suppose x1,x2,x3 are independent random variables uniformly distributed over (0, 1).

The answer of the given question based on the supplementary angle is  the two angles are 58° degrees and 122° degrees.

An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called  sides or arms of  angle. Angles are typically measured in the degrees or the radians.

The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.

Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:

x + y = 180

We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:

x = 2(y + 3)

Now we can substitute the second equation into the first equation to eliminate "x":

(2(y + 3)) + y = 180

Simplifying the equation, we get:

3y + 6 = 180

Subtracting 6 from both sides, we get:

3y = 174

Dividing both sides by 3, we get:

y = 58

Now that we know "y", we can substitute it back into the equation for "x" to find its value:

x = 2(y + 3) = 2(58 + 3) = 122

Therefore, the two angles are 58° degrees and 122° degrees.

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The data collected from the customers in restaurants about the quality of food is an example of a(n); Observational Study

There are four types of statistical studies namely;

Observational studies

Surveys

Experiments

Meta-analytical studies.

1) An observational study involves observing and recording data on some variable(s) of interest.

2) A (sample) survey uses questioning to gather data.

3) An experiment also referred to as experimental study attempts to give an answer to a statistical question by manipulating all or part of the sample.

Now, we are told that some data was collected from the customers in restaurants about the quality of food.

This is a type of observational study because it involves observing and recording data on an interest which is quality of food

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Answer:

A positive association between two variables means that as the values of one variable increase, so do the values of the other variable. This is often represented by a line or curve that slopes upward to the right on a scatterplot. On the other hand, a negative association between two variables means that as the values of one variable increase, the values of the other variable decrease. This is often represented by a line or curve that slopes downward to the right on a scatterplot.

The behavior of the sequence =⋅n. cos (n)/ (6n +2) can be described as oscillatory and convergent.

Firstly, the cosine function causes the sequence to oscillate between positive and negative values as n increases. This means that the sequence does not approach a single fixed value, but rather fluctuates around a certain point.

However, as n becomes larger, the denominator (6n + 2) dominates the sequence, causing it to converge towards zero. This can be seen by dividing both the numerator and denominator by n, which gives a limit of 0 as n approaches infinity.

Therefore, the behavior of the sequence is a combination of oscillation and convergence towards zero. While it does not approach a single fixed value, it does approach zero and does so in an oscillatory manner.

Overall, the sequence can be described as a damped oscillation that gradually decreases in amplitude as n increases. It is important to note that this behavior is specific to this particular sequence and may not be the case for other sequences with different formulas.

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Answer:

Yes, Triangle A

Step-by-step explanation:

To figure out what a fraction is as a decimal u would do the top divided by the bottom

For this fraction it would look like this,

8 divided by 9 which would get you 0.88888888888

So your decimal is  0.889

Its not 0.888 because with decimals since a typical decimal is show as 2-3 numbers it would be rounded up to keep it as 3 numbers or less. so this would be 0.889 or if that doesnt work 0.888 with a line over the last 8.

Answer:

0.889

Step-by-step explanation:

0.88888888 repeating the 3rd 8 is the thousandth place so you look at your neighbor and it is 5 or higher so you round up to 0.889

Answer:

X-2 And X+10

Step-by-step explanation:

That would be the answer for the problem.

Answer:

Step-by-step explanation:

(a) This statement is false. The probability of getting heads or tails on a fair coin is always 50%, regardless of previous outcomes.  

(b) This statement is true. Drawing a face card and drawing a red card from a full deck of playing cards are mutually exclusive events.

(a) The statement is false. The outcome of each coin toss is independent of the previous tosses. Therefore, the chance of getting heads on the next toss is still 50%, regardless of the outcome of the previous eight tosses.

