over the interval [24,25] is approximately -239.1 meters per second.

This is a good estimate of the velocity at which the object hits the ground because the average rate of change represents the average velocity over a specific time interval.

In this case, the interval [24,25] is very close to the time when the object hits the ground.

However, since the object's velocity is changing continuously, the estimate can be improved by finding the instantaneous velocity using calculus.

To improve the estimate, we can take the derivative of the position function with respect to time, which gives us the instantaneous velocity function. The derivative of s(t) = -4.9t² + 3062.5 is:

s'(t) = -9.8t

By substituting the time at which the object hits the ground (the value of t found in part (b)) into the derivative, we can determine the instantaneous velocity at that specific moment.

Taking the derivative and evaluating it at the time of impact provides a more accurate estimate of the velocity at which the object hits the ground.

Learn more about instantaneous velocity click;

https://brainly.com/question/14365341

#SPJ4

The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

Given that,

The function is f(x)= (x-5)³(x+2)²

We have to find at which root does the graph function touch the x-axis.

We know that,

Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.

Take the function

f(x) = (x-5)³(x+2)²

f(x) = 0 if a curve touches the x-axis.

⇒ (x - 5)³(x + 2)² = 0.

But if ab = 0

So, a=0 and b=0

⇒ (x - 5)³ = 0 and (x + 2)² = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x=5 and x=-2.

Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

To learn more about function visit: https://brainly.com/question/28135761

#SPJ4

Given that sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are as follows: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

We are given that sec(t) = -2.475, which represents the reciprocal of the cosine of angle t. Since sec(t) is negative and angle t is in Quadrant III, we can deduce that the cosine of t is negative. To find cos(t), we can use the identity sec(t) = 1/cos(t) and solve for cos(t), resulting in cos(t) ≈ 0.404.

Using the Pythagorean identity \(sin^2(t) + cos^2(t)\) = 1, we can find sin(t) as sin(t) = ±\(\sqrt(1 - cos^2(t))\). Since angle t is in Quadrant III, where sine is negative, we take the negative value. Thus, sin(t) ≈ -0.916.

By dividing sin(t) by cos(t), we obtain the tangent of t. Hence, tan(t) ≈ sin(t)/cos(t) ≈ -0.916/0.404 ≈ 2.268.

Cosecant (csc) is the reciprocal of sine, so csc(t) ≈ 1/sin(t) ≈ -1.092.

Similarly, cotangent (cot) is the reciprocal of tangent, so cot(t) ≈ 1/tan(t) ≈ 1/2.268 ≈ 0.441.

In conclusion, when sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are approximately: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

Learn more about Quadrant here:

https://brainly.com/question/26426112

#SPJ11

Double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

The matrix calculator is a useful tool for solving equations involving matrices. To find the values of the variables in the matrix calculator, follow these steps:

1. Enter the coefficients of the variables and the constant terms into the calculator. For example, if you have the equation 2x + 3y = 10, enter the coefficients 2 and 3, and the constant term 10.

2. Select the appropriate operations for solving the equation. The calculator will provide options such as Gaussian elimination, inverse matrix, or Cramer's rule. Choose the method that suits your equation.

3. Perform the selected operation to solve the equation. The calculator will display the values of the variables based on the solution method. For instance, Gaussian elimination will show the values of x and y.

4. Check the solution for consistency. Substitute the obtained values back into the original equation to ensure they satisfy the equation. If they do, you have found the correct values of the variables.Remember to double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

Learn more about Matrix here,https://brainly.com/question/27929071

#SPJ11

Answer:

1.50$

Step-by-step explanation:

difference in money amount: $6

difference in hours: 4

6 divided by 4 equals 1.50.

1.50 times 4 equals 6, hence its 1.50 per hour.

The rate of change in the Starbucks stock value is 150%.

Given that, At 10 AM, one share of Starbucks stock was $35. By 2 PM the price was $41.

We need to find the rate the Starbucks stock value was changing is - per hour.

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Now, the difference in money=41-35=$6

The number of hours between 10 AM to 2 PM is 4 hours.

The rate of change = The difference in money/Number of hours × 100

=6/4 × 100

=150%

Therefore, the rate of change in the Starbucks stock value is 150%.

To learn more about the rate of change visit:

https://brainly.com/question/12786410.

#SPJ2

Given the expression :

The expression will be equal:

so, the answer is option 4)

Answer:

875 Watts

Step-by-step explanation:

Given that :

P α s²

P = ks²

Where k is the proportionality constant

When ; p = 1260 ; s = 30

1260 = k * 30²

1260 = 900k

k = 1260 / 900

k = 1.4

Value of p ; when s = 25

P = 1.4 * s²

P = 1.4 * 25²

P = 1.4 * 625

P = 875 watt

Answer:

28.8 cm

Step-by-step explanation:

Since a square's length is the same for all four sides, we have

7.2 + 7.2 + 7.2 + 7.2 or 7.2(4)

We should get 28.8 cm as our answer.

Answer:

P =28.8 cm

Step-by-step explanation:

The perimeter of  square is given by

P = 4s where s is the side length

P = 4* 7.2

P =28.8 cm

The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

know more about mathematics here

https://brainly.com/question/15209879#

#SPJ11

Not exactly sure lol

Answer: Graphing

Step-by-step explanation:

Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods.

