Mean, Median, Mode and Range. Easy hard math. Please show work and give answers . Need help appreciate you all

Quiz Scores:
You and your friend are having a friendly competition about the scores on your math quizzes. Both of your scores for the first five quizzes are given below:
Your quiz scores: 18, 16, 19, 15, 17
Friend’s quiz scores: 20, 20, 13, 12, 17
a. Find the mean, median, and mode of both sets of data.
b. Which person – you or your friend – has the higher mean?

World Populations:
The populations (in millions) in 2000 on each of the six inhabited continents were:
803, 487, 348, 368, 730, and 31
a. What is the range of the populations?
b. Find the mean, median, and mode(s) of the populations.

Tomato Plants:
The heights (in inches) of eight tomato plants are:
36, 45, 52, 40, 38, 41, 50, and 48
a. What is the range of the tomato plant heights?
b. Find the mean, median, and mode(s) of the tomato plant heights.

The probability of a household having more than 12 TVs is 0.7386.

(a) To find the probability of a household having 12 or 14 TVs, we need to find the probability of getting exactly 12 TVs and exactly 14 TVs and then add these probabilities together. The probability of getting exactly k successes in n trials with probability of success p is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Using this formula, we have:

P(12 TVs) = (17 choose 12) * (0.8)^12 * (0.2)^5 = 0.0411

P(14 TVs) = (17 choose 14) * (0.8)^14 * (0.2)^3 = 0.176

Therefore, the probability of a household having 12 or 14 TVs is:

P(12 or 14 TVs) = P(12 TVs) + P(14 TVs) = 0.0411 + 0.176 = 0.2171

(b) To find the probability of a household having 12 or fewer TVs, we need to find the probability of getting 12 or fewer TVs. We can use the binomial probability formula to find the probabilities of getting 0, 1, 2, ..., 12 TVs and then add these probabilities together. Alternatively, we can use the cumulative distribution function (CDF) of the binomial distribution. The CDF gives the probability of getting k or fewer successes in n trials with probability of success p:

P(X ≤ k) = Σ P(X = i) from i = 0 to k

Using a binomial calculator or a statistical software, we can find that:

P(X ≤ 12) = 0.0604

Therefore, the probability of a household having 12 or fewer TVs is 0.0604.

(c) To find the probability of a household having 15 or more TVs, we need to find the probability of getting 15, 16, 17 TVs. Again, we can use the binomial probability formula or the CDF. Using a binomial calculator or a statistical software, we can find that:

P(X ≥ 15) = 0.0152

Therefore, the probability of a household having 15 or more TVs is 0.0152.

(d) To find the probability of a household having fewer than 14 TVs, we need to find the probability of getting 0, 1, 2, ..., 13 TVs. Using a binomial calculator or a statistical software, we can find that:

P(X < 14) = P(X ≤ 13) = 0.3152

Therefore, the probability of a household having fewer than 14 TVs is 0.3152.

(e) To find the probability of a household having more than 12 TVs, we need to find the probability of getting 13, 14, 15, 16, 17 TVs. Using a binomial calculator or a statistical software, we can find that:

P(X > 12) = P(X ≥ 13) = 0.7386

Therefore, the probability of a household having more than 12 TVs is 0.7386.

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The answer is (B) converges, since the terms alternate.

The Alternating Series Test states that if the following conditions are met, the series converges:

The absolute value of the terms a_n approaches zero as n approaches infinity.

The terms of the series are alternately positive and negative (i.e., the series is an alternating series).

The absolute value of the terms is decreasing (i.e., |a_n+1| < |a_n| for all n).

The series Σ (-1)^n/(n^2 + 7) can be tested for convergence using the Alternating Series Test.

The terms of the series alternate in sign and the absolute value of each term is decreasing, since:

|a(n+1)| = 1/((n+1)^2 + 7) < 1/(n^2 + 7) = |an|

Also, lim n->∞ an = 0.

Therefore, the series converges by the Alternating Series Test.

The answer is (B) converges, since the terms alternate.

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Answer:

322850405

Step-by-step explanation:

the value of n is 17 and the value of r is 3.

Answer:

C. 49

Step-by-step explanation:  

Cats  :   dogs

  7     :     8

  59  :     56

8 x 7= 56

so, 7 x 7= 49

Answer:

$ 5555555&-&+--7+&+6-34'+

Answer:He can 360 days since 50.4 ÷ 0.14 .but Owen only has 280

Step-by-step explanation:

Where is the image?

