find a 3×3 matrix with exactly one (real) eigenvalue 2, such that the 2-eigenspace is a line.

Answer:

Step-by-step explanation:

An advantage of within-subjects designs is that individual differences remain constant across comparison groups.

In a within-subjects design, each participant serves as their own control group, meaning that the same participant is tested under different conditions or at different time points. This eliminates the potential influence of individual differences between participants, such as age, gender, intelligence, or personality traits, on the results of the study.

By eliminating individual differences between comparison groups, within-subjects designs increase the statistical power of the study, which means that the study is more likely to detect meaningful differences between conditions or time points. This can lead to more precise and accurate conclusions about the effects of the independent variable on the dependent variable.

However, within-subjects designs are also vulnerable to other types of bias, such as practice effects or carryover effects, where the effects of one condition carry over to the next condition. These effects can be controlled by counterbalancing the order of conditions or using a washout period between conditions.

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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Answer:

Step-by-step explanation:

The value of b according to the binomial expansion expressed in the form, (ax + b)⁴ is; b = 15.

The binomial expansion given is;

625x4 – 7,500x3 + 33,750x2 – 67,500x + 50,625.

While expressing the binomial expansion in the form; (ax + b)⁴;

The value of b can be evaluated as follows;

In essence, the quartic root of 50625 is the value of b as follows;

\(b = \sqrt[4]{50625} \)

b = 15. OR. b = -15

However, more convincingly, the value of b is; Choice D: 15

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The proper answer from each drop-down menu in the system depicted by the graph. Reset In the Next'system of Inequalities, the graph stands for 4x-y.

The system of inequality is depicted in the graph. 1. 4x-y less than or equal to 4 and 2x-2y less than or equal to 3, 2. 4x-y greater than or equal to 4 and 2x-2y less than or equal to 3, 3. 4x-y less than or equal to 4 and 2x-2y larger than or equal to 3, 4. 4x-y greater than or equal to 4 and 2x-2y greater than or equal to 3. In the graph-representation of the system, the test point fulfils both of the inequalities.

Pick the appropriate response from each drop-down menu in the system shown by the graph. Reset The graph represents 4x-y in the Next'system of Inequalities.. Equations simultaneously, or a system of equations Multiple equations must be solved simultaneously in algebra. There must be an equal number of equations and unknowns for a system to have a singular solution.

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The correct option from the given choices is 4) 5,070. Determine the reorder point in a continuous review policy with a cycle service level of 95%,

We can use the following formula:

Reorder Point = R + Z * sqrt(L * \(σ^2_R\))

Where:

- R is the average demand during lead time

- Z is the Z-score corresponding to the desired service level (95% corresponds to a Z-score of approximately 1.645)

- L is the lead time

- \(σ^2_\)R is the variance of demand during lead time

Given:

R = 1500

\(σ^2\)R = 200

L = 3

Using the formula, we can calculate the reorder point:

Reorder Point = 1500 + 1.645 * sqrt(3 * 200)

Reorder Point ≈ 1500 + 1.645 * sqrt(600)

Reorder Point ≈ 1500 + 1.645 * 24.4948974

Reorder Point ≈ 1500 + 40.2570784

Reorder Point ≈ 1540.2570784

Rounding the reorder point to the nearest whole number, we get:

Reorder Point ≈ 1540

Therefore, the correct option from the given choices is 4) 5,070.

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Answer:

The triangle is not right angled.

Step-by-step explanation:

According to the Pythagoras theorem, the sum of the squares of the two legs of a triangle is equal the square of the third side.

For example, in triangle ABC,

\(AB^{2} = BC^{2}+CA^{2}\)

It shows, that the triangle ANBC is right angled and right angle is at C.

So if the sum of the squares of the two legs of a triangle does not equal the square of the third side, it shows that the triangle is not right angled.

2.1  The mean for the grouped data is approximately 68.47.

To calculate the mean for this grouped data, we use the midpoint of each interval and the corresponding frequency.

The midpoint for each interval can be calculated by taking the average of the lower and upper bounds.

