Given x~U(5, 15), what is the variance of x?

Answer:

Step-by-step explanation:

y = 10x + 100

y = 15x

15x = 10x + 100

5x = 100

x = 20 movies

Answer:

137.5

Step-by-step explanation:

2=25

4=50

6=75

8=100

10=125

11=125+12.5 = 137.5

The mean absolute deviation for the group of household incomes is approximately 14.8 (rounded to the nearest tenth).

To calculate the mean absolute deviation (MAD) for a group of data, we follow these steps:

Find the mean (average) of the data set.

Subtract the mean from each data point, obtaining the deviations.

Take the absolute value of each deviation.

Find the mean of the absolute deviations.

Given the household incomes for 10 different households:

38, 45, 76, 93, 50, 54, 29, 44, 62, 31

Let's calculate the MAD step by step:

Find the mean (average):

Mean = (38 + 45 + 76 + 93 + 50 + 54 + 29 + 44 + 62 + 31) / 10

Mean = 482 / 10

Mean = 48.2

Calculate the deviations:

Deviation for each data point = Data point - Mean

Deviation for 38 = 38 - 48.2 = -10.2

Deviation for 45 = 45 - 48.2 = -3.2

Deviation for 76 = 76 - 48.2 = 27.8

Deviation for 93 = 93 - 48.2 = 44.8

Deviation for 50 = 50 - 48.2 = 1.8

Deviation for 54 = 54 - 48.2 = 5.8

Deviation for 29 = 29 - 48.2 = -19.2

Deviation for 44 = 44 - 48.2 = -4.2

Deviation for 62 = 62 - 48.2 = 13.8

Deviation for 31 = 31 - 48.2 = -17.2

Take the absolute value of each deviation:

Absolute deviation for each data point = |Deviation|

Absolute deviation for -10.2 = 10.2

Absolute deviation for -3.2 = 3.2

Absolute deviation for 27.8 = 27.8

Absolute deviation for 44.8 = 44.8

Absolute deviation for 1.8 = 1.8

Absolute deviation for 5.8 = 5.8

Absolute deviation for -19.2 = 19.2

Absolute deviation for -4.2 = 4.2

Absolute deviation for 13.8 = 13.8

Absolute deviation for -17.2 = 17.2

Find the mean of the absolute deviations:

Mean Absolute Deviation (MAD) = (10.2 + 3.2 + 27.8 + 44.8 + 1.8 + 5.8 + 19.2 + 4.2 + 13.8 + 17.2) / 10

MAD = 148 / 10

MAD = 14.8

To the nearest tenth, this means that the mean absolute deviation for the group of household incomes is around 14.8.

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Answer:

Step-by-step explanation:

X=59/95

The matrix A is:

A =

[-7 7 -2 ]

[ 0 0 0 ]

[ 0 0 2 ]

To find the matrix A using diagonalization, we can utilize the eigenvectors and eigenvalues provided.

Diagonalization involves expressing A as a product of three matrices: A = PDP⁻¹, where D is a diagonal matrix containing the eigenvalues on its diagonal, and P is a matrix consisting of the eigenvectors.

Given eigenvectors v₁ = [1 0], v₂ = [2], and v₃ = [3], we can construct the matrix P by placing these eigenvectors as columns:

P = [v₁ | v₂ | v₃] = [1 2 3 | 0 | 1]

Next, we construct the diagonal matrix D using the given eigenvalues:

D = diag(X₁, X₂, X₃) = diag(-1, 0, 2) = [-1 0 0 | 0 0 0 | 0 0 2]

To complete the diagonalization, we need to find the inverse of matrix P, denoted as P⁻¹.

