what is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.

The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.

Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.

Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).

The correlation coefficient is computed as,

\($ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}\)

\($=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}\)

= -0.6675

Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.

Learn more about correlation coefficient

https://brainly.com/question/15577278

#SPJ1

Answer:

Step-by-step explanation:

Given the points R(-4, 5) and S(2, -1), to get the distance between the points, we will use the formula;

D = √(x2-x1)²+(y2-y1)²

Given x1= -4, y1 = 5, x2 = 2 and y2 = -1

RS = √(2-(-4))²+(-1-5)²

RS = √(6)²+(-6)²

RS = √36+36

RS = √72

RS = √2×36

RS = 6√2units

To get the midpoint, we will use the formula M(X,Y) = (x1+x2/2, y1+y2/2)

(X,Y) = (-4+2/2, -1+5/2)

(X,Y) = (-2/2, 4/2)

(X,Y) = (-1,2)

Hence the midpoint is (-1,2)

To get a point P 1/3 of the distance of RS, we will multiply 1/3 with the the distance RS as shown

P = 1/3 × 6√2

P = 2√2

The probability of people in the survey who likes dogs is given by the equation P ( D ) = 26 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of people who likes dogs be represented as P ( D )

Now , the equation will be

The probability of people who likes cats P ( C ) = 4 %

The probability of people who likes cats and dogs = P ( C ∩ D ) = 63 %

The probability of people who likes dogs P ( D ) = 26 %

The probability of people who doesn't like cats or dogs 1 - P ( C∪D ) = 7 %

Therefore , the value of P ( D ) = 26%

Hence , probability of people in the survey who likes dogs is 26 %

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ1

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

<95141404393>

The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".

This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,

collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

Answer:

work attached and shown

Answer:

2

Step-by-step explanation:

There are 2 terms

Hope this helps!

Answer: 21

Step-by-step explanation: 3 new girls join the class and if you subtract 24 - 3 its 21.

Answer:

see explanation

Step-by-step explanation:

if the denominator of a rational expression is zero then the expression will be undefined.

the numerator is the part of the rational expression that makes it zero.

solve the numerators in each to find values of x

1

\(\frac{x+6}{x-4}\)

x + 6 = 0 ( subtract 6 from both sides )

x = - 6 ← value that makes expression equal to zero

2

\(\frac{(x+4)(x-2)}{x+6}\)

(x + 4)(x - 2) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x = - 4 and x = 2 make the expression equal to zero

3

\(\frac{2x+10}{3x-12}\)

2x + 10 = 0 ( subtract 10 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5 ← value that makes expression equal to zero

Answer:

1)  x = -6

2)  x = -4  and  x = 2

3)  x = -5

Step-by-step explanation:

A rational expression is undefined when the denominator equals zero.

A rational expression equals zero when the numerator equals zero.

Given rational expression:

\(\dfrac{x+6}{x-4}\)

Set the numerator to zero and solve for x:

\(\implies x+6=0\)

\(\implies x=-6\)

Given rational expression:

\(\dfrac{(x+4)(x-2)}{x+6}\)

Set the numerator to zero:

\(\implies (x+4)(x-2)=0\)

Apply the zero-product property and solve for x:

\(\implies x+4=0 \implies x=-4\)

\(\implies x-2=0 \implies x=2\)

Given rational expression:

\(\dfrac{2x+10}{3x-12}\)

Factor the numerator and denominator:

\(\dfrac{2(x+5)}{3(x-4)}\)

Set the numerator to zero and solve for x:

\(\implies 2(x+5)=0\)

\(\implies x+5=0\)

\(\implies x=-5\)

Answer:

107

Step-by-step explanation:

7 + (5^2) x4

= 7 + 25x4

= 7 + 100

= 107

Rounding to three decimal places, we get:

P(Z > -0.77) ≈ 0.779

To obtain P(Z > -0.77) using Z Standard Normal probability distribution tables, we can look for the area under the standard normal curve to the right of -0.77 (since we want the probability that Z is greater than -0.77).

We find that the area to the left of -0.77 is 0.2206. Since the total area under the standard normal curve is 1, we can calculate the area to the right of -0.77 by subtracting the area to the left of -0.77 from 1:

P(Z > -0.77) = 1 - P(Z ≤ -0.77)

= 1 - 0.2206

= 0.7794

Rounding to three decimal places, we get:

P(Z > -0.77) ≈ 0.779

Learn more about decimal from

https://brainly.com/question/1827193

#SPJ11

The augmented matrix [a b] is constructed in MATLAB, and row reduction is performed using the rref() function. The reduced matrix is obtained, and the free and basic variables of the system are identified.