Answer:

sas - meaning side angle side

Step-by-step explanation:

Answer:

Step-by-step explanation:

First of all it should be like fractions

So -2/3 becomes -10/15

and -3/5 becomes -9/15

-9/15 is greater than -10/15

-3/5 is greater than -2/3

Answer:

-2/3 < -3/5

Explanation:

to convert the fractions to equivalent forms, we need to make sure that they have the same denominator (number on the bottom). the lowest common multiple of both 3 and 5 is 15, hence:

-2/3 = -10/15 (×5)

-3/5 = -9/15 (×3)

thus, we can see that -10/15 is smaller than -9/15, and -2/3 is smaller than -3/5.

i hope this helps! :D

\(110 = 16 + 10h\)

\(110 - 16 = 10h\)

She needs $110 for a concert ticket.

she already has $16 . She can earn the rest by working 10 hours at her job.

\(\bold{h = hourly \ rate}\)

she needs to work 10 hours to add to the $16 she already has to get a total of $110 required for the concert ticket.

Therefore, Her hourly rate can be solved with the following equation

Every coordinate point of the initial triangle has its coordinates increased by the scaling factor if it is 2. As a result, A'(0, 4), B'(4, 2), and C' are the coordinate points of the dilated triangle, which will be A'B'C' (-4, -4). multiplying by two after dilation with a scale factor of two.

Dilation is a method for generating analogous figures. By dividing distances by the scale factor, each point is stretched outward from the central point D. (If the scaling factor is more than 1), outward.) To alter the triangle's shape, move the points A, B, and C.

A'(-2, 2)

B'(-2, 1)

C'(-1, 1)

For scale factor k and center of dilation (p, q), the transformation is

 (x, y) ⇒ (kx +(1-k)p, ky +(1-k)q)

For k=1/4 and (p, q) = (-3, 3), the coordinates are transformed to

 (x, y) ⇒ (1/4x -9/4, 1/4y +9/4)

Then the preimage points are dilated to

 A(1, -1) ⇒ A'(1/4 -9/4, -1/4 +9/4) = A'(-2, 2)

 B(1, -5) ⇒ B'(1/4 -9/4, -5/4 +9/4) = B'(-2, 1)

 C(5, -5) ⇒ C'(5/4 -9/4, -5/4 +9/4) = C'(-1, 1)

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If the data of the research subjects are presented in a frequency distribution graph, a histogram-type graph should be used.

If the data are presented in a frequency distribution graph, then the type of graph that should be used is a histogram. A histogram is a type of bar graph that displays the distribution of a continuous variable by dividing the range of values into intervals, and bins, and counting the number of observations that fall within each bin.

If the academic majors were nominal a bar graph could also be used to display the frequency of each major. In a bar graph, each category would be plotted on the horizontal axis, and the frequency of students in each category would be plotted on the vertical axis.

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The value of 3⋅C⋅(2A×B) is 126.00. This is obtained by calculating the cross product of A and B, then taking the dot product with C and multiplying by 3.



To find the value of the expression 3⋅C⋅(2A×B), we need to calculate the cross product of vectors A and B, and then perform the dot product with vector C. Let's break it down step by step.

Vector A = 3.00i^ + 3.00j^ - 3.00k^

Vector B = -3.00i^ + 3.00j^ + 4.00k^

Vector C = 7.00i^ - 7.00j^

Step 1: Calculate the cross product of A and B.

A × B = (3.00i^ + 3.00j^ - 3.00k^) × (-3.00i^ + 3.00j^ + 4.00k^)

The cross product of two vectors can be calculated using the following formula:

A × B = (AyBz - AzBy)i^ + (AzBx - AxBz)j^ + (AxBy - AyBx)k^

Using the given vectors A and B:

A × B = (3.00 * 4.00)i^ + (-3.00 * -3.00)j^ + (3.00 * -3.00 - 3.00 * 3.00)k^

     = 12.00i^ + 9.00j^ - 18.00k^

So, A × B = 12.00i^ + 9.00j^ - 18.00k^

Step 2: Perform the dot product of C and (2A×B).

C ⋅ (2A×B) = (7.00i^ - 7.00j^) ⋅ (2(12.00i^ + 9.00j^ - 18.00k^))

The dot product of two vectors can be calculated by multiplying corresponding components and summing them up:

C ⋅ (2A×B) = 7.00 * 2 * 12.00 + (-7.00) * 2 * 9.00 + 0

          = 168.00 - 126.00 + 0

          = 42.00

Therefore, 3⋅C⋅(2A×B) = 3 * 42.00 = 126.00.

