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The bias of mu1 is 0, the variance of mu1 is 1/2, and the mean squared error of mu1 is 1/2.

We need to find the bias, variance, and mean squared error of mu1, given that x1 and x2 are independent with an unknown mean (mu) and a known variance (sigma^2 = 1), and mu1 = (x1 + x2)/2.

Step 1: Compute the expected value of mu1.
E(mu1) = E((x1 + x2)/2) = (E(x1) + E(x2))/2 = (mu + mu)/2 = mu

Step 2: Calculate the bias of mu1.
Bias (mu1) = E (mu1) - mu = mu - mu = 0

Step 3: Calculate the variance of mu1.
Var(mu1) = Var((x1 + x2)/2) = (1/4) * (Var(x1) + Var(x2)) = (1/4) * (1 + 1) = 1/2

Step 4: Calculate the mean squared error of mu1.
MSE(mu1) = Bias(mu1)^2 + Var(mu1) = 0^2 + 1/2 = 1/2

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True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

7

Step-by-step explanation:

because  49 divied into 7 is 7 and 7x7 is 49

Answer:

The second image.. Happy to Help :)

Step-by-step explanation:

Therefore, at the same constant speed, the plane would travel approximately 507,406.89 miles in 3.33 hours.

To determine the number of miles the plane would travel in 3.33 hours at the same constant speed, we can use a proportion based on the given information.

The plane traveled 762,762 miles in 5 hours. We can set up the proportion:

762,762 miles / 5 hours = x miles / 3.33 hours

To solve for x (the number of miles traveled in 3.33 hours), we cross-multiply and divide:

(762,762 miles) * (3.33 hours) = (5 hours) * x miles

2,537,034.46 miles = 5x miles

Dividing both sides of the equation by 5:

2,537,034.46 miles / 5 = x miles

x ≈ 507,406.89 miles

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To find out how many milliliters of a 25% acid solution you need to add to a 60 mL of 60% acid solution to obtain a 40% acid solution, you can use a mixture equation.

Let's assume that x represents the amount of 25% acid solution you need to add.

To solve the equation, we need to consider the acid content in both solutions. The acid content is the percent of acid in the solution multiplied by the volume of the solution. So for the 25% acid solution, the acid content would be 0.25x, and for the 60% acid solution, the acid content would be 0.6 * 60 mL.

The total acid content in the resulting solution should be 40% of the total volume, which is 60 mL + x mL. Therefore, the equation is:

0.25x + 0.6 * 60 = 0.4 * (60 + x)

Simplifying the equation, we have:

0.25x + 36 = 24 + 0.4x

0.15x = 12

x = 80

Therefore, you need to add 80 mL of the 25% acid solution to the 60 mL of the 60% acid solution to obtain a 40% acid solution.

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Answer:

3 5/9

Step-by-step explanation:

Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.

The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.

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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the

highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure

of variation.

The measure of variation that is affected most by a few extreme scores is the standard deviation.

The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared

deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.

On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.

The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.

The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.

The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme

enough to change the position of the middle value.

The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less

pronounced than on the standard deviation.

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To find the probability that a randomly purchased item will last longer than 11 years, we can use the normal distribution and the given mean and standard deviation.

Let X be the lifespan of the item. We are interested in finding P(X > 11).

First, we need to standardize the value 11 using the z-score formula:

z = (x - μ) / σ

where x is the value (11 years), μ is the mean (10.8 years), and σ is the standard deviation (0.5 years).

z = (11 - 10.8) / 0.5

z = 0.4 / 0.5

z = 0.8

Next, we look up the z-score of 0.8 in the standard normal distribution table or use a calculator to find the corresponding probability.

Using the standard normal distribution table, the area to the left of 0.8 is approximately 0.7881. Since we want the area to the right of 0.8, we subtract the value from 1:

P(X > 11) = 1 - 0.7881

P(X > 11) ≈ 0.2119

Therefore, the probability that a randomly purchased item will last longer than 11 years is approximately 0.2119 or 21.19%.

