Find the range, median, first and third quartiles, and interquartile range for each data set OF THE NUMBERS 52 72 96 21 58 40 75

Answer: Decrease it’s a negative

Step-by-step explanation:

Answer:

Its right infront of you.....

1/5

Step-by-step explanation:

The general solution to the given system of differential equations is:

x(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

where c1, c2, and c3 are constants determined by initial conditions or specific constraints.

To solve the system using the elimination method, we need to eliminate one variable at a time. Let's start by eliminating x.

x' = x - y ...........(1)

y'' = -2x' + e^t ...........(2)

First, differentiate equation (1) with respect to t to get:

x'' = x' - y' ...........(3)

Now substitute the value of x' from equation (3) into equation (2):

y'' = -2(x' - y) + e^t

y'' = -2x' + 2y + e^t ...........(4)

To eliminate x', we subtract equation (4) from equation (2):

y'' - y' = e^t ...........(5)

Next, differentiate equation (5) with respect to t:

y''' - y'' = e^t ...........(6)

Now we have two equations:

y'' - y' = e^t ...........(5)

y''' - y'' = e^t ...........(6)

To solve these equations, we can solve equation (6) for y'' and substitute it into equation (5):

(y''' - e^t) - (y'' - y') = e^t

y''' - y'' + y' - e^t = e^t

y''' - y'' + y' = 2e^t ...........(7)

Equation (7) is a third-order linear homogeneous differential equation for y.

To find the general solution to equation (7), we solve its characteristic equation:

r^3 - r^2 + r = 0

Factoring out an r, we get:

r(r^2 - r + 1) = 0

This equation has one real root r = 0 and two complex roots r = (1 ± √3i)/2.

Therefore, the general solution for y is:

y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)

Now, we can substitute the general solution for y into equation (5) to solve for x:

y'' - y' = e^t

(c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2))' - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t

Differentiating and simplifying, we get:

(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t

Simplifying further, we get:

(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - c2e^tcos((√3t)/2) - c3e^tsin((√3t)/2) = e^t

Now, equating the coefficients of e^t and the trigonometric terms, we can solve for c1, c2, and c3.

This completes the solution process using the elimination method for the given system of differential equations.

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Answer:

The first option.

Step-by-step explanation:

Add all the numbers together and voila you get 27

Answer:

C

Step-by-step explanation:

basically see where each dot is and the number its beside and the number its above answer for example the first one is in between 20 and 30 so its 25 and its above 1  so it would 1, 25 u just do that for all the dots :)

Answer:

d. 9

Step-by-step explanation:

i friken used all my attempts guessing on this and got it wrong all times so 9 is the last answer

Answer:

Altitude of the right triangle is 4 cm.

Step-by-step explanation:

The altitude divides the right triangle's hypotenuse as 2 cm and 8 cm long.Let's use formula for similar right triangles proportional equation.I'll show you the diagram with steps.

(a) The Y-intercept, bo = 6, implies that when the value of X is 0, the mean value of Y is 6.

(b) The slope, by = 4, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 4 units.

(c) The mean value of Y for X = 4 is predicted to be 22.

The Y-intercept, bo, represents the starting point of the prediction line. In this case, when X is 0, the mean value of Y is expected to be 6. This implies that before any increase or decrease in X, the average value of Y starts at 6.

The slope, by = 4, indicates the rate at which Y is expected to change for each unit increase in X. Therefore, for every 1 unit increase in X, the value of Y is expected to increase by 4 units. This implies a linear relationship between X and Y, where the increase or decrease in X directly influences the corresponding change in Y.

To predict the mean value of Y for X = 4, we can use the prediction line equation: Y = 6 + 4x. Substituting X = 4 into the equation, we get: Y = 6 + 4(4) = 6 + 16 = 22. Therefore, the mean value of Y for X = 4 is predicted to be 22.

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a) John withdraws $1,300.

b) The annual effective yield rate for John's six-year investment is 2.09%.

a) To find the amount that John withdraws, we need to calculate the future value of his deposits after six years.

For the first three years, the deposits gain interest at a force of interest of 0.06. So after three years, the balance becomes $500 * (1 + 0.06)^3 = $595.44.

After three years, the interest rate changes to an effective rate of discount of 8%. Using the formula for the future value of a single sum with a discount rate, we can calculate the balance after six years:

$595.44 * (1 - 0.08)^3 = $429.97.

Therefore, John withdraws $429.97.

b) The annual effective yield rate can be found by calculating the rate of return on John's initial deposit over six years.

Let's assume John's initial deposit is $D. After three years, it grows to $D * (1 + 0.06)^3 = $1.191D. After six years, it becomes $1.191D * (1 - 0.08)^3 = $0.924D.

To find the annual effective yield rate, we need to solve the equation:

$D * (1 + r)^6 = $0.924D,

where r is the annual effective yield rate.

Simplifying the equation:

(1 + r)^6 = 0.924,

Taking the sixth root of both sides:

1 + r = 0.924^(1/6),

r = 0.0209.