For the first interval [50-58), the midpoint is (50 + 58) / 2 = 54.

For the second interval [58-66), the midpoint is (58 + 66) / 2 = 62.

For the third interval [66-74), the midpoint is (66 + 74) / 2 = 70.

For the fourth interval [74-82), the midpoint is (74 + 82) / 2 = 78.

For the fifth interval [82-90), the midpoint is (82 + 90) / 2 = 86.

For the sixth interval [90-98), the midpoint is (90 + 98) / 2 = 94.

To calculate the mean, we multiply each midpoint by its corresponding frequency, sum up these products, and divide by the total frequency.

Mean = (543 + 627 + 7012 + 780 + 862 + 946) / (3 + 7 + 12 + 0 + 2 + 6)

Calculating this expression, we find that the mean is approximately 68.47.

2.2 The first quartile for the grouped data can be found by determining the cumulative frequency at which the first 25% of the data falls.

We start by calculating the cumulative frequencies.

Cumulative frequency for the first interval is 3.

Cumulative frequency for the second interval is 3 + 7 = 10.

Cumulative frequency for the third interval is 10 + 12 = 22.

Cumulative frequency for the fourth interval is 22 + 0 = 22.

Cumulative frequency for the fifth interval is 22 + 2 = 24.

Cumulative frequency for the sixth interval is 24 + 6 = 30.

Since the first quartile represents the 25th percentile, we look for the interval that contains the 25th percentile. In this case, it is the second interval [58-66).

To find the first quartile within this interval, we use the formula:

First Quartile = L + (N/4 - CF) * (W / f)

Where L is the lower bound of the interval, N/4 is the 25th percentile position, CF is the cumulative frequency of the previous interval, W is the width of the interval, and f is the frequency of the interval.

Plugging in the values, we get:

First Quartile = 58 + ((30/4 - 10) * (8 / 7))

Calculating this expression, we find that the first quartile for the grouped data is approximately 60.57.

2.3 The cumulative frequency table can be derived by summing up the frequencies for each interval, starting from the first interval.

Interval Frequency    Cumulative Frequency

     [50-58)                           3 3

     [58-66)                           7 10

     [66-74)                           12 22

     [74-82)                           0 22

    [82-90)                           2 24

    [90-98)                           6 30

The cumulative frequency for each interval is the sum of its own frequency and the cumulative frequency of the previous interval. This table shows the running total of frequencies as we move through the intervals from left to right.

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We can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women

an SRS?

the leader of a student organization wishes to form a committee that will consist of 5 of the 50 members.

he decides to take an SRS of size five from the members and those selected will comprise the committee.

he chooses an SRS of size five and all are men.

he would like to have some women on the task force, so he decides to take another SRS.

this time there are three women and two men in the sample, so he decides these five will form the committee.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling.

an SRS because all members had the same chance of being in the final sample.

not an SRS because a sample consisting entirely of men is not allowed.

not an SRS because the first sample was not balanced between men and women.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women.

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The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.

In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.

It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.

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The  particular solution of the differential equation that satisfies the initial condition  \(\frac{du}{dv} = uvsin v^{2} u(0)= e^{4}\)  is  \(u(v)=sin v^{2} + e^{4}-\frac{1}{2}\)

To find the particular solution of the differential equation that satisfies the initial condition                                                              

 \(\frac{du}{dv} = uv sin v^{2} u(0) = e^{4}\)

we must follow the steps below: Initial Equation \(\frac{du}{dv} = uv sin\)

v²Separating variables gives us: \(u du = v sinv^{2} dv\)

a) Integrating both sides, we have:

\(\int\limits {u} \, du = \int\limits {v sin v^{2} } \, dv(\frac{u^{2} }{2} )\)

\(= \frac{-1}{2} cos v^{2} +C1 u^{2}\)

\(= -cosv^{2} + C2\)

b) Differentiate both sides to get:

\(2u \frac{du}{dv} = 2v^{2} cosv^{2}\)

c) We replace du/dv in the equation above with the equation given in the initial condition to obtain:                                                      

  = \(2u (uv) sinv^{2}\)