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there must be two distinct subsets of a whose elements when added up give the same sum.

Let the six positive integers in the set a be a₁, a₂, a₃, a₄, a₅, and a₆.

The maximum possible sum of any subset of a is 14+13+12+11+10+9 = 69 (when all six elements are chosen).

The minimum possible sum of any subset of a is 1+2+3+4+5+6 = 21 (when none of the elements are chosen).

Thus, the possible range of sums for any subset of a is from 21 to 69.

There are 2^6 = 64 possible subsets of a.

If we consider the sums of all possible subsets of a, there are 64 different sums.

Since the range of possible sums is only 49 (69-21), by the pigeonhole principle, there must be at least two distinct subsets of a that have the same sum.

Therefore, there must be two distinct subsets of a whose elements when added up give the same sum.

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Draw the angle \( u \):The angle u lies in the first quadrant and tan inverse of x/4 = u..

Therefore,tan u = x/4The diagram of angle u is as follows:(b)

Determine the value of\(\[\frac{d}{d x}\left(\tan ^{-1}\left(\frac{x}{4}\right)\right)\]:We have \[\tan (u)=\frac{x}{4}\]\)

Differentiating with respect to x we get:\(\[\frac{d}{d x} \tan (u)=\frac{d}{d x}\left(\frac{x}{4}\right)\]\)

Using the identity:\(\[\sec ^{2}(u)=\tan ^{2}(u)+1\]\)

Thus,\(\[\frac{d}{d u} \tan (u)=\frac{d}{d u}\left(\frac{x}{4}\right)\]\[\sec ^{2}(u) \frac{d u}{d x}=\frac{1}{4}\]\)

Since \(\[\sec ^{2}(u)=\frac{1}{\cos ^{2}(u)}\]\)

Therefore,\(\[\frac{d u}{d x}=\frac{\cos ^{2}(u)}{4}\]\)

Now, since\(\[\tan (u)=\frac{x}{4}\]\)

Therefore, \(\[\cos (u)=\frac{4}{\sqrt{x^{2}+16}}\]\)

Thus\(,\[\frac{d}{d x}\left(\tan ^{-1}\left(\frac{x}{4}\right)\right)=\frac{1}{4} \times \frac{16}{x^{2}+16}\]\[\frac{d}{d x}\left(\tan ^{-1}\left(\frac{x}{4}\right)\right)=\frac{4}{x^{2}+16}\]\)

Therefore,\(\[\frac{d}{d x}\left(\tan ^{-1}\left(\frac{x}{4}\right)\right)=\frac{4}{x^{2}+16}\]\)

and it satisfies the limit condition of\(\[0 \leq \frac{d}{d x}\left(\tan ^{-1}\left(\frac{x}{4}\right)\right) \leq \frac{1}{4}\]\)which is a characteristic of any derivative of a function.

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Generally, using a protractor we see x to be an angle 32 degrees

Hence, we solve

since the angle in point is given by 360 and x=35

Therefore

y=360-x

y=360-32

y=328 degrees

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The measure of angle x would be 35° and the measure of angle y would be 325°

From the question, we are to determine the measures of angle x and angle y.

The measure of angle x can be determined with the aid of a protractor.

From the given diagram, we can observe that angle x is an acute angle. That is, the measure of angle x is less than 90°.

After determining the measure of angle x by using a protractor, for example, let us say the measure of angle x is 35°.

We can determine the measure of angle y by using the sum of angles at a point theorem.

Sum of angles at a point is 360°.

Thus, we can write that

x + y = 360°

Then,

35° + y = 360°

y = 360° - 35°

y = 325°

Hence, the measure of x = 35° and the y = 325°

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Answer:

X-intercept is -4

Step-by-step explanation:

Answer:

C.1,384.7mm

Step-by-step explanation:

Area of a circle is pi R Square

R =D/2

R=42/2=21

Area=3•14×21×21=1384•7mm

Answer:

5/9

Step-by-step explanation:

brainliest when possible.

