The following set of data is from a sample of n = 6.
8 9 7 8 2 13
a. Compute the mean, median, and mode.
b. Compute the range, variance, and standard deviation
a. Compute the mean, median, and mode.
Mean = ________Type an integer or decimal rounded to four decimal places as needed.)
Compute the median
Median= ________(Type an integer or a decimal. Do not round.)
What is the mode? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The mode(s) is/are _______ (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.)
B. There is no mode for this data set.
b. Compute the range
Range = ____ (Type an integer or a decimal. Do not round.)
Compute the variance.
S^2= _______ (Round to three decimal places as needed.)
Compute the standard deviation.
S=______(Round to three decimal places as needed.)

Answer:

option a is the answer to the question

a) The required conditions are i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).

b) |x1 - 1| ≤ a|x0 - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.

1. Consider the fixed-point iteration Pk= g(Pk), where g is continuously differentiable on [a, b].

(a) To converge to the fixed point p ∈ (a, b) for any p0 in that interval, the following conditions are required:

i. g(p) = p for p ∈ [a, b].ii. | g'(p) | < 1 for p ∈ (a, b).

(b) For g(x) = 1/3x²-2/3x+4/3, we have two fixed points: 1 and 4.

Let x be sufficiently close to 1:Then, x₁ = g(x₀) = 1/3x₀²-2/3x₀+4/3.

Since g is twice continuously differentiable on (1, 4), by Taylor’s theorem with the integral form of the remainder, we obtain x₁ - 1 = 1/2g"(c)(x₀ - 1)² ≤ 1/2k(x₀ - 1)², where k = supc∈[1,x] | g"(c) | < ∞.

Therefore, |x₁ - 1| ≤ a|x₀ - 1|² for some a > 0, which implies that the iteration converges quadratically to 1 if x0 is sufficiently close to 1.

Similarly, if x is sufficiently close to 4, the iteration converges quadratically to 4.

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Answer:

The value of g is  144 when h is 2 and j is 3 .

Step-by-step explanation:

If g varies jointly with h and j.

g = khj

Where k is the constant of proportionality.

Put value in the above

k = 4 × 6

k = 24

As when  h = 2 , j = 3 and k = 24 .

Put in the above

g = 2 × 3 × 24

g = 144

Therefore the value of g is 144 when h is 2 and j is 3 .

Answer:

In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers

Step-by-step explanation:

Answer: 3, -2

Step-by-step explanation: Just divide 6,1 i guess

Answer:

2m+12

Step-by-step explanation:

add like terms

2m+12

Answer:

its 22 a yusd the cauculader on mi iPhone ll pro max luser b an f

Answer:

The polyhedron has 8 faces

Step-by-step explanation:

I got it right on the quiz

edge 2021

Answer:

x= 24 and y = 6

Step-by-step explanation:

I think that the right answer

The correct statement is : W is a subspace of M2x2.

TO show that W is a subspace of M2x2, we need to verify that it satisfies the three properties of a subspace:

1. W contains the zero matrix:

The zero matrix in M2x2 is the 2x2 matrix with all entries equal  to zero, which is not in W . However , we can see that the matrix {0,0;0,0} can be obtained as the difference between two matrices in W: {9,0;0,0} -{0,ber;0,0} = {0,0;0,0}. So , W does contain the zero matrix.

2. W is closed under addition:

Let A and B be two matrices in W. Then, A ={9,0;0,0} + {0,ber;0,0} and B = {9,0;0,0} + {0,ber;0,0}, which is also in W. Therefore, W is closed under addition.

3. W is closed under scalar multiplication:

Let A be a matrix in W and c be a scalar. Then ,A = {9,0;0,0} + {0,ber;0,0}, and c A = c {9,0;0,0} + c{0,ber;0,0}.

Since {9,0;0,0} and {0,ber;0,0} are both scalar multiples of A, c {9,0;0,0} and c{0,ber;0,0} are also in W . Therefore , W is closed under scalar multiplication.

Since W satisfies all three properties of a subspace, we can conclude that W is a subspace of M2x2.

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Answer:

Step-by-step explanation:

Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?

We solve using the formula

Distance on the fulcrum × Weight of the boy

= 4 × 240 = x × 160

4 × 240 = 160x

x = 4 × 240/169

Answer:

234.9 million km

Step-by-step explanation:

The central angle is a quarter of a circle: 360° / 4 = 90°. Use the central angle calculator to find arc length. You can try the final calculation yourself by rearranging the formula as: L = θ * r. Then convert the central angle into radians: 90° = 1.57 rad, and solve the equation: L = 1.57 * 149.6 million km. L = 234.9 million km.