= \(2v^{2} cosv²u\)

= \(2v cosv^{2} dv + C3\)

d) Integrating both sides gives:

\(\int\limits {u} \, dv = \int\limits {2v cos v^{2} } \, dv + \frac{C3}{2v} (v)\)

\(= sinv^{2} + C4 + \frac{C3}{2}\)

e) We substitute the initial condition to obtain the value of

\(C4.e^{2}= sin 0^{2}+ C4+ \frac{C3}{2C4}\)

\(= e^{4} - \frac{1}{2}\)

The particular solution is obtained by replacing the value of C4 and is as follows: \(u(v) = sin v^{2} + e^{2} - \frac{1}{2}\)

Answer: \(u(v) = sin v^{2} + e^{2} - \frac{1}{2}\)

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Step-by-step explanation:

the amount per unit size

Answer:

"statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = \(4x\)

Let, Number of girls = \(5x\)

Total number of students = Number of boys + Number of girls = 270

\(\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}\)

Therefore, number of boys = 4 \(\times\) 30 = 120

And, number of girls = 5 \(\times\) 30 = 150

As per Statement 1:

Finding \(\frac{4}5\) of the number of girls:

\(\dfrac{4}{5}\times 150 = 4 \times 30 = 120\) = Number of boys.

Finding \(\frac{4}9\) of the total number of students:

\(\frac{4}{9}\times 270= 4 \times 30 = 120\) = Number of boys.

Number of boys is equal to \(\frac{4}9\) of total number of students.

So, "statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Answer:

10.

Step-by-step explanation:

If you're subtraction a negative number, you are basically adding a positive number. 5-(-5) = 5+5.

Hey there!

GUIDE:

2 negatives = positive

2 positives = positive

1 negative & 1 positive = negative

1 positive & 1 negative = negative

Negatives are BELOW 0 and they are to the LEFT of 0

Positives are ABOVE 0 and they are to the RIGHT of 0

ANSWERING the QUESTION

5 - (-5)

= 5 + 5

= 10

Therefore, your answer is: 10

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Hence, r=2cosθ represents a circle with centre (1,0) and radius 1 and (1,0) in polar coordinates too is (1,0

Step-by-step explanation:

hope this helps;)

The name of the shape graphed by the function \(r^{2} = 4\;cos\) θ is Limaçon with inner loop.

We have the following function -

\(r^{2} = 4\;cos\) θ

We have to find the shape represented by this function.

Polar coordinates are used to represent a point in a two - dimensional plane. In polar coordinate system, the point under consideration is represented with the help of two variables namely \(r\) and θ. (Take the reference from the figure attached)

We have -

\(r^{2} = 4\;cos\) θ

The relation between variables in polar coordinates and cartesian coordinates is -

\(x = rcos\theta\\y=rsin\theta\\r=\sqrt{x^{2} +y^{2} }\\\)

First, lets convert this equation in the rectangular coordinates -                                                      

\(r^{3} =4\;r\;cos\;\theta\\r\times\;r^{2} = 4\;r\;cos\;\theta\\\sqrt{x^{2} +y^{2} }\;\times\;(x^{2} +y^{2}) = 4x\\(x^{2} +y^{2})=\frac{4x}{\sqrt{x^{2} +y^{2} }}\)

The above equation in rectangular coordinate system represents a Limaçon with inner loop.

Hence, the name of the shape graphed by the function \(r^{2} = 4\;cos\) θ is

Limaçon with inner loop.

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Answer:

\(\sqrt{5*4-3*2}\)=\(\sqrt{14}\)

Step-by-step explanation:

Operations are used to represent algebraic expressions

The value of 4∎2 is \(\mathbf{ \sqrt{14}}\)

The operation is given as:

\(\mathbf{a\ n\ b = \sqrt{(5a - 3b)}}\)

4∎2 means that a = 4 and b = 2.