We can compute it by performing Gaussian elimination on the augmented matrix [P | I], where I is the identity matrix of the same size as P:

[P | I] = [1 2 3 | 0 1 0 | 0 0 1]

[0 1 0 | 1 0 0 | 0 0 0]

[0 0 1 | 0 0 1 | 1 0 0]

By applying row operations, we can transform the left side into the identity matrix:

[P | I] = [1 0 0 | -2 3 -2 | 3 -2 1]

[0 1 0 | 1 0 0 | 0 0 0]

[0 0 1 | 0 0 1 | 1 0 0]

Therefore, P⁻¹ is given by:

P⁻¹ =

[ -2 3 -2 ]

[ 1 0 0 ]

[ 0 0 1 ]

Now, we can calculate A using the formula A = PDP⁻¹:

A = PDP⁻¹

[1 2 3 | 0 | 1] [-1 0 0 | -2 3 -2 | 3 -2 1] [-2 3 -2 ]

[ 1 0 0 ] [ 1 0 0 ]

[ 0 0 2 ] [ 0 0 1 ]

Performing matrix multiplication, we get:

A =

[1 2 3 | 0 | 1] [-1 0 0 | -2 3 -2 | 3 -2 1] [-2 3 -2 ]

[ 1 0 0 ] [ 1 0 0 ]

[ 0 0 2 ] [ 0 0 1 ]

=

[-1(1) + 2(0) + 3(-2) -1(2) + 2(0) + 3(3) -1(3) + 2(0) + 3(1) ]

[0 0 0 ]

[0 0 2 ]

=

[-7 7 -2 ]

[ 0 0 0 ]

[ 0 0 2 ]

Hence, the matrix A is:

A =

[-7 7 -2 ]

[ 0 0 0 ]

[ 0 0 2 ]

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To identify the surface with the given vector equation, we need to examine the coefficients of the variables in each component of the equation. In this case, we have:

r(u,v) = (u+v)i + (3-v)j + (1+4u+5v)k

This represents a vector-valued function in three-dimensional space. To see what surface it describes, we can look at the coefficients of u, v, and constants in the equation.

The coefficient of u is 4 in the k-component, so the surface will have a slope in the u-direction. The coefficient of v is 5 in the k-component, so the surface will also have a slope in the v-direction. The constant term is 1 in the k-component, so the surface will be offset by 1 unit in the positive k-direction.

Based on this information, we can conclude that the surface described by the given vector equation is a plane with a slope in the u and v directions, and is offset from the origin by 1 unit in the positive k-direction.

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The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

Yes, Nadhii and Dylan agree

Step-by-step explanation:

You created a new playlist, and 100 of your friends listened to it and shared if they liked the new playlist or not. Nadhii said the ratio of the number of people who liked the playlist to the number of people who did not like the playlist is 75: 25. Dylan said that for every three people who liked the playlist, one person did not.

Do Nadhii and Dylan agree? Prove your answer using the values of the ratios.

Total number of friends who listened = 100

Nadhii said the ratio of the number of people who liked the playlist to the number of people who did not like the playlist is 75: 25.

Nadhii

Number of people who liked the playlist : Number of people who did not like the playlist

= 75 : 25

= 75 / 25

= 3/1

= 3 : 1

Dylan said that three people who liked the playlist, one person did not.

Number of people who liked the playlist : Number of people who did not like the playlist

= 3 : 1

Yes, Nadhii and Dylan agree

Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.

Here,

Given:

Lacrosse balls cost $10 per pack

while golf balls price $25 per pack.

Total funds equal $250.

In order to create an inequality,

we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.

So, the inequality is:

25g + 10l ≤ 250

Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

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Answer:

1: 7x+19=40

2: 19+7x=40

Step-by-step explanation:

There are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.

What is Combinations ?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

The number of different collections (hands) of 5 cards from a standard deck of 52 cards is calculated using combinations. In combinatorics, the number of ways to choose k items from a set of n items is given by the formula:

C(n, k) = n! / (k! (n-k)!)

where n! represents the factorial of n, which is the product of all positive integers less than or equal to n.

In this case, n = 52 and k = 5, so the number of different hands is:

C(52, 5) = 52! / (5! (52-5)!)

= 52! / (5! 47!)

= 2598960

Therefore, there are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.