To construct the augmented matrix [a b] in MATLAB, we can define a matrix with two columns containing the values of variables a and b. For example, if we have a = 2 and b = 3, the augmented matrix can be constructed as follows:

```

A = [2 3];

```

Next, we can use the rref() function in MATLAB to perform row reduction on the augmented matrix. The rref() function returns the reduced row echelon form of the matrix. We can store the result in a new matrix, let's say R:

```

R = rref(A);

```

The reduced matrix R will contain the coefficients of the variables and the constants of the system. By analyzing the reduced matrix, we can determine the basic and free variables. Basic variables are those corresponding to the leading entries (pivots) in each row of the reduced matrix. Free variables, on the other hand, are associated with the columns that do not contain a pivot.

The reduced matrix R will have a row of zeros for any free variables. By observing which columns have pivots and which do not, we can identify the basic and free variables. The basic variables correspond to the columns with pivots, while the free variables are associated with the columns without pivots.

In summary, by constructing the augmented matrix [a b] and performing row reduction using the rref() function in MATLAB, we obtain a reduced matrix R. By analyzing the structure of R, we can identify the basic and free variables of the system.

Learn more about augmented matrix here:
https://brainly.com/question/16932004

#SPJ11

Answer:

I'm pretty sure its -11

Answer:

f(3) = -11

Step-by-step explanation:

Substitute 3 in wherever you see an x:

f(3) = -4 * 3 + 1

f(3) = -12 + 1

f(3) = -11

Step-by-step explanation:

oh, come on ! we are dealing with rectangles.

and you know how to get the perimeter and the area of a rectangle. upper elementary school students can do that.

remember, the perimeter is the distance when you walk all around the rectangle.

so, 2 times the length and 2 times the width.

and the area is simply length × width.

but your teacher was very lazy and careless with some phrasing about what is needed.

the original room is 8 ft × 3 ft.

1.

the length of border needed is exactly the perimeter.

so,

2×8 + 2×3 = 16 + 6 = 22 ft

2.

the area of the floor is

8×3 = 24 ft²

this is the amount of floor panels to be bought. we buy them in ft².

3.

the new room is (8+3) ft × (3-2) ft. = 11 ft × 1 ft.

that is a very strange room. no human can live in such a room.

I think your teacher meant (8-2) ft × (3+3) ft = 6 ft × 6 ft.

but let's stick with the original information.

the border for this room (perimeter) is

2×11 + 2×1 = 22 + 2 = 24 ft

4.

the floor area is

11 × 1 = 11 ft²

if we consider my correction of the room size, it is

6×6 = 36 ft²

5.

"difference in size" is not clear. regarding the dimensions (side lengths and correspondingly the perimeter) or regarding the floor size ?

if we consider the perimeter, the difference is

24 - 22 = 2 ft

the new room's perimeter is 2 ft less.

if we consider the floor area, the difference is

24 - 11 = 13 ft²

the new room is 13 ft² smaller.

or for my size correction, the difference is

36 - 24 = 12 ft²

the new room is then 12 ft² larger.

The answer which we get after calculating from the data given is that  Larry has 15 dollars more than Lenny.

Let the amount which Lenny is having be x

then the amount which Larry is having will be (2/5)x

and on combining them it makes $35 .

Which means,  x + 2x/5 = 35

On simplifying this equation we will get ,

(7/5)x= 35   ,

multiplying both the sides by 5/7

x= (5/7)*35 = $25

Therefore , Lenny is having 4 25.

So Larry must be having ,  $(35 - 25) = $10

So , we can conclude that Lenny has more dollars. The difference is of 15 dollars.

To learn more about equations

brainly.com/question/29168024

#SPJ4

Answer:

c

Step-by-step explanation:

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

To know more about orthogonal visit

https://brainly.com/question/32250610

#SPJ11

Using the ANOVA model, you can determine if the surface type has a significant impact on the speed of guineas.

Given that you are comparing the speed of guineas across three different surface types (grass, turf, and concrete), you would use an Analysis of Variance (ANOVA) model to analyze this data.

An ANOVA model allows you to compare the means of the speeds for each group (grass, turf, and concrete) and determine if there are any significant differences between them. The model takes into account the variability within each group and the variability between the groups to determine if the differences observed are due to chance or if they are statistically significant.