Answer:

1/2 × |AB| × |OE|

Step-by-step explanation:

use the formula for finding the area of a triangle.

Answer:

The length is 5 inches and the width is 4 inches

Step-by-step explanation:

Steffie makes a scale drawing for a crate with a scale factor of 1:3. The dimensions of her scale drawing are 15 inches long by 12 inches wide. The builder creates a scale drawing of the crate with a scale factor of 1:9. What are the dimensions of the builder's scale drawing? A. The length is 4 inches and the width is 5 inches B. The length is 45 inches and the width is 36 inches. C. The length is 5 inches and the width is 4 inches. D. The length is 36 inches and the width is 45 inches

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

dimensions of the image steffie scaled = (15 x 3) by (12 x 3) = 45 by 36

Builders scaled image = (45 / 9) by (36 /9) = 5 by 4

Answer:

-24

Hope that this helps!

Answer:

448 ribbons

Step-by-step explanation:

in order to find this, you need to convert the yards into inches. there are 36 inches is a yard (a yard is 3 feet and one foot is 12 inches ) so you would multiply 112 and 36 to find the total number of inches it woulde be. 112x36=4,032. Now that you know the total number of inches, divide it by 9 to find the total number of ribbions you can make.

4,032/9= 448

so you could make a total of 448 ribbons

Answer:

12.4

Step-by-step explanation:

Do 112 divided by 9

Answer:

About 71% of Earth's surface is covered in water.

Step-by-step explanation:

About 97% of Earth's water is salt water.

About 3% of Earth's water is fresh water.

The numbers in the ascending order is given by A , where

-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given data ,

Let the set of numbers be represented as set P

The value of set P is P = { -4.7 , 11 , 13 , -21 , 8 8/9 , 0 , -6 1/2 , 38 , -73 }

On simplifying the equation , we get

The larger the negative number , the lesser is its value

And , larger the positive number , the greater is its value

So ,

The ascending order of the numbers are

-73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

Hence ,

The ascending order is -73 < -21 < -6 1/2 < -4.7 < 0 < 8 8/9 < 11 < 13 < 38

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Answer:

$787.5

Step-by-step explanation:

first, you have to find how much ginny makes in a week w/o her raise\

17.5*40=700

then, you have to raise it by 12.5%, so her new salary is 112.5% of 17.5

112.5% = 1.125

700*1.125=787.5

Answer:

0.25 meters is the same as A. 25 centimeters

Explanation:

multiply the length value (0.25) by 100 to get to cm from m

hope this helps chu <3

Answer:

m∠1 = 90°

Step-by-step explanation:

Since the line is tangent to the circle, it creates a perpendicular bisector with the diameter. That means that the m∠1 has to be 90°

A change of one standard deviation in x corresponds to a change of r standard deviations in y.False

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, but it does not necessarily indicate that a change of one standard deviation in x corresponds to a change of r standard deviations in y. The magnitude of this correspondence depends on the slope of the regression line, which is determined by both the correlation coefficient and the standard deviations of the variables.

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If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

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Step-by-step explanation:

tan 51= jl/jm = jl/14

jl = 17.28

cos 72=kl/jl

kl = 5.33

Answer:

2 inch

Step-by-step explanation:

3 - 1 = 2

Answer:

1518.25=836.50+24.75p;

p=(1518.25-836.50)/24.75=681.75/24.75

Step-by-step explanation:

24.75 is about 25, so 681.75 is about 700, so that's about 28 people. If you don't have an option, do the math

Answer:

Equation: 24.75p+836.5=1158.25

Answer: p = 13

Step-by-step explanation:

Cost per player = 24.75

number of players = p

cost of bus = 836.50

total raised = 1158.25