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4cm = 5km

5/4 = 1.25

1cm = 1.25km

5 × 1.25 = 6.25

6.25km

Hope this helps! :)

The length and the width of the rectangle are 1cm and 8/3cm

The formula that is used to calculate the area of a rectangle is expressed with the equation;

A = lw

Given that the parameters are;

From the information given, we have that;

Length = 3w - 7

Substitute the values, we have;

40 = (3w - 7)w

expand the bracket

40 = 3w² - 7w

3w² - 7w - 40 = 0

3w² + 15w - 8w - 40 = 0

3w(w + 5) - 8(w + 5) = 0

w = 8/3 or - 5

Length = 3(8/3) - 7 = 1

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Answer:

[-3,∞)

Step-by-step explanation:

Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.

Answer:

The given system of equations is ''consistent and independent''.

Step-by-step explanation:

Given the system of equations

2x-y=-3    ---- Equation A

4x-2y=-6  ---- Equation B

Please observe that each line of the system of equations can be written in two different forms

For example,

2x-y=-3    ---- Equation A

multiply Equation A by the number 2

2(2x-y) = -3×2

4x-2y = -6  ---- Equation B

So, when we multiplied Equation A by 2, we got the Equation B

We know that when the same line can be written in two different forms, then the system will be termed as the dependent system of equations and there would be infinite solutions.

In other words, it would contain the same line.

From the attached diagram, it is clear that 2x-y=-3 and 4x-2y=-6 represent the same line.

Thus,

The given system of equations is ''consistent and independent''.

The equation is a plane.

given that the surface in R3 represented by the equation x+y=2.

now take the plane with x , y and z axis.

z value can take any value.

x and y must be satisfied with the equation x+y=2.

when y = 0

\(x + y = 2 \\ x + 0 = 2 \\ x = 2\)

when x = 0

\(x + y = 2 \\ 0 + y = 2 \\ y = 2 \)

when take x = 1 and y = 1

\(x + y = 2 \\ 1 + 1 = 2\)

so, the points are (0,2,0) , (2,0,0) , (1,1,3)

Then plot the point and using this points draw the plane.

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Yes we should be concerned; the probability that we get a sample of 5 with a mean salary of $49,000 or greater is 0.0083.

How to determine if a sample accurately reflects a population using sample means and standard deviation ?

We can use a t-test to determine if the sample accurately reflects the population. The null hypothesis is that the sample mean is equal to the population mean, and the alternative hypothesis is that the sample mean is greater than the population mean.

t = (sample mean - population mean) / (standard deviation / square root of sample size)

Determine if a sample accurately reflects a population :

Plugging the given values in the above formula, we get:

\(t = (49000 - 43000) / (5600 / \sqrt{5}) = 2.60\)

Using a t-distribution table with 4 degrees of freedom (sample size - 1), we can find the probability of getting a t-value of 2.60 or greater. The probability is 0.0083, which is less than the usual significance level of 0.05.

Therefore, we can reject the null hypothesis and conclude that the sample mean of $49,000 is significantly different from the population mean of $43,000.

This suggests that the sample may not accurately reflect the population, and we should be concerned about the validity of our sample.

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Answer:

-64 is the 26th number

it's an arithmetic sequence because the difference between the number is constant : -3

they are all -3 in difference

Step-by-step explanation:

an = a1 + (n-1)d

an = the nᵗʰ term in the sequence

a1=the first term in the sequence

d=the common difference between terms

-64 = 11 + (n - 1)-3

-64=11 -3n+3

-78 = -3n

n = 26

Answer: 90 x 4 x 1

Step-by-step explanation:

90 x 4 x 1 = 360

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Answer:

360

Step-by-step explanation:

2³x3²x5

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Answer:

{x | −3 ≤ x ≤ 3

Answer:

{x | −3 ≤ x ≤ 3}

Step-by-step explanation:

pretty sure its right

Answer:

-20 (or C)

Step-by-step explanation:

When you get f(10), that means you plug the value given into x, then solve.