The value of 3⋅C⋅(2A×B) is 126.00.

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Answer:

here, 1m= 100 cm

so, 5m= 5 ×100 cm=500cm

and 150 cm

now, the ratio of 154cm to 5m is = 154÷500

therefore the ratio is 77/250.

hope its helpful..

Answer:

The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles. Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.

Answer:

The answer is -164.37 dollars in there bank account.

Step-by-step explanation:

you subtract the two fees first and then you subtract the two deposits from the bank and then you have your answer. I hope that this helps you :)

Answer:

(x-6)3

hope it helps

Answer:

30 stamps each

Step-by-step explanation:

This is the correct question:

Jessica has 120 stamps in a collection she bought 60 more Jessica wants to place the stamps equally and 6 pages of a book how many stamps will be on each page of the book

Total stamps = 120 + 60

= 180

Jessica wants to place the stamps equally on 6 pages of a book

how many stamps will be on each page of the book?

Each page of the book = Total stamps / number of pages in the book

= 180 / 6

= 30

Each page of the book will have 30 stamps each

Respuesta:

$81.250.

Explicación paso a paso:

Datos dados

Principal = $ 65,000

Tasa = 5%

Tiempo = 5 años

La expresión de interés simple se da como

A = P (1 + rt)

Substiute

A = 65000 (1 + 0,05 * 5)

A = 65000 (1 + 0,25)

A = 65000 (1,25)

A = $ 81,250

Por lo tanto, la inversión después de 5 años es de $81,250

Using the first x y:

16/4 = 4

Y is equal to x multiples by 4

3 x 4 = 12

8/4 = 2

The missing y is 12

The missing x is 2

Answer:

6/4=4

Step-by-step explanation:

lol

Answer: Rs. 2000

Step-by-step explanation:

Given that: height of room= 5m

volume of room= 2000m³

cost of plastering per metre square= Rs. 4

To find: cost of platering on the floor

Solution:

volume of room = 2000m³

l×b×h = 2000m³

l×b × 5 = 2000m³

l×b = 2000/5

l×b = 400\(m^{2}\)

area of floor = 400\(m^{2}\)

cost of plastering on the floor= area of floor × cost per m square

                                  = 400\(m^{2}\) × 5

  cost of plastering on the floor = Rs. 2000

Answer:

The answer is D

Step-by-step explanation:

use the quadratic formula, plug and chug, and voila!

Answer:

Irrational

Step-by-step explanation:

40 is not a perfect square.

Answer:

irrational

Step-by-step explanation:

40 isnt a perfect square where if you want to know weather it is or not you put the square root of any number on the calculator and if it's the same answer or in the answer there is a square root then it is an irrational number

Answer:

The area is about 96.06 or 96.1

Step-by-step explanation:

I tried my best to solve it, I'm sorry if it's wrong.

False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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From a regular Octagon, the number of triangles formed is 56 triangles .

What is an Octagon ?

An Octagon is defined as a shape that has eight straight sides .

we have to find the number of triangles in a regular octagon .

the number of vertices that a regular octagon have = 8 vertices , and

the number of vertices required to form a triangle is = 3 vertices ,

So , the number of triangles formed by the regular octagon can be calculated by ⁸C₃ .

So , ⁸C₃ = 8!/[ 3! × 5! ]

= 8×7×6×5!/[ 3! × 5! ]

= 8×7×6/3!

= 8×7

= 56 triangles .

Therefore , the number of triangles formed is 56 triangles .

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Answer:

21

Step-by-step explanation:

ffr

Answer:

about 0.233

Step-by-step explanation:

700÷3=233.33333333...

233.333333333... rounded to nearest hundredth is 233.33

0.233

Answer:

A. (-1,-2)

Step-by-step explanation:

hope this helps :) and can i ask is that a leg next to the screen?