* Hopefully this helps!

At the time when we have to decide whether the system of equations has a solution so here we do the graphing.

It is considered to be the best method at the time when it introduced to the new student for solving the system of 2 equations  in 2 variables as it provides the visual to record what actually they have looking.

Also, graphing is considered to be less exact and taken more time as compared to the other methods.

Learn more about graph here: https://brainly.com/question/24299008

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

  (x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

  if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

  magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

  by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

 and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

Learn more about reflection here brainly.com/question/11203617

#SPJ1

The composition of transformations that maps BCD to B"C"D" is described by the following rule:

Composition translation of 6 units x, negative 5 units y across the y-axis last response

Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.

1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)

2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)

3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)

∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.

The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)

The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)

The x-coordinates of the triangle B'C'D' vertices are added by 6.

The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.

The y-coordinates of triangle B'C'D' vertices are subtracted by 5.

∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

Learn more about reflection here:

brainly.com/question/11203617

#SPJ1

Answer:

64x²y²

Step-by-step explanation:

Use the great smart calculator

hope it helpz uuuuuuu

Answer:

see explanation

Step-by-step explanation:

Given

10 = 7 - m ( subtract 3 from both sides )

3 = - m ( multiply both sides by - 1 )

- 3 = m , or

m = - 3

As a check

Substitute m = - 3 into the right side of the equation and if equal to the left side then it is the solution

7 - m = 7 - (- 3) = 7 + 3 = 10 = left side

Thus m = - 3 is the solution to the equation

There are two free variables, so the dimension of the eigenspace is 2. So the dimensions of the associated eigenspaces are 2 for all three eigenspace.

To determine which of the given values are complete eigenvalues, we need to find the characteristic polynomial of the matrix. This is done by finding the determinant of (A - λI), where A is the matrix and λ is the eigenvalue:

| 3-λ   2    0   -4    1 |
| 0     1-λ  3    1    0 |
| 1     -1   -1-λ 4    0 |
| -1    0    2    -4-λ 0 |
| 1     1    -1   0    1-λ|

Expanding along the first row, we get:

(3-λ) | 1-λ  3   1   0 |
    |-1   2-λ 4   0 |
    |1    -1  -4-λ 0 |
    |1    -1  0    1-λ |

= (3-λ)[(2-λ)(1-λ)(1-λ) + 4(-1)(1-λ) + 0(4-λ)] - (-1)[(1-λ)(1-λ)(4-λ) + 0(1-λ) + 0(-1)] + (1)[(1-λ)(4-λ)(0) - (2-λ)(1-λ)(-1)] - (1)[(1-λ)(-1)(-1) - (2-λ)(-1)(0)]

= (3-λ)[λ^3 - 6λ^2 + 9λ - 4] + (λ-1)[4λ^2 - 10λ + 6] + (λ-1)(λ-4) - (λ-2)

= λ^5 - 11λ^4 + 44λ^3 - 78λ^2 + 60λ - 16

Now we can check which of the given values satisfy the characteristic polynomial:

(a) 3, († 2), 0, 1
Substituting each value into the polynomial, we get:
3^5 - 11(3^4) + 44(3^3) - 78(3^2) + 60(3) - 16 = 0
2^5 - 11(2^4) + 44(2^3) - 78(2^2) + 60(2) - 16 ≠ 0
0^5 - 11(0^4) + 44(0^3) - 78(0^2) + 60(0) - 16 ≠ 0
1^5 - 11(1^4) + 44(1^3) - 78(1^2) + 60(1) - 16 = 0

So the complete eigenvalues for this matrix are 3, 0, 1.

To find the dimension of the associated eigenspace for each eigenvalue, we need to find the nullspace of (A - λI). For each eigenvalue, we can do this by row reducing the matrix (A - λI) and finding the number of free variables. The dimension of the associated eigenspace is then equal to the number of free variables.

(a) λ = 3:

| 0 -1  1  1 -1 |
| 0 -2  4  0  1 |
| 1 -1 -4  2  1 |
|-1  0  2 -7  1 |
| 1  1 -1  0 -2 |

RREF:

| 1  0 -2  0  0 |
| 0  1 -2  0  0 |
| 0  0  0  1  0 |
| 0  0  0  0  1 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

(a) λ = 0:

| 3  2  0 -4  1 |
| 0  1  3  1  0 |
| 1 -1 -1  4  0 |
|-1  0  2 -4  0 |
| 1  1 -1  0  1 |

RREF:

| 1  0 -2  0  0 |
| 0  1 -2  0  0 |
| 0  0  0  1  0 |
| 0  0  0  0  0 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

(a) λ = 1:

| 2  2  0 -4  1 |
| 0  0  3  1  0 |
| 1 -1 -2  4  0 |
|-1  0  2 -5  1 |
| 1  1 -1  0  0 |

RREF:

| 1  0 -1  0  0 |
| 0  1 -1  0  0 |
| 0  0  0  1 -1 |
| 0  0  0  0  0 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

So, the dimensions of the associated eigenspaces are 2 for all three eigenvalues.

Learn more about eigenspace here:

brainly.com/question/30715889

#SPJ1

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

Learn more about probability here;

https://brainly.com/question/29087823

#SPJ4