\(f(x)\frac{-120}{(10)} -8\)

First we would divide -120/10

\(-12-8\)

f(10)=-20

Answer:

\( - 20\)

(1) firstly put x=10 in the given equation

(2) divide 120 by 10 then we will get 12-8

(3) the subtract 12from 8

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Answer:

Step-by-step explanation:

m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.

m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.

m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.

The three right options are:

m∠5 ₊ m∠6 = 180° which represents a linear pair.

∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.

m∠2  m∠3  m∠5 = 180° as the sum-triangle

sum-triangleproperty.

Given,

the interior angles of the triangle are 2,3,5

the exterior angle at ∠2 is ∠1.

the exterior angle at ∠3 is ∠4.

the exterior angle at ∠5 is ∠6.

Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.

Apply the exterior angle property of a triangle.

The sum of the opposing internal angles determines the outer angle of a triangle.

For exterior ∠1 we get

∠1 = ∠5 ₊ ∠3

Similarly, for exterior ∠4 we get

∠4 = ∠5 ₊ ∠2

Then for exterior ∠6 we get

∠6 = ∠2 ₊ ∠3

∴ through the exterior angle property we get the correct option as

m∠6 = m∠2 ₊ m∠3

Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°

∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°

We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,

∴ m∠5 ₊ m∠6 = 180°

Hence we get the statements which match the diagram are:

m∠5 ₊ m∠6 = 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

m∠6 = m∠2 ₊ m∠3

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Answer:

Step-by-step explanation:

As with decimal multiplication, a 1 in a multiplier bit means the multiplicand is copied to the partial sum list, with attention paid to place value.

The partial sums are added base 2, which means 1+1 = 10, generating a carry into the next column to the left.

The attachment shows what we believe to be the multiplications you want carried out. The right-most column is the decimal equivalent.

Answer:

Answer and Explanation: Given polynomial expression is: (5x2+3x−5)−(x2 −6x−4) ( 5 x 2 + 3 x − 5) − ( x 2 − 6 x − 4).

Step-by-step explanation:

Answer:

25x^2 -20x +4

Step-by-step explanation:

(5x-2)^2

FOIL

(5x-2)(5x-2)

25x^2 -10x -10x +4

25x^2 -20x +4

Answer:

Option C

Step-by-step explanation:

Consider the function f ( x ) = 3x^2 + 4;

\(f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\\)

Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;

\(4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C\)

* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane

Hope that helps!

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

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Answer:

c is the answer

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

and if you do not have a b or c it will be 50

Given:

Radius of a circle = 21 m

Area of a sector of the circle = 27.72 m²

To find:

The angle at the center of the circle.​

Solution:

The area of a second is:

\(A=\pi r^2\times \dfrac{\theta}{360^\circ}\)

Where, r is the radius of the circle and \(\theta\) is the central angle.

Putting \(\pi=\dfrac{22}{7},\ r=21,\ A=27.72\) in the above formula, we get

\(27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}\)

\(27.72=1386\times \dfrac{\theta}{360^\circ}\)

\(27.72=3.85^\circ \times \theta\)

\(\dfrac{27.72}{3.85^\circ }=\theta\)

\(7.2^\circ=\theta\)

Therefore, the central angle of the sector is \(7.2^\circ\).

(2, 2), (3, 1), (4, 2) are ordered pairs are in the solution set of the system of linear inequalities.

What are linear inequalities, exactly?

A mathematical expression that compares two expressions using the inequality symbol is known as a linear inequality. The expression may be either a numerical or an algebraic expression, or it may be both.

                               x - 5 > 3x - 10 is an illustration of a linear inequality. Since greater than is utilized in this inequality, the LHS is indubitably greater than the RHS. The inequality is represented by the formula 2x 5 x (5/2).

y >-1/3x+2

y < 2x + 3

The answer is "None" of the given choices satisfy the linear inequality. Each choice has a point (2,2) which dissatisfy the equation.

(2, 2), (3, 1), (4, 2)

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