6 9/10 as a decimal number

The probability that player 1 wins m times is \($\frac{m}{n}\).

Assume that the numbers 1,2, ....., and n are randomly given to players.

Consider,

\(\Omega & =\{1,2, \ldots, n\} \\\)

\(& =\left\{\omega_1, \omega_2, \ldots, \omega_n\right\}\)

Here, player 1 and player 2 compare their numbers.

The one with the largest number wins and compares her number with player 3 and So on...

If all outcomes are equally likely,

\(\Omega=\left\{\omega_1, \omega_2, \ldots . ., \omega_n\right\}\)

Then \($\Omega$\) is equiprobable sample space.

The probability of each \($\omega_i$\) is \($\frac{1}{n}\) for i = 1, 2, ..........., n

\($P\left\{w_1\right\}=P\left\{\omega_2\right\}=P\left\{\omega_3\right\}............P\left\{\omega_n\right\} = \frac{1}{n}\)

These numbers are randomly given then it has m Sample points.

Probability = P (player 1 wins m times)

For every subset of numbers chosen uniformly at random all possible permutations of these numbers are equally likely.

\($\Rightarrow P(A)=\frac{1}{n}+\frac{1}{n}+\cdots \cdots+\frac{1}{n} \text { ( mimes) }\)

The number of sample points in A is divided by a number of Sample points in \(} \Omega}$\).

\($=\frac{\text { number of sample points in } A}{\text { number of Sample points in } \Omega}\)

\($=\frac{\text { number of favorable cases to event } A}{\text { number of possible cases }}$\)

\($=\frac{m}{n} \\\)

Therefore P(A) = \($\frac{m}{n}\)

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Answer:

\(TU = 15\)

Step-by-step explanation:

Given

\(\square MNOP \simeq\ \square STUV\)

\(NO = 10\)

\(OP = 4\)

\(TU = x\)

\(UV = 6\)

Required

Determine the length of TU (i.e. x)

Because both shapes are similar, then the following equivalent ratios exist:

\(NO : OP = TU : UV\)

Substitute values for NO, OP, TU and UV

\(10 : 4 = x : 6\)

Represent as fraction

\(\frac{10 }{ 4 } = \frac{x }{ 6}\)

Multiply both sides by 6

\(6 * \frac{10 }{ 4 } = \frac{x }{ 6} * 6\)

\(6 * \frac{10 }{ 4 } = x\)

\(x = 6 * \frac{10 }{ 4 }\)

\(x = \frac{60 }{ 4 }\)

\(x = 15\)

Hence:

\(TU = 15\)

Answer:

Step-by-step explanation:

Given:

Number of fruit flies = 200

Rate of growth = 3 times per day

Find:

A . Equation

B . Number of fruit flies after 3 days

Computation:

A . Equation = 3n(200)

Equation = 600n

B. Number of fruit flies after 3 days

Number of fruit flies after 3 days = 600(3).

Number of fruit flies after 3 days = 1800 fruit flies

Answer:

x)45

y)45

z)135

Step-by-step explanation:

Let us first understand what the y-axis is and what a coordinate plane is. A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line and a horizontal line at a point called the origin. The vertical line is the y-axis, while the horizontal line is the x-axis. These axes are numbered by counting the units.

A point is represented in the coordinate plane as an ordered pair (x,y), where x is the coordinate on the x-axis, and y is the coordinate on the y-axis. In the given answer choices, (-3,4) and (5,-2) are on the far left and right sides of the coordinate plane, respectively. (-5,3) and (4,5) are in the middle. The point nearest to the y-axis is (-3,4), which is located closest to the y-axis. Therefore, (-3,4) is the answer. Hence, the answer is (-3,4).