Therefore, the annual effective yield rate for John's six-year investment is 2.09%.

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Answer:

The answer would have to be shown in your working out, so look down below for an explanation.

Step-by-step explanation:

You would make each equation with the same letter equal to each other

5x- 10= 7x-20

3y= 5y-16

Then you would solve the equations

5x-10 = 7x-20

+20        +20

5x +10= 7x

-5x        -5x

10= 2x

x= 5

-

3y = 5y-16

+16      +16

3y+16=5y

-3y       -3y

16 = 2y

y = 8

And there's  how you would prove that x=5 and y=8

Answer:

2. n(2n+5)=26.

Step-by-step explanation:

If Sam has n stamps, and Nate has 5 more than twice that amount, the equation would be: 2. n(2n+5)=26.

Answer:

axis of symm:  x = -1

vertex:  (-1, -4)

domain:  all real numbers

range:  y ≥ -4

x-intercepts:  1, 3

y-intercept:  -3

minimum at (-1, -4)

Step-by-step explanation:

Answer:

C

24Step-by-step explanation:

Trust me on this one.

Answer: See explanation

Step-by-step explanation:

Total number of children = 369

Percentage of children on museum trip = 20%

Number of children on museum trip = 20/100 × 369

= 1/5 × 369

= 73.8 = 74 approximately

Number of children in school = 369 - 73.8 = 295.2 = 295 approximately

i)

The graph is attached  as an image.

ii.)  We notice that all the lines have the same slope of 2 which shows a consistent rate of change

A graph is described as as the pictorial representation of that represents any given data in a chronological manner that is ascending to descending type.

1. y =2x+8

x = 1

Y = 2(1)+8

Y= 2+8

Y = 10

2. y =2x + 2

x=2

Y= 2(2) +2

=4+2

Y=6

3. y= 2x – 3

x = 3

Y = 2(3) -3

Y= 6-3

Y=3

4. y = 2x -6

x=4

Y = 2(4) -6

Y= 8-6

Y=2

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Answer:

Angle K is 55 degrees

Step-by-step explanation:

Angle K corresponds to Angle R

Answer:

No x-intercepts

y-intercepts: (0,2)

Step-by-step explanation:

The sample space, in terms of the condition (functional or defective) of each nozzle after a year, can be represented using the symbols "f" and "d" to denote a functional and defective nozzle, respectively.

The possible outcomes in the sample space can be described as a combination of these symbols. For example, if we have three nozzles, the sample space could include outcomes such as "fff" (all three nozzles are functional), "dfd" (the first and third nozzles are functional, while the second one is defective), "ffd" (the first two nozzles are functional, while the third one is defective), and so on.

Each outcome in the sample space corresponds to a particular arrangement or configuration of functional and defective nozzles after a year. The sample space encompasses all the possible combinations and provides a comprehensive representation of the different outcomes that can occur.

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Answer:

false

it can have more

Answer:

Yes

What solid shape do the two nets make?

1. Rectangular Prism

2. Triangular Prism

Brainlist Pls!

Given a 3x3 matrix A with eigenvalues -1 and 3, and corresponding eigenvectors V1 = [-1, 3, -1] and V2 = [0, 2, 3], we can determine various products and properties of the matrix A.

(a) To find the product Av2, we simply multiply the matrix A by the vector V2. The resulting product is [0, 2, 10].

(b) To find the product A(3v1 - v3), we first calculate 3v1 - v3, which is equal to [-4, -10, 6]. Then, we multiply the matrix A by this vector to obtain the product [-4, -10, 10].

(c) Two eigenvectors corresponding to the eigenvalue -1 can be identified as V1 = [-1, 3, -1] and any scalar multiple of V1, such as [2, -6, 2].

(d) To determine if A is diagonalizable, we check if it has three linearly independent eigenvectors. In this case, A has two distinct eigenvalues (-1 and 3), and we are given that the eigenspace corresponding to each eigenvalue has a basis with two vectors in total. Since the sum of the dimensions of the eigenspaces is equal to the dimension of A (3), A is diagonalizable.

To diagonalize A, we construct a matrix P with the eigenvectors as its columns. We have P = [V1, V2, V3] = [-1, 0, 2; 3, 2, -6; -1, 3, 2]. Then, we calculate P-1 and find D, the diagonal matrix of eigenvalues: D = diag(-1, 3). Finally, we obtain the diagonalized form P-1AP = D, where P-1 is the inverse of matrix P.

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Answer:

V = 314

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

Given:

r = 5

h = 12

Work:

V = πr²(h/3)

V = 3.14(5²)(12/3)

V = 3.14(25)(4)

V = 314

Answer:

The volume of the cone is 311.1in³.

Step-by-step explanation:

V = ⅓Bh where B = πr²

V = ⅓πr²h

V = ⅓(22/7)(5²)12

V = 0.33(3.142)(25)12

V = 311.1in³

Answer:

y=9

x= -2, 4

Step-by-step explanation:

The given boundary value problem, y'' + 4y = 0, with boundary conditions y(0) = 0 and y(L) = 0, has a unique solution. Therefore, the solution to the given boundary value problem is y(x) = c2 sin(2x), where c2 is a constant and L = nπ/2.