(b) The events of drawing a face card and drawing a red card are not mutually exclusive events. There are 12 face cards in a deck of playing cards, and 6 of them are red (2 jacks, 2 queens, and 2 kings). Therefore, the probability of drawing a face card and a red card from a full deck of playing cards is:

P(face card and red card) = P(face card) x P(red card|face card)
P(face card and red card) = (12/52) x (6/12)
P(face card and red card) = 3/52 or about 5.77%

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Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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b) To find the joint density of the minimum and maximum of the U_i's, we can use the following approach:

Let M = min(U_1, U_2, U_3, U_4, U_5) and let X = max(U_1, U_2, U_3, U_4, U_5). Then we have:

P(M > m, X < x) = P(U_1 > m, U_2 > m, U_3 > m, U_4 > m, U_5 > m, U_1 < x, U_2 < x, U_3 < x, U_4 < x, U_5 < x)

Since the U_i's are independent and uniformly distributed on (0,1), we have:

P(U_i > m) = 1 - m, for 0 < m < 1

P(U_i < x) = x, for 0 < x < 1

Substituting these expressions, we get:

P(M > m, X < x) = (1 - m)^5 * x^5

Therefore, the joint density of M and X is:

f(M,X) = d^2/dm dx (1-m)^5 * x^5 = 30(1-m)^4 * x^4, for 0 < m < x < 1.

c) To find P(R > 0.5), we need to find the probability that the distance between the minimum and maximum of the U_i's is greater than 0.5. We can use the following approach:

P(R > 0.5) = 1 - P(R <= 0.5)

Now, R <= 0.5 if and only if the difference between the maximum and minimum of the U_i's is less than or equal to 0.5. Therefore, we have:

P(R <= 0.5) = P(X - M <= 0.5)

To find this probability, we can integrate the joint density of M and X over the region where X - M <= 0.5:

P(R <= 0.5) = ∫∫_{x-m<=0.5} f(M,X) dm dx

The region of integration is the triangle with vertices (0,0), (0.5,0.5), and (1,1). We can split this triangle into two regions: the rectangle with vertices (0,0), (0.5,0), (0.5,0.5), and (0,0.5), and the triangle with vertices (0.5,0.5), (1,0.5), and (1,1). Therefore, we have:

P(R <= 0.5) = ∫_{0}^{0.5} ∫_{0}^{m+0.5} 30(1-m)^4 * x^4 dx dm + ∫_{0.5}^{1} ∫_{x-0.5}^{x} 30(1-m)^4 * x^4 dm dx

Evaluating these integrals, we get:

P(R <= 0.5) ≈ 0.5798

Therefore,

P(R > 0.5) = 1 - P(R <= 0.5) ≈ 0.4202.

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The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.

In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.

The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.

The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}\)

Answer:

83.75%

Step-by-step explanation:

67/80 = 83.75%

The values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

To determine the values of W and X that make NOPQ a parallelogram, we need to find the conditions under which the opposite sides of the quadrilateral are parallel.

The coordinates of the points N, O, P, and Q are given as follows:

N: (w+7, 5w-5)

O: (3/2x, 3)

P: (?, ?)

Q: (?, ?)

For NOPQ to be a parallelogram, the vector from N to O should be equal to the vector from P to Q, and the vector from O to P should be equal to the vector from Q to N.

The vector from N to O is:

NO = (3/2x - (w+7), 3 - (5w-5))

   = (3/2x - w - 7, -5w + 8)

The vector from O to P should be equal to the vector from Q to N. Thus:

OP = (P_x - (3/2x), P_y - 3)

QN = ((w+7) - Q_x, (5w-5) - Q_y)

Equating the corresponding components, we get the following equations:

3/2x - w - 7 = P_x - (3/2x)

-5w + 8 = P_y - 3

w + 7 = (w+7) - Q_x

5w - 5 = (5w-5) - Q_y

Simplifying these equations, we find:

P_x = 3x

P_y = -5w + 11

Q_x = w + 7

Q_y = 5w

Therefore, the values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

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Answer:

1). y= -5+3x

2). y= -2x-13

3). y= -6x+2

4). y= -x+4

5). y≈ 0.57x

6). y=2x-9

7). Equation incomplete

8). y=3x+23

Step-by-step explanation:

1).