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Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as:  \(A1=\frac{(base)(height)}{2}\)

Area of a rectangle is calculated as: \(A2=(side)(side)\)

Area of a right trapezoid is: \(A3=\frac{(a+b)h}{2}\), where:

a is short base

b is long base

h is height

1) Expressing areas in terms of x:

Area of triangle S1:

\(S1=\frac{(2x-3)(4x-6)}{2}\)

\(S1=4x^{2}-12x+9\)

Area of rectangle S2:

\(S2 = (4x-6)(3x-2)\)

\(S2=12x^{2}-26x+12\)

Area of trapezoid S3:

\(S3=\frac{(2x+3+4x+1)(2x-3)}{2}\)

\(S3=\frac{(6x+4)(2x-3)}{2}\)

\(S3=6x^{2}-5x-6\)

2) a) \(S=4x^{2}-12x+9+12x^{2}-26x+12-(6x^{2}-5x-6)\)

\(S=4x^{2}-12x+9+12x^{2}-26x+12-6x^{2}+5x+6\)

\(S=10x^{2}-33x+37\)

Which is the same as S = (2x-3)(5x-9)

b) For the areas to be the same:

\(\frac{(3x-2+3x-2+2x-3)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}\)

\(\frac{(8x-7)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}\)

\(32x^{2}-48x-28x+42=12x^{2}+8x-18x-12\)

\(20x^{2}-66x+54=0\)

Using Bhaskara to solve the second degree equation:

\(\frac{66+\sqrt{(-66)^{2}-(4.20.54)} }{2(20)}\)

\(x_{1}=\frac{66+6}{40}\) = 1.8

\(x_{2}=\frac{66-6}{40}\) = 1.5

For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.

c) Expand a polynomial (or equation) is to multiply all the terms, remiving the parenthesis. Reduce a polynomial (or equation) is to combine terms alike,e.g.:

\(S=(2x-3)(5x-9)\)

\(S=10x^{2}-18x-15x+27\) (expand)

\(S=10x^{2}-33x+27\) (reduce)

d) For area of AFCG to be bigger than area of ADEB by 27:

\(32x^{2}-48x-28x+42=12x^{2}+8x-18x-12+27\)

\(32x^{2}-48x-28x+42=12x^{2}+8x-18x+15\)

\(20x^{2}-66x+27=0\)

Solving:

\(\frac{66+\sqrt{(-66)^{2}-(4.20.27)} }{2(20)}\)

\(\frac{66+46.86}{40}\)

\(x_{1}=\frac{66+46.86}{40}=\) 2.82

\(x_{2}=\frac{66-46.86}{40}\) = 0.48

According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles, with these functions one can answer virtually all questions about.

Answer:

(a/sinA)＝(b/sinB)＝(c/sinC)

Step-by-step explanation:

a and b and c is the length

A,B,Cis angle.

This is a formula.

E.g. the angle opposite of the length a is A.

               - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\diamond\large\textsf{\textbf{Question:-}}}}\)

-7n-15≤21. find n

\(\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\)

 ❖ Add 15 to both sides:-

      -7n≤21+15

        -7n≤36

❖ Now divide by -7 on both sides:-

               n≥-5.14 or

                n≥-5

The inequality sign changed because we divided both sides by a negative number.

        - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - -

From the given equation, we are to solve for b.

Hence the answer of b is -108.

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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Answer:

B

Step-by-step explanation:

We can see in the expression that there are 2 x² blocks, 4 -x blocks, and 3 -1 blocks. Therefore, we can write this as

2 * x² + 4 * (-x) + 3 * (-1) = 2x²-4x-3

Comparing this with each answer, we have

A: x²-2x-4 + x² + 2x-1 = 2x²-5. This is not correct

B: 3x²-7x+1-(x²-3x+4) = 3x²-7x+1 -x²+3x-4 = 2x²-4x-3. This seems correct but we can check the other answers to be sure

C: (2x+1)(x-3) = 2x²-6x+x-3 = 2x²-5x-3. This is incorrect

D: \(\frac{8x^{12} - 16x^7 - 12x^6}{4x^6} = 2x^6 - 4x - 3\). This is incorrect

Answer:

C. 2(x + 10)(x - 10)

Step-by-step explanation:

2x^2-200\\2(x^2-100)\\2(x+10)(x-10)

Answer:

bought = £3000

sold = £3375

profit = sold price - bought price

= £3375 - £3000

= £375

percentage of profit = (profit/bought price) × 100

=(£375/£3000) × 100

= 0.125 × 100

= 12.5%

The original price is £3000

The selling price is £3375

Calculate the profit gained.

(Sell price-Original price)

\(= 3375-3000\)

\(= 375\)

The profit is £375.

Calculate the profit percentage.

(Profit/Original price × 100)

\(=375/3000 \times 100\)

\(=1/8 \times 100\)

\(=12.5\%\)

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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In the graph of a function there exist a point where function is not defined is known as a hole of a function.

Hole of a function is defined as:

Therefore, the hole of a function is a point where function does not defined only approaches.

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Answer:

Step-by-step explanation:

5 - 2(x - 3) and (m+5)(m+5)​

\(5 - 2(x-3)\\5 - 2x + 6\\-2x + 11\)

\((m+5)(m+5)\\m^2+5m+5m+25\\m^2+10m+25\)

Hope this helps!

El valor que satisface D es 188.

El modelo matemático será así:

D/d = 12(resto 8)

si escribimos 8 como resto de D, entonces:

(D-8) /d=12

D-8= 12d o se puede escribir D= 12d+8

luego sustituya D= 12d+8 por D+d= 203

D+d= 203

(12d +8) +d= 203

13d= 203-8

13d= 195

re=15

sustituir d=15 en D+d= 203

D+d= 203

D+15=203

D=203-15

D=188

El modelo matemático es una forma de interpretación humana al traducir o formular problemas existentes en forma matemática, de modo que el problema pueda resolverse utilizando las matemáticas.

El uso principal de los modelos matemáticos es ayudar a las personas a comprender los problemas y simplificarlos para que puedan resolverse.

, los siguientes son algunos de los usos que se obtienen al utilizar un modelo matemático, a saber:

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Answer:

i think 58, but if not, go to khan academy and watch a video!

Step-by-step explanation:

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Using vector concepts, it is found that:

------------------------------

------------------------------

Item 1:

------------------------------

Item 2:

------------------------------

Item 3:

------------------------------

Item 4:

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A vector can be represented by a line on the coordinate plane such that the length of the line and the direction of the line gives the magnitude and direction of the vector

The components and magnitudes of the vectors are;

1. The vertical component of the vector is 9

2. The horizontal component of a vector is 13

3. The magnitude of the vector is 3

4. The horizontal component of the pulling force is approximately 9.23 N

The reason the above values are correct are as follows:

The given coordinates of the vectors are as follows;

1. Starting point coordinate: (8, -1), ending point coordinate (5, 8)

Required:

The vertical component of the vector

Solution:

The vertical component of the vector is given by the difference of the y-coordinates (-1, and 8) as follows;

Vertical component = 8 - (-1) = 9

The vertical component of the vector = 9

2. The known parameter:

The starting point coordinate is (-5, 8), and the ending point coordinate is (8, -9)

Required:

The horizontal component of the vector

Solution:

The horizontal component of a vector is given by the difference of the x-coordinate values (-5 and 8), taking into consideration of the direction of the vector, as follows;

The horizontal component of a vector = 8 - (-5) = 13

3. Known parameter

Starting point coordinate of the vector (-9, -4), the ending point coordinate of the vector (-1, -5)

Required:

The magnitude of the vector

Solution:

The magnitude of the vector is given by the length of the line on the x, y-coordinate plane as follows;

\(Magnitude = Length \ of \ representative \ line \ l \ = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

Therefore, we have;

Magnitude of the vector = √((-5 - (-4))² + (-1 - (-9))) = 3

The magnitude of the vector  = 3

4. The known parameters are;

The pulling force by Jason = 27 N

The angle which his arm makes with the horizontal = 70°

Required:

The horizontal component of the pulling force

Solution:

The component of a vector is given by the projection of the vector unto the axis being referenced

The horizontal component of the vector is given by the component in the x-axis direction

∴ The horizontal component of the vector = 27 × cos(70°) ≈ 9.23 N

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The experimental probability of drawing a heart is given as follows:

0.30.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes is given as follows:

6 + 4 + 7 + 3 = 20.

Out of these 20 trials, 6 resulted in a heart, hence the experimental probability of drawing a heart is given as follows:

p = 6/20

p = 0.3

p = 30%.

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The reliability of the given system is 0.4033.