To multiply 4/5 by 1/3 using the rectangular model, follow the given steps below:

Step 1: Draw a rectangle and divide it into equal parts (columns and rows) based on the denominator of the given fractions. Here, 5 parts in a row (horizontally) and 3 parts in a column (vertically).

Step 2: Shade in the portion of the rectangle that corresponds to 4/5.

Step 3: Shade in the portion of the rectangle that corresponds to 1/3. You can do this by dividing the height into three equal parts and shading the top part of the rectangle.

Step 4: Find the area of the shaded region of the rectangle. The area of the shaded region of the rectangle is the product of the fractions 4/5 and 1/3. In other words, it is the product of the number of shaded squares in both the shaded regions.

Step 5: Simplify the answer. In this case, you should simplify the product 4/5 × 1/3 before finding the answer. The rectangular model of 4/5 by 1/3 is shown below:

Given fractions: 4/5 and 1/3To find: Multiplication of 4/5 and 1/3 using the rectangular model. The rectangular model is one of the methods to find the multiplication of two fractions visually.

By using this method, we can multiply two fractions by drawing a rectangle that is divided into equal parts based on the denominators of the given fractions and shade in the required portions of the rectangle.

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Answer:

Volume of the figure = 68 in.³

Step-by-step explanation:

The figure is composed of a rectangular prism and 2 equal triangular prism

Volume of the figure = volume of rectangular prism + 2(volume of triangular prism)

✔️Volume of triangular prism = L*W*H

L = 14 in.

W = 2 in.

H = 2 in.

Volume = 14*2*2 = 56 in.³

✔️Volume of triangular prism = ½*a*c*h

a = 3 in.

c = 2 in.

h = 2 in.

Volume = ½*3*2*2 = 6 in.³

✅Volume go the figure = 56 + 2(6) = 56 + 12

Volume of the figure = 68 in.³

Answer:

Brand A

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )

Brand A

V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³

Brand B

V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³

Brand A have the largest volume

Answer: x= −27 or x = 27

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Subtract 2 from both sides

2x= -54

Divide both sides by 2

x = -27

Answer:

20m

Step-by-step explanation:

Given:

Number of players per team = m

Number of teams in the league = 20

The number of players in the league is the product of the number of payers in each team and the number of teams in the league.

This the expression to obtain the total number of players goes thus :

Total number of players in the league = 20 * m

Total Numbr of players in the league = 20m

The surface area of the cylinder is 60π cm².

What is the surface area of a cylinder?

The surface area of a cylinder indicates the total area of two plane surfaces (bases) and one curved surface.

If a cylinder has a radius of r cm and height of h cm, then the total surface area of the cylinder = 2πr(r + h)

Given, r = 3 cm and h = 7 cm.

Therefore, the total surface area of the cylinder

= 2πr(r + h)

= 2π × 3(3 + 7) cm²

= 2π × 3 × 10 cm²

= 60π cm²

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Answer:

C. 60π cm2

Step-by-step explanation:

Answer: 12.5 litres

Step-by-step explanation:

The SUV takes 2.5 litres for every 20 km driven.

The trip to work is 20 km which means that going to work costs Marie's father 2.5 litres every day in fuel.

In a week, there are 5 working days.

The amount of fuel used per week is therefore:

= 2.5 * 5

= 12.5 litres

Answer:

Just multiply the exponents of the numbers

So this is the order from top to below and I'll mark as 1 to 5

2

1

4

5

3

Answer:

this is hard to tell and sorry if I'm wrong but I would say it is only a

Step-by-step explanation:

Aanything in the shaded area is correct if it's not it's wrong

Answer: C!!!!!!!

Step-by-step explanation:

Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste

Since events A and B are mutually exclusive, they cannot occur together. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities. P(AUB) = P(A) + P(B) - P(A ∩ B) Where, P(A) = 0.9P(B) = 0.1Since the events are mutually exclusive, P(A ∩ B) = 0Thus,P(AUB) = P(A) + P(B) - P(A ∩ B)= 0.9 + 0.1 - 0= 1 Hence, the value of P(AUB) is 1.