Answer

5

Step-by-step explanation:

Pls give brainliest to me

Answer: x = 5

Step-by-step explanation:

4x + 3 = x + 18

- 3 - 3

4x = x + 15

Do 4x-x and x-x

3x = 15

Do 3x/3 and 15/3

x= 5

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

Given the system of linear differential equations can be put in the form (A - λI)X = 0, where λ and X are the eigenvalue and eigenvector of the matrix A, respectively. Determine λ and X and determine whether the system is homogeneous or non-homogeneous. Choose the largest interval such that a unique solution of the initial value problem is guaranteed to exist.For the given system of linear differential equations:

dx/dt = 4x + 6y

dy/dt = -2x - 4y

the matrix A is given by:

 [4   6 ][-2 -4 ]

The eigenvalue λ can be found from the characteristic equation det(A - λI) = 0 as follows:

[4 - λ   6    ][-2    -4 - λ] = 0λ² - λ - 8 = 0

Solving the above equation, we get, λ = -1 and λ = 8.

Therefore, λ1 = -1 and λ2 = 8 are the eigenvalues of matrix A.

To find the eigenvectors, we solve the equation (A - λI)X = 0 for each λ separately.

For λ1 = -1, we get[A - (-1)I]X = 0

⇒[5   6 ][x    ] = 0[-2   -3][y    ]      [x    ][-2y  ]

Therefore, the eigenvector corresponding to

λ1 = -1 is

X1 = [x y]T = [2 -1]T.

For λ2 = 8, we get

[A - 8I]X = 0⇒[-4   6 ][x    ]

= 0[-2  -12][y    ]  [x    ][3y   ]

Therefore, the eigenvector corresponding to

λ2 = 8 is

X2 = [x y]T = [3 1/2]T.

The given system of linear differential equations can be written in the matrix form as

dX/dt = AX,

where A is the matrix [4 6][-2 -4] and X is the column vector [x y]T.

The general solution of this system is given by

X(t) = c1 e^(λ1t)X1 + c2 e^(λ2t)X2,

where c1 and c2 are constants of integration and X1 and X2 are the eigenvectors corresponding to the eigenvalues λ1 and λ2, respectively. Therefore, the general solution of the given system is given by

x(t) = 2c1 e^(-t) + 3/2 c2 e^(8t)y(t)

= -c1 e^(-t) + 1/2 c2 e^(8t)

where c1 and c2 are constants of integration to be determined from the initial conditions. Since the system of differential equations is homogeneous, the trivial solution x(t) = y(t) = 0 is a solution of the system. Hence, the system is homogeneous.

The given initial value problem has initial conditions x(0) = 1 and y(0) = 0.

Therefore, we have

c1 + 3/2 c2 = 1 and

-c1 + 1/2 c2 = 0

Solving these two equations, we get c1 = 1/5 and c2 = 2/5.

Therefore, the particular solution of the given initial value problem is given by

x(t) = (2/5) e^(-t) + (6/5) e^(8t)y(t)

= -(1/5) e^(-t) + (1/5) e^(8t)

Hence, the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

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The correct statement is option (d): aₙ = Sₙ₊₁ - Sₙ₋₁.  The nth partial sum, Sₙ, represents the sum of the first n terms of the infinite series ∑ₙ₌₁ aₙ. We are given that n > 3.

To determine the relationship between the nth term, aₙ, and the partial sums, we can examine the pattern of the series. Looking at the options, we observe that option (d) is the difference between Sₙ₊₁ and Sₙ₋₁.

Let's consider an example to understand why this is the correct choice. Suppose we have the series 1 + 2 + 3 + 4 + 5 + ... and we want to find the relationship between the terms and the partial sums. The partial sums would be 1, 3, 6, 10, 15, ... We can see that the difference between consecutive partial sums is 2, 3, 4, 5, ... which corresponds to the terms of the series. Thus, aₙ = Sₙ₊₁ - Sₙ₋₁.

In general, for any infinite series with n > 3, the correct relationship between the nth term, aₙ, and the partial sums, Sₙ, is given by aₙ = Sₙ₊₁ - Sₙ₋₁, which is option (d).

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The perimeter of square ABCD is 28 units.

The perimeter of a square is the sum of all its sides. In this case, we need to find the perimeter of square ABCD.

The question provides two possible answers: 28 units and 37 units. However, we can only choose one correct answer. To determine the correct answer, let's think step by step.

A square has all four sides equal in length. Therefore, if we know the length of one side, we can find the perimeter.

If the perimeter of the square is 28 units, that would mean each side is 28/4 = 7 units long. However, if the perimeter is 37 units, that would mean each side is 37/4 = 9.25 units long.

Since a side length of 9.25 units is not a whole number, it is unlikely to be the correct answer. Hence, the perimeter of square ABCD is most likely 28 units.

In conclusion, the perimeter of square ABCD is 28 units.

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