So, we have:

\(\mathbf{4\ n\ 2 = \sqrt{(5(4) - 3(2))}}\)

Expand

\(\mathbf{4\ n\ 2 = \sqrt{(20 - 6)}}\)

\(\mathbf{4\ n\ 2 = \sqrt{14}}\)

Hence, the value of 4∎2 is \(\mathbf{ \sqrt{14}}\)

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Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9

Answer:

3 + 2y = 2 + 4y

Step-by-step explanation:

1. Create the equation

3 + 2y = 2 + 4y

There are 3 "1" blocks and 2 "y" blocks on the left. There are 2 "1" blocks and 4 "y" blocks on the right. The scale shows both are equal.

Answer:

3 + 2y = 2 + 4y

Step-by-step explanation:

To create an equation from this model, we look at both sides of the scale. The left has three 1 units and two y units, and there are two 1 units and four y units on the right side. Since the scale shows that both sides are equal in weight, we know that our equation would have an equal sign to show they are equal.

Left: Three 1 units can be written as 3 and two y units could be written as 2y.

Right: Two 1 units can be written as 2 and four y units could be written as 4y.

Now, we put these values together (with an equal sign) to get:

3 + 2y = 2 + 4y.

Hope this helps!

It is important to carefully select the survey population and explain why the survey is necessary. It is also important to limit the number of questions and ask them in a clear and concise manner.

Select the survey population carefully: This means selecting a group of people who are representative of the target population and have the relevant knowledge or experience to answer the survey questions. For example, if the survey is about customer satisfaction with a product, the survey population should be customers who have used the product.

Limit the number of questions: It's important to keep the survey short and focused to reduce the risk of respondent fatigue and increase the response rate. A shorter survey also makes it easier to analyze the data.

Explain why the survey is necessary: This helps to increase the response rate by providing a clear explanation of why the survey is being conducted, what the data will be used for, and how it will benefit the target population.

Select the survey population randomly: Random selection helps to ensure that the survey results are representative of the target population and minimize the risk of bias in the sample.

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what tips can you share with the group? check all that apply.

a. The radius of the balloon originally can be found by substituting the initial volume (500 cubic inches) into the formula.

b. The radius after inflating the balloon to 800 cubic inches can be found by substituting the final volume (800 cubic inches) into the formula.

c. The amount of increase in the radius can be calculated by subtracting the original radius from the radius after inflation.

a. To find the radius of the balloon originally, we substitute the initial volume of 500 cubic inches into the formula:

r = ³√(3V / 4π) = ³√(3*500 / 4π).

b. To find the radius after inflating the balloon to 800 cubic inches, we substitute the final volume of 800 cubic inches into the formula:

r = ³√(3V / 4π) = ³√(3*800 / 4π).

c. To find the amount of increase in the radius, we subtract the original radius from the radius after inflation:

Amount of increase = Radius after inflation - Original radius.

By calculating the expressions in parts (a) and (b), we can find the original radius and the radius after inflating the balloon. Then, by subtracting the original radius from the radius after inflation, we can determine the amount of increase in the radius.

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The Solution.

The total number of people surveyed = 750.

The number of age group 41 - 50 that favored the Do-It-Yourself books = 69

The percentage of the people in age group 41 - 50, and favored the Do-It-Yourself books is calculated as below:

Hence, the correct answer is 9 percent.

Answer:

Step-by-step explanation:

This is a trick question,  about the red marks again.   those marks are important b/c they tell you that the lengths are the same, so that the angles MUST also be the same.  That is  ,  D and E are equal

so set up your equations with that info

180 = 84 +2p

now use your algebra skillz to solve

180-84 / 2 = p

96/2 = p

48 = p

see??

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

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The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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Answer:

100 miles they willl be the same price

Step-by-step explanation:

Answer:

Step-by-step explanation:

Try to remember the properties of each of the mentioned figures like the square is a parallelogram with all sides equal and all interior angles equal to 90o . Once you are able to recollect the definitions of each figure, use the definitions to reach an answer. Drawing the figures might be very helpful.

Complete step-by-step answer:

Let us try to remember the definitions of all the figures mentioned one by one. First let us start with Rhombus. So, rhombus is a parallelogram with all its sides equal and diagonals perpendicular to each other.