3x-y=5

Subtract 3x from both sides

-y=5-3x

Multiply both sides by -1

y= -5+3x

2).

y+7= -2(x+3)

y+7= -2x-6

Subtract 7 from both sides

y= -2x-13

3).

y= -10-6(x-2)

y=  -10-6x+12

y= -6x+2

4).

3x=12-3y

Add 3y to both sides

3x+3y=12

Subtract 3x from both sides

3y=12-3x

Divide both sides by 3

y= -x+4

5).

-4x-7y=0

Add 4x to both sides

-7y= -4x+0

Multiply both sides by -1

7y= 4x

Divide both sides by 7

y≈ 0.57x

6).

4x-2y=18

Subtract 4x from both sides

-2y= -4x+18

Multiply both sides by -1

2y=4x-18

Divide both sides by 2

y=2x-9

7).

y= 5-

Equation is incomplete.

8).

y-2=3(x+7)

y-2=3x+21

Add 2 to both sides

y=3x+23

Answer:

Angle C is the opposite angle of AB

Side AB is opposite to angle ∠ACB in triangle ABC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given rectangle, AC is the diagonal

ABC and ADC are two right triangles.

We have to find the angle which is opposite to the side AB.

The angle opposite to side AB is angle C.

In the option we have angle ∠ACB.

Hence, Side AB is opposite to angle ∠ACB in triangle ABC

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Answer:

number : number

Step-by-step explanation:

for example, 1:3

this means 1 to 3

so for every 1 banana there are 3 apples

Answer:

i think the correct answer of these qusion is -2,3

Answer:

The answer is Door you can choose C because is likely to be the answer

Two similar figures have a ratio of areas 72:32. The ratio of similarity between the two figures is 3:2.

The ratio of areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. Let's assume the ratio of side lengths is a:b.

Given: Ratio of areas = 72:32

The ratio of areas is the square of the ratio of side lengths. So, we have:

(a/b)^2 = 72/32

Simplifying the equation:

(a/b)^2 = 9/4

Taking the square root of both sides:

a/b = √(9/4)

a/b = 3/2

Hence, the ratio of side lengths of the two similar figures is 3:2.

Since similarity is based on corresponding side lengths, the ratio of similarity is the same as the ratio of side lengths. Therefore, the ratio of similarity between the two figures is 3:2.

This means that for every unit increase in the length of the corresponding side in the smaller figure, the corresponding side in the larger figure increases by 1.5 units.

In summary, the ratio of similarity between the two figures is 3:2, indicating that they are scaled versions of each other with the smaller figure being 3/2 times smaller in each dimension compared to the larger figure.

Hence, the ratio of similarity is 3:2.

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Answer: y-intercept

Step-by-step explanation:

Answer:

Identity property

Step-by-step explanation:

Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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Answer:

a : c = 7 : 10

Step-by-step explanation:

The two ratios (a : b and b : c) both have b in common, so to work out what a : c is, we can use b to 'bridge' the two ratios together.

However, in a : b, b is 4. But in b : c, b is 2. We need to make sure b is the same in both ratios before we can combine the ratios together. The easiest way to do this is to multiply b : c by 2 to get b : c = 4 : 10. Now b is 4 in both ratios.

So now, we can combine the two ratios together to get a : b : c = 7 : 4 : 10. Since we only want a : c though, we can just drop the b and get a : c = 7 : 10. No simplifying is necessary since the ratio is already in its simplest form.

Hope that helps! :)

There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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Step-by-step explanation:

angle 1 & angle 2 are linear pair. That means both the angles form a straight angle (or 180°). Hence ,

\(m(1) + m(2) = 180\)

\( = > m(1) = 180 - m(2)\)

Also it's given that angle 1 & angle 3 are supplementary. It means that their sum will be equal to 180° . So ,

\(m(1) + m(3) = 180\)

Putting the value of m(1) in above eqn. gives :-

\(m(1) + m(3) = 180\)

\( = > 180 - m(2) + m(3) = 180\)

\( = > - m(2) + m(3) = 180 - 180\)

\( = > m(3) - m(2) = 0\)

\( = > m(3) = m(2)\)