Here are the steps to perform an ANOVA analysis:

1. Collect the speed data for each guinea in the three groups (grass, turf, and concrete).
2. Calculate the means of the speeds for each group.
3. Calculate the overall mean of the speeds for all groups combined.
4. Calculate the Sum of Squares Within (SSW), which measures the variability within each group.
5. Calculate the Sum of Squares Between (SSB), which measures the variability between the groups.
6. Calculate the Mean Squares Within (MSW) and Mean Squares Between (MSB) by dividing the respective sums of squares by their degrees of freedom.
7. Calculate the F-statistic by dividing MSB by MSW.
8. Compare the F-statistic to the critical value from the F-distribution table based on the chosen level of significance (e.g., 0.05) and the degrees of freedom for the numerator and denominator.
9. If the F-statistic is greater than the critical value, you can conclude that there are significant differences between the groups' mean speeds, and further analysis can be conducted to determine which specific groups differ.

Using the ANOVA model, you can determine if the surface type has a significant impact on the speed of guineas.

To know more about "ANOVA model" refer here:

https://brainly.com/question/30409322#

#SPJ11

Answer:

Step-by-step explanation:

The strategy to determine the boundary line is that we need to remove the inequality sign and replace it with and equal to sign and then sketch the equation of the function which is

\(4x+3y=12\)

to sketch the function we need the function's x-intercept which means the graphs crosses the x-axis at that specific point (x , 0) and y-intercept which means the graph crosses the y-axis at that specific point (0 , y).

Since both these points lie on line we can substitute it into the equation to find the x-y intercepts and hence sketch the line so here goes.

For x-intercept:

\(4x+3y=12\\4(x)+3(0)=12\\4x=12\\x=12/4\\x=3\)

so the x-intercept is (3 , 0)

For y-intercept:

\(4x+3y=12\\4(0)+3(y)=12\\3y=12\\y=12/3\\y=4\)

so the y-intercept is (0 , 4)

now we sketch these 2 points and draw a straight line joining both the points as shown in the image below.

Step-by-step explanation:

A straight line has an angle of 180

132+(2x+3)=180

2x+3=48

2x=45

x=45/2

PLEASE GIVE BRAINLY

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Let the amount of the 30% solution be x gallons.

Then the amount of the 10% solution is (100 - x) gallons.

The amount of juice in the 30% solution is 0.3x gallons.

The amount of juice in the 10% solution is 0.1(100 - x) gallons.

When the two solutions are mixed, we get 100 gallons of a 12% juice solution, which means:

0.3x + 0.1(100 - x) = 0.12(100)

Simplifying this equation, we get:

0.3x + 10 - 0.1x = 12

0.2x = 2

x = 10

Therefore, 10 gallons of the 30% solution was used.

Know more about Quantities here:

https://brainly.com/question/29610435

#SPJ11

Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

Learn more about equilibrium here: https://brainly.com/question/13463225

#SPJ4

Answer: x = 40

Step-by-step explanation:

3x ÷ 8 = 15

Multiply 8 in both sides

3x = 120

Divide both sides by 3

x = 40

Out of the 500 people surveyed, we would expect approximately 155 of them to consider reading books or surfing the Internet as the best entertainment value.

To calculate the expected number of people who considered reading books or surfing the Internet as the best entertainment value out of the 500 surveyed, we need to calculate the percentage corresponding to reading books and surfing the Internet.

The percentage for reading books is 22% and the percentage for surfing the Internet is 9%. To find the combined percentage, we add these two percentages:

22% + 9% = 31%

Now, we can calculate the expected number by multiplying the combined percentage by the total number of people surveyed:

Expected number = 31% of 500 = (31/100) * 500 = 155

The complete question is:

Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value?

Best Entertainment Value

Type of Entertainment               Percent

Playing Interactive Games            48

Reading Books                              22

Renting Movies                              10

Going to Movie Theaters               10

Surfing the Internet                          9

Watching Television                         1

To know more about entertainment:

https://brainly.com/question/20740738

#SPJ4

The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

Learn more about inequality on:

brainly.com/question/25275758

#SPJ1

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{h}~,~\stackrel{y_2}{28}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{(-14)}}}{\underset{run} {\underset{x_2}{h}-\underset{x_1}{(-2)}}} \implies \cfrac{28 +14}{h +2}~~ = ~~\text{\LARGE 6}\implies \cfrac{42}{h+2}=6 \\\\\\ 42=6h+12\implies 30=6h\implies \cfrac{30}{6}=h\implies \boxed{5=h}\)

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

Learn more about variance here:

https://brainly.com/question/31432390

#SPJ1