To solve the given boundary value problem, we start by finding the general solution to the homogeneous differential equation y'' + 4y = 0. The characteristic equation associated with this differential equation is r^2 + 4 = 0, which has complex roots: r1 = 2i and r2 = -2i.

The general solution to the homogeneous equation is y(x) = c1 cos(2x) + c2 sin(2x), where c1 and c2 are constants. Now, we apply the boundary conditions to determine the specific solution.

Using the first boundary condition y(0) = 0, we have 0 = c1 cos(0) + c2 sin(0), which simplifies to c1 = 0. Therefore, the solution becomes y(x) = c2 sin(2x).

Now, we use the second boundary condition y(L) = 0. Substituting L for x in the solution, we get 0 = c2 sin(2L). For this equation to hold for all L, sin(2L) must be equal to zero, which means 2L = nπ, where n is an integer. Solving for L, we have L = nπ/2.

Therefore, the solution to the given boundary value problem is y(x) = c2 sin(2x), where c2 is a constant and L = nπ/2. Since both boundary conditions are satisfied for y(x) = 0, we conclude that the only solution to the problem is y(x) = 0.

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

4+3+2+5=14

Answer:

a) x-intercepts at -6 and 2

b) y-intercept at -12

c) minimum at (-2, -16)

Step-by-step explanation:

Answer:

f(3) = 3

Step-by-step explanation:

f(1) = 1

f(2) = 2

f(n) = f(n − 2) + f(n − 1)

f(3) = f(3 - 2) + f(3 - 1)

     = f(1) + f(2) = 1 + 2 = 3

Special Note:  Have you heard of the Fibonacci sequence?  

The formula f(n) = f(n − 2) + f(n − 1) is used to find the terms of the of the  Fibonacci sequence

The approximately 59.90 percent of the observations differ from the mean by less than 0.56o.

The standard deviation is a measure of the amount of variation or dispersion in a set of observations.

For a normal distribution, it is straightforward to determine the proportion of values that are more than a certain number of standard deviations above or below the mean.

Here's how to determine the percentage of observations that differ from the mean by more than 2.50 or less than 0.56o in a normally distributed set of observations.

Solution:

(a)  The percentage of observations that differ from the mean by more than 2.50 is given by the formula below:P(Z > 2.50) + P(Z < -2.50) = 0.00621 + 0.00621 = 0.0124

To obtain the proportion in percentage, multiply by 100: 0.0124 * 100 = 1.24%.

Therefore, about 1.24 percent of the observations differ from the mean by more than 2.50.

(b) The proportion of observations that differ from the mean by less than 0.56o is given by:

P(-0.56/σ < Z < 0.56/σ) = P(Z < 0.84) − P(Z < -0.84) = 0.7995 - 0.2005 = 0.5990

To obtain the proportion in percentage, multiply by 100: 0.5990 * 100 = 59.90%.

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If a set of observations is normally distributed.

Therefore, about 0.62% of the observations differ from the mean by more than 2.50.

About 29.24% of the observations differ from the mean by less than 0.56.

Solution: (a) If a set of observations is normally distributed, then the percentage of observations that differ from the mean by more than 2.50 is given by:

This is calculated using the z-score formula: where x is the observation value, μ is the mean of the distribution, and σ is the standard deviation of the distribution. When we substitute the values of the given parameters, we get: Therefore, about 0.62% of the observations differ from the mean by more than 2.50.

(b) Similarly, the percentage of observations that differ from the mean by less than 0.56 is given by: This is calculated using the z-score formula: When we substitute the values of the given parameters, we get: Therefore, about 29.24% of the observations differ from the mean by less than 0.56.

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Answer:

x=10

Step-by-step explanation:

x+1=11

Answer:

X-10

Step-by-step explanation:

3(x+1)=33

3x+3=33

3x+3-3=33-3

3x=30

x=10

We can conclude that r - s is rational.

Proof: Suppose r and s are rational numbers.

We must show that r - s is rational.

To prove this, we will use the closure property of rational numbers under subtraction.

Starting point: Suppose r and s are rational numbers.

Conclusion to be shown: We must show that r - s is rational.

By definition, a rational number can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero.

Let r = a/b and s = c/d, where a, b, c, and d are integers and b, d are not equal to zero.

Now, we can express r - s as (a/b) - (c/d).

By the closure property of rational numbers under subtraction, the difference of two rational numbers is also a rational number.

Therefore, we can conclude that r - s is rational.

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Given question is incomplete, the complete question is below

Outline a proof of the following statement by writing the "starting point" and the "conclusion to be shown" in a proof of the statement.

∀ real numbers r and s, if r and s are rational then r−s is rational.

That is, complete the sentences below.

Proof: Suppose ___________.

We must show that ______________.