To calculate the reliability of a system, we need to multiply the reliability values of all the components in the system. In this case, we have a system composed of three components with the following reliability values:

Component 1: 0.90

Component 2: 0.90 0.90 0.85

Component 3: 0.85 0.85 0.92

To find the overall system reliability, we multiply these values together:

System reliability = Component 1 reliability x Component 2 reliability x Component 3 reliability

System reliability = 0.90 x (0.90 x 0.90 x 0.85) x (0.85 x 0.85 *x 0.92)

System reliability ≈ 0.90 x 0.6831 x 0.6528 ≈ 0.4033

Therefore, the reliability of the given system is 0.4033.

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Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).

The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.

To calculate the X-coordinate of the center of gravity, we use the formula:

Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)

Similarly, for the Y-coordinate:

Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)

Substituting the given values:

Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92

Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08

Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.

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The equivalent expression is 7^7. 2^7.

Option C is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

(7 . 2)^7

Now,

This expression can be written as,

7^7 . 2^7

Thus,

The equivalent expression is 7^7. 2^7.

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The mean should be set to 12.07 ounces, so that 1% of the cups will overfill.

12 + (0.07 * 2) = 12.14; 12.14 - (12.14 * 0.01) = 12.07

The mean amount of coffee to be dispensed should be set to 12.07 ounces in order to allow 1% of the cups to overfill. This is calculated by taking the normal value of 12 ounces, and adding the standard deviation of 0.07 ounce, resulting in 12.14 ounces. Then, 1% of that value is subtracted, giving 12.07 ounces. This amount will ensure that 1% of the cups will overfill, while the other 99% will be filled to the normal value of 12 ounces. This is beneficial for the customer, as it guarantees that no cup will be underfilled. It also ensures that the vending machine will not waste any coffee by overfilling the cups too much. Setting the mean to 12.07 ounces is the best solution for both the customer and the vending machine.

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Answer:

The mean would increase

The sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

To determine whether the sequence {an} = {\(8n^4 + n + 1\)} is convergent, we need to examine the behavior of the terms as n approaches infinity.

The sequence {an} is said to be convergent if there exists a real number L such that the terms of the sequence get arbitrarily close to L as n approaches infinity.

To investigate convergence, we can calculate the limit of the sequence as n approaches infinity.

lim(n→∞) \((8n^4 + n + 1)\)

To evaluate this limit, we can look at the highest power of n in the sequence, which is \(n^4.\) As n approaches infinity, the other terms (n and 1) become insignificant compared to n^4.

Taking the limit as n approaches infinity:

lim(n→∞) \(8n^4 + n + 1\)

= lim(n→∞) \(8n^4\)

Here, we can clearly see that the limit goes to infinity as n approaches infinity.

Therefore, the sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

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This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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To calculate SAM and SOM, you need to follow the following steps:

1. SAM (Simple Arithmetic Mean): SAM is calculated by adding up all the values in a set of data and then dividing that sum by the number of values in the dataset.

Formula: SAM = (x1 + x2 + ... + xn)/n

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SAM would be (2+4+6+8+10)/5 = 30/5 = 6

2. SOM (Simple Geometric Mean): SOM is calculated by multiplying all the values in a set of data and then taking the nth root of that product, where n is the number of values in the dataset.

Formula: SOM = (x1 * x2 * ... * xn)^(1/n)

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SOM would be (2*4*6*8*10)^(1/5) = 3840^(1/5) = 5.16

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The age of Jordan today is 16

From the question, we have the following mathematical statements:

Today

Tien's age = 1/4 of Jordan's age.

In 2 years,

Tien's age = 1/3 of Jordan's age

Represent Tien's age with x and Jordan's age with y

So, we have the following equations

x = 1/4y

x + 2 = 1/3(y + 2)

Make y the subject in x = 1/4y

y = 4x

Substitute y = 4x in x + 2 = 1/3(y + 2)

x + 2 = 1/3(4x + 2)

Multiply through by 3

3x + 6 = 4x + 2

Collect the like terms

4x - 3x = 6- 2

Evaluate the like terms

x = 4

Substitute x = 4 in y = 4x

y = 4 x 4

Evaluate

y = 16

Recall that Represent Jordan's age with y

This means that

Jordan's age = 16

Hence, Jordan's age as per the mathematical statement is 16

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