The most common method for distinguishing between integers and non-integers is the decimal numeral system. It is the expansion to non-number quantities of the Hindu-Arabic numeral framework. Decimal notation is the method used to represent numbers in the decimal system.

Decimal spots are places of the digits to one side of a decimal point. The process of reducing a decimal number to a specified degree of accuracy is known as rounding. To do this we find the decimal spot we wish to adjust to and check out at the digit to one side of that number.

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Answer:

true

Step-by-step explanation:

(a) If a person who identifies as a man is 6 feet 3 inches tall, his z-score will be 2.96.

(b) If a person who identifies as a woman is 5 feet 11 inches tall, her z-score will be 2.17.

(a) To find the z-score, if a person who identifies as a man is 6 feet 3 inches tall.

Explanation: First, convert 6 feet 3 inches to inches.

6 feet 3 inches = (6 x 12) + 3 inches

= 72 + 3 inches

= 75 inches

The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

Substitute the given values in the above formula.

z = (75 - 69.2) / 2.63

= 2.21 / 2.63

= 0.8382

≈ 2.96 (to two decimal places)

(b) To find the z-score, if a person who identifies as a woman is 5 feet 11 inches tall..

Explanation: First, convert 5 feet 11 inches to inches.

5 feet 11 inches = (5 x 12) + 11 inches

= 60 + 11 inches

= 71 inches

The formula for calculating the z-score is: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

Substitute the given values in the above formula.

z = (71 - 64.6) / 2.53

= 6.4 / 2.53

= 2.5336

≈ 2.17 (to two decimal places)

Therefore, the z-score for the given heights of men and women in the US are 2.96 and 2.17 respectively.

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The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.

(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.

(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.

To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.

By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

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9514 1404 393

Answer:

  9

Step-by-step explanation:

There are 9 such numbers:

  1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360

_____

For each ABCD, where BCD = x, we want ...

  26x = 1000A +x

  25x = 1000A

  x = 40A

The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.

Answer:

9 is correct but if you are here from caribou math it is 7

Step-by-step explanation:

don't dislike what they said because it is the right formula. 25x = 1000A

you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7

The probability that the second ball drawn is yellow is 4/9. This is determined by considering the initial probabilities and applying the law of total probability.

Initially, there are a total of 10 balls in the container: 5 red, 3 yellow, and 2 blue. The probability of drawing a yellow ball on the first draw is P(yellow) = 3/10. In this case, the yellow ball is replaced back into the container, so the number of yellow balls remains the same.

If the first ball drawn is not yellow, it means a red or blue ball was drawn. These balls are kept outside the container, so they are not available for the second draw. Now, there are 7 balls remaining in the container: 2 yellow and 5 red (initially there were 5 red and 2 blue, but we only consider the red balls since the blue balls are not relevant for the second draw). The probability of drawing a yellow ball on the second draw, given that the first ball was red or blue, is P(yellow | red or blue) = 2/7.

To find the overall probability that the second ball drawn is yellow, we need to consider the probabilities of the different scenarios and their corresponding probabilities. Since the first ball can either be yellow or not yellow, we can use the law of total probability:

P(second ball is yellow) = P(yellow) * P(yellow on second draw | yellow) + P(not yellow) * P(yellow on second draw | not yellow)

P(second ball is yellow) = (3/10) * (2/10) + (7/10) * (2/7) = 4/9

Therefore, the probability that the second ball drawn is yellow is 4/9.

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Answer:

Steps:

SA = 2LW + 2WH + 2LH

SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)

SA = 2×18 + 2×22/2 + 2×99/2

SA = 36 + 22 + 99

SA = 157 in²

Answer:

20 books

Step-by-step explanation:

Well 14 books in 7 months.

Find the unit rate

14/7=2

So 2 books each month

We have Ruth here that was in the book club for 10 months.

And since 2 books each month,

2*10=20

20 books

Answer:

Step-by-step explanation:

Left hand side.

The left hand side is the general equation that includes the center of the circle.

The center is at -10,-4

(x + 10)^2 + (y + 4)^2 = r^2

Finding the radius.

the radius is found from the given point on the circle

Givens

x1 = -10

x2 = 4

y1 = - 4

y2 = - 2

Equation

r^2 = (y2 - y1)^2 + (x2 - x1)

r^2 = (-2 - - 4)^2 + (4 - - 10)^2

r^2 = 2^2 + 14^2

r^2 = 200

Note: