please give a detailed explanation ​

For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, the outliers are 3, 3, 3, 3, 15, and 27.

In statistics, outlier refers to the data point from a given data set that differs significantly from the other data points.

One way to determine the outlier in a given data set is to calculate the interquartile range.

1. Arrange the data set in ascending or descending order.

3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27

2. Divide the data set into two sets and find the median.

{3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6} , {6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27}

Q1 median = 4

Q3 median = 8

3. Solve for the IQR.

IQR = Q3 - Q1

IQR = 8 - 4

IQR = 4

4. Determine the outlier if

high outlier ≥ Q3 + (1.5 x IQR) = 8 + (1.5 x 4) = 14

high outlier ≥ 14

low outlier ≤ Q1 − (1.5 x IQR) = 4 - (1.5 x 4) = 3

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The values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.

A sequence is defined as an arrangement of numbers in a particular order.

Given aₙ = crⁿ⁻¹ - d, then;

c - d = 0...(1)

cr - d = 7...(2)

cr² - d = 21...(3)

from equal (1), c = d so that equation (2) becomes;

cr - c = 7 and;

c = 7/(r - 1)...(4)

put 7/(r - 1) for c and d in equation (3);

7/(r - 1)(r²) - 7/(r - 1) = 21

7r² - 7 = 21(r - 1)

7r² - 21r + 14 = 0

r² - 3r + 2 = 0

by factorization;

r = 1 or r = 2

denominator in equation (4) will be zero if r = 1, so we put 2 for r in equation (4) to get c;

c = 7/(2- 1)

c = 7.

Therefore, values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.

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The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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The approximate Debye shielding length of a spacecraft in 600 km orbit under the following conditions: Night, Minimum solar cycle: 0.3 mm and Day, Maximum solar cycle: 1.5 mm

The Debye shielding length is a measure of the distance over which the electric field of a charged particle is screened by the presence of other charged particles. The Debye shielding length is given by the following formula: λD = √(kT/ne)

where k is Boltzmann's constant, T is the temperature, n is the number density of charged particles, and e is the elementary charge.

In the case of a spacecraft in 600 km orbit, the temperature is approximately 300 K. The number density of charged particles in the night, minimum solar cycle is approximately 100 cm-3.

The number density of charged particles in the day, maximum solar cycle is approximately 1000 cm-3.

Substituting these values into the formula for the Debye shielding length, we get:

Therefore, the approximate Debye shielding length of a spacecraft in 600 km orbit under the following conditions:

Night, Minimum solar cycle: 0.3 mm

Day, Maximum solar cycle: 1.5 mm

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Answer:

35 red apples and 35 green apples

Step-by-step explanation:

70 divided by 2 = 35

The statement about the rates of change is (b) Function 1 and Function 2 have the same rate of change

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

Function 1:

Multiply the input by-3 and then add 4.

From the above, we have the function to be

f(x) = -3x + 4

For the graph, we have the equation to be (See attachment)

g(x) = -3x + 5

By comparison, the rates of the two functions are

Rates = -3 and -3

Hence, the statement about the rates of change is (b)

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To compute the stationary distribution π of the given Markov chain, we need to solve the equation πP = π, where P is the transition probability matrix.

The stationary distribution represents the long-term probabilities of being in each state of the Markov chain.

Let's denote the stationary distribution as π = (π1, π2, π3), where πi represents the probability of being in state i. We can set up the equation πP = π as follows:

π1 * 0.5 + π2 * 0.4 + π3 * 0.1 = π1

π1 * 0.3 + π2 * 0.4 + π3 * 0.3 = π2

π1 * 0.2 + π2 * 0.3 + π3 * 0.5 = π3

Simplifying the equations, we have:

0.5π1 + 0.4π2 + 0.1π3 = π1

0.3π1 + 0.4π2 + 0.3π3 = π2

0.2π1 + 0.3π2 + 0.5π3 = π3

Rearranging the terms, we get:

0.5π1 - π1 + 0.4π2 + 0.1π3 = 0

0.3π1 + 0.4π2 - π2 + 0.3π3 = 0

0.2π1 + 0.3π2 + 0.5π3 - π3 = 0

Simplifying further, we have the system of equations:

-0.5π1 + 0.4π2 + 0.1π3 = 0

0.3π1 - 0.6π2 + 0.3π3 = 0

0.2π1 + 0.3π2 - 0.5π3 = 0

Solving this system of equations, we can find the values of π1, π2, and π3, which represent the stationary distribution π of the Markov chain.

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Answer:

\(78 \frac{5}{8} \)

Step-by-step explanation:

\(for \: the \: width = 8 \tfrac{1}{2} \\ = \frac{17}{2} \\ sine \: the \: width \: is \: 9 \frac{1}{4} a \: long \\ 9 \ \frac{1}{4} = \frac{37}{4} \\ lenht \: of \: the \: plot = \ \frac{17}{2} \times \frac{37}{4} = \frac{629}{8} = 78 \ \frac{5}{8} \\ it \: will \: be78 \ \frac{5}{8}long \)

The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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Answer:

17

Step-by-step explanation:u will make the second fraction postive it will be 12+4 which is 16 and a half plus a half is a whole

Answer: 17

Step-by-step explanation:

Answer:

Sn=a1(1−rn)1−r,r≠1 C.

The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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Answer:

(-9, 9), Quadrant II

Step-by-step explanation:

Start at (0, 0), the origin, where the x-axis and the y-axis intersect.

Go left 9 units. x = -9

Go up 9 units. y = 9

The quadrants start with the top right as quadrant I and go counterclockwise to quadrants II II and IV.

Answer: (-9, 9), Quadrant II

The combined present worth of the costs associated with the proposed bridge design is $9,583,333.

This value is obtained by calculating the present worth of both the construction cost and the annual operating cost over an infinite life of the bridge, considering a MARR (Minimum Attractive Rate of Return) of 12%.

To determine the present worth, we use the formula:

PW = A / (1 + i)^n

Where PW is the present worth, A is the annual cost, i is the interest rate, and n is the number of years.

For the construction cost, we have a one-time expense of $9,000,000. Since it is a single payment, the present worth is equal to the construction cost itself.

For the annual operating cost, we need to calculate the present worth over an infinite life. Using the formula above, we divide the annual cost of $700,000 by the MARR of 12% to obtain $5,833,333.33. Thus, the combined present worth is the sum of the construction cost and the present worth of the annual operating cost, resulting in $9,000,000 + $5,833,333.33 = $9,583,333.

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Answer:

5/6

Step-by-step explanation:

The results of previous dice rolls don't have any effect on the result the next time the die is rolled.

The relative frequency of getting a 5 on the next roll is 5/6

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency). Conditional relative frequency is relative frequency conditional to some special characteristic.

We are given that a fair die is rolled 25 times. it landed on the number 5 eight times.

We need to find the relative frequency of getting a 5 on the next roll

relative frequency = 5/6

The results of previous dice rolls that have any effect on the result the next time the die is rolled.

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5 cups=1 quart and 1 cup

1 quart=1 quart

take the cup from the top and add the 3 cups of crushed ice so that 4 cups

4 cups=1 quart

thats 3 quarts

3 quarts has 12 cups

12 cups divided by 6 is 2

each cup has 2 cups of smoothie

Division is one of the four fundamental arithmetic operations. The number of cups in each glass will be 2 cups per glass.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Kyle uses 5 cups of mangoes, 1 quart of yogurt, and 3 cups of crushed ice.

Now, since the yogurt quantity is given in quarts, therefore, the yogurt quantity in terms of cups is needed to be calculated.

Since 1 quart is equal to 4 cups, therefore, yogurt used by Kyle will be either 1 quart or 4 cups.

Further, the total amount of smoothies will be,

Total smoothie

= 5 cups of mangoes + 4cups of yogurt + 3 cups of crushed ice

= 12 cups

Furthermore, there are 6 large glasses, therefore, the number of cups in each glass will be,

Number of cups in each glass = Total smoothie / Number of glasses

                                                  = 12cups / 6 glass

                                                  = 2 cups per glass

Hence, the number of cups in each glass will be 2 cups per glass.

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Answer:

y/4 + x/12

Step-by-step explanation:

The number of working toys = x

The number of broken toys = y

Bert breaks 1/3 of the working toys, that is:

1/3 * x = x/3

The number of broken toys is now:

y + x/3

Ernie then throws away 1/4 of the broken toys. In terms of x and y, the number of broken toys that Ernie threw away is:

1/4 *(y + x/3)

= y/4 + x/12

Answer:

Domain: {1,3,−5,4}

Range: {2,4,−6,10}

Step-by-step explanation:

The domain is the set of all the values of x. The range is the set of all the values of y.

The unit rate of gallon to mile is calculated as: 5/6 gallon per mile.

The unit rate between two variables is simply the ratio of the quantity of one variable to the quantity of the other variable, such that the the denominator of the will be equal to exactly 1.

We are given the variables gallons and miles, where 1/4 of a gallon is to 3/10 mile.

The unit rate between these two variables would be an amount of gallons per mile.

Thus, find the unit rate by dividing 1/4 by 3/10:

1/4 ÷ 3/10

= 1/4 × 10/3

= 10/12

= 5/6

The unit rate is therefore, 5/6 gallon per mile.

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Answer:

Hello! :) have a good day!

(10x+6)4 = 40x +24

If Arturo lives in colorado, which has a state income tax rate of 4.63% and he earns $1,345 biweekly, then the amount of state income tax withheld from each of his paychecks is equal to $62.27.

The state income tax withheld from each of his paychecks can be determined by the percentage formula;

P% × x = y

Here,

P% is the state income tax rate

x is the dollars earned biweekly

y = state income tax withheld from each of his paychecks

As the state income tax rate is equal to 4.63% and the amount earned biweekly is equal to $1345, therefore;

P% × x = y

4.63% × 1345 = y

4.63% can be converted into decimal form as follows,

4.63% = 4.63 / 100 = 0.0463

Therefore,

0.0463 × 1345 = y

y = 62.27

Hence, the state income tax withheld from each of his paychecks is calculated to be $62.27

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Answer:

all we need to do is keep on adding 1/4 until you get to 1 1/2 its lik dividing to how muc times con 1/4 go into 1 1/2. so you run 7 laps

this is you answer

Step-by-step explanation:

example: at home you walk around your yard and you walked 4 1/2 miles. and yard is 1/2 of a mile. 1/2+1/2+1/2+1/2+1/2+1/2+1/2+1/2+1/2=4 1/2

so 1/2 can go into 4 1/2 9 times.

B) "Some goat was eaten by a wolf" is a correct interpretation of the statement, because it means that there exists at least one goat that was eaten by a wolf.

The given statement can be translated as: "For all goats z, if z is eaten by a wolf, then there exists a wolf w such that w has eaten z."

A) "Every goat is eaten by a wolf" is not a correct interpretation of the statement. The correct interpretation is that if a goat is eaten by a wolf, then there exists at least one wolf that has eaten a goat.

B) "Some goat was eaten by a wolf" is a correct interpretation of the statement, because it means that there exists at least one goat that was eaten by a wolf.

C) "There is a wolf who has eaten every goat" is not a correct interpretation of the statement. The correct interpretation is that for each goat that is eaten, there exists at least one wolf that has eaten it.

D) "Every goat has eaten a wolf" is not a correct interpretation of the statement. The correct interpretation is that if a goat is eaten by a wolf, then there exists at least one wolf that has eaten a goat, but it does not imply that every goat has eaten a wolf.

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The amount of money in Sam's account in 2016, after investing $3,890 with an annual interest rate of 4.8% compounded annually, can be approximated as $3,890 multiplied by 1.048 raised to the power of 17. It can be calculated as approximately $7,536.48

To calculate the amount of money in Sam's account in 2016, we need to consider the annual compounding interest. The formula to calculate the future value of an investment with compound interest is:

\(\[A = P \left(1 + \frac{r}{n}\right)^{n(t-t_0)}\]\)

Where:

\(A\) is the future value of the investment

\(P\) is the principal amount (initial investment)

\(r\) is the interest rate (in decimal form)

\(n\) is the number of times interest is compounded per year

\(t\) is the number of years

\(\(t_0\)\) is the initial year

Given that Sam's initial investment is $3,890 in 1999, the interest rate is 4.8% (0.048 in decimal form), and interest is compounded annually, we can plug these values into the formula:

\(\[A = 3890 \left(1 + \frac{0.048}{1}\right)^{(2016-1999)}\]\)

Simplifying the equation, we find:

\(\[A \approx 3890 \times (1.048)^{17}\]\)

It can be calculated as approximately $7,536.48

Therefore, The amount of money in Sam's account in 2016, after investing $3,890 with an annual interest rate of 4.8% compounded annually, can be approximated as $3,890 multiplied by 1.048 raised to the power of 17. It can be calculated as approximately $7,536.48.

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Answer:

A.

Step-by-step explanation:

B.  (-1,1) (-1,-5)  ... can't pass vertical line test

C.  (-1,7) (-1,1)

D. (3,2) (3,4)

Each individual result of a probability experiment is called an "outcome" (d).

An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.

For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.

Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.

In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.

Thus, each individual result of a probability experiment is called an "outcome" (d).

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Answer:

4x + 12 ≤ -8

Step-by-step explanation:

I hope this helps!

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

Given,

A spherical golf ball is measured to have a radius of $$5 mm, with a possible measurement error of $$0.1 mm

How to determine the volume

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

r is the radius of the sphere

pi takes the value 3.14

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

v = 4/ 3 (392.5)

v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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The orthogonal projection of f(x)=4x^2-3 onto the subspace V spanned by g(x)=x-1/2 and h(x)=1 is:
projV(f(x)) = -2/15sqrt(10) * 3sqrt(10) * (x - 1/2)^2 = -(2/5)(x - 1/2)^2

To find the orthogonal projection of f(x)=4x^2-3 onto the subspace V spanned by g(x)=x-1/2 and h(x)=1 in the vector space C0[0,1], we first need to find an orthonormal basis for V.

We can use the Gram-Schmidt process to find an orthonormal basis for V. Starting with the given basis vectors, we have:

v1 = g(x) = x-1/2
v2 = h(x) = 1

To normalize v1, we divide it by its norm:
u1 = v1 / ||v1|| = (x - 1/2) / sqrt(integral from 0 to 1 of (x-1/2)^2 dx)
    = 2sqrt(3) * (x - 1/2)

To find v2 orthogonal to u1, we subtract its projection onto u1:

v2' = v2 - u1
    = 1 - integral from 0 to 1 of (x - 1/2) dx * 2sqrt(3) * (x - 1/2)
    = 2sqrt(3) * (x - 1/2)^2

To normalize v2', we divide it by its norm:
u2 = v2' / ||v2'|| = 3sqrt(10) * (x - 1/2)^2

So our orthonormal basis for V is {u1, u2}.

Now we can use the projection formula:
projV(f(x)) = u1 + u2

where  = integral from 0 to 1 of 4x^2-3 * 2sqrt(3) * (x - 1/2) dx = 0
and  = integral from 0 to 1 of 4x^2-3 * 3sqrt(10) * (x - 1/2)^2 dx = -2/15sqrt(10)

So the orthogonal projection of f(x)=4x^2-3 onto the subspace V spanned by g(x)=x-1/2 and h(x)=1 is:
projV(f(x)) = -2/15sqrt(10) * 3sqrt(10) * (x - 1/2)^2 = -(2/5)(x - 1/2)^2

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The density of water is approximately 1 g/ml at standard temperature and pressure (STP)

Density is defined as the amount of mass per unit volume of a substance, and it is usually expressed in units of grams per milliliter or grams per cubic centimeter.

The density of water is approximately 1 gram per milliliter (g/ml) at room temperature and atmospheric pressure. This means that one milliliter of water has a mass of one gram.

The density of water is an important physical property that is used in many applications, such as in the calculation of the buoyant force on objects submerged in water, in the design of ships and submarines, and in the determination of the concentration of solutions in chemistry and biology.

It is also worth noting that the density of water is an important reference point in the metric system. The gram, which is the standard unit of mass in the metric system, is defined as the mass of one cubic centimeter of water at its maximum density, which occurs at a temperature of 4 degrees Celsius.

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