Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 *Explain your answer (2pt cach) a. 20, 24, 21, 19, 18 b. 20, 20, 20, 20, 20

Answer:

- [tex]\frac{8}{13}[/tex]

Step-by-step explanation:

let n be the other rational number , then

- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]

[a number × its reciprocal = 1 ]

multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]

n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex]  ( cancel the 3 on numerator/ denominator )

n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]

The cost of petrol for the trip to UWC is R1.2384.

In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.

To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.

Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:

[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]

where k stands for liters of petrol.

To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:

[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]

Now we can calculate the cost of petrol for the trip:

[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]

Therefore, the cost of petrol for the trip to UWC is R1.2384.

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Answer:

Step-by-step explanation:

[tex](x-20)^2=x^2-20[/tex]

Expanding LHS gives:

  [tex]x^2-40x+400=x^2-20[/tex]

         [tex]-40x+400=-20[/tex]          (subtracted [tex]x^2[/tex] from both sides)

                   [tex]-40x=-420[/tex]        (subtracted 400 from both sides)

                         [tex]x=\frac{-420}{-40}[/tex]          (divided both sides by-40)

                         [tex]x=\frac{21}{2} =10\frac{1}{2}[/tex]

Answer: 11

Step-by-step explanation:

Turn it into an improper fraction so 8 from 8 1/4 to 33/4

Then just divide by 3/4

This will give you 11

Answer: 37.85

Step-by-step explanation:

Substitute: 3.2x0.2+6.1^2

Calculate the product or quotient: 0.64+6.1^2

Calculate the power: 0.64+37.21

Calculate the sum or difference: 37.85

Answer:  37.85

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The number of students who did not enroll in the college given that only 3/5th of the total students accepted the admission is equal to 80 students.

Let us consider that the total number of students who enrolled for the process is equal to x. Since it is given that three-fifth of the total students who enrolled positively are equal to 120, this means that 3/5*x = 120.

Thus value of x can be calculated by cross multiplication as follows:

3/5*x = 120

x = 120 * 5/3 = 200

Now, since two third of the students didn't respond/ enroll, then this number can be calculated as the difference between the total numbers who joined and the number of students who accepted the enrollment process.

Number of students who accepted but did not enroll = 200 - 120 = 80

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Answer: 240 miles in 2 hours

Step-by-step explanation:

we know the car is traveling 60 km per half hour (30 minutes)

so to find km per hour, multiply both by 2.

the rate of speed is 120 miles per 60 minutes (1 hour)

multiply 120 mph by the 2 hours given = 240 miles in 2 hours

Answer:

240 km in 2 hours

Step-by-step explanation:

If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:

Speed = distance ÷ time

Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour

Since the car is traveling at a constant speed, we can use the formula:

Distance = Speed × Time

To find how far the car will travel in 2 hours, we can substitute the values we have found:

Distance = Speed × Time

Distance = 120 km/hour × 2 hours

Distance = 240 km

Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.

To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:

bank account = β0 + β1 * age + ε

where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.

Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:

residual = bank account - (β0 + β1 * age)

We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.

In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.

Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.

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According to the formula, the length of one side of the hexagon is 21/4 or 5.25 units.

What is the perimeter of the regular hexagon?

Let's call the length of one side of the regular hexagon "s". Since a hexagon has six sides, the perimeter of the hexagon is 6s.

According to the problem, this is equal to the perimeter of an isosceles triangle with legs of x+4 and a base that is 3 less than one of the legs.

The perimeter of the isosceles triangle is given by:

perimeter = 2(x+4) + (x+1)

where (x+1) is the length of the base (which is 3 less than one of the legs).

Setting the perimeters equal, we get:

6s = 2(x+4) + (x+1)

6s = 3x + 9

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

We also know that the side lengths of the hexagon are 2x. Substituting this into the equation for "s", we get:

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

x = 3

Therefore, the length of one side of the hexagon is:

s = (3/2)x + (3/4) = (3/2)(3) + (3/4) = 9/2 + 3/4 = 21/4

So the length of one side of the hexagon is 21/4 or 5.25 units.

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The measure of the side MR is given as 20

We have to first find the value of the angle

∠TQR = 180 - (35 + 25)

= 180 - 60

= 120 degrees

180 - 120 = 60 degrees

angle TPR  = 90 degrees

next we have to find ∠PTQ

= 180 - (90 + 60)

= 180 - 150

= 30 degrees

given that TMN = TQR

TNP = PTQ

So if TMN = 35 degrees since TQR = 35 degrees

PTQ = 30, so TNP = 30 degrees

The measure of QR = 4 since MN = 4

NP = pq

np = 6

Hence the measure of MR

= 4 + 6 + 6 + 4

= 20

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The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:

Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.

Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

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Number of  prints Jim ordered last month is 271

Let's assume Jim ordered "P" prints last month. The cost of ordering "P" prints would be the sum of the monthly charge and the cost of each print, which is given by the equation:

Cost = Monthly Charge + (Cost per Print x Number of Prints)

Substitute the values in the equation

$17.79 = $6.95 + ($0.04 x P)

Simplifying the equation, we get:

$10.84 = $0.04 x P

Dividing both sides by $0.04, we get:

P = $10.84 / $0.04

Divide the numbers

P = 271

Therefore, Jim ordered 271 prints last month.

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Answer:

Here, x represents the amount (in liters) of the 25% saline solution to be added.

We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:

x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3

Multiplying both sides by 3.33 - x, we get:

x = (1/3) (3.33 - x)

Multiplying both sides by 3, we get:

3x = 3.33 - x

Solving for x, we get:

x = 0.833 liters

Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.

Step-by-step explanation:

When a 666-sided fair die is rolled, then the probability of rolling greater than 4 is  0.9940 or 99.40%.

Given that the die is fair and has 666 sides. So, each face of the die will have a probability of 1/666, i.e.,

p(1) = p(2) = ... = p(666) = 1/666.

The probability of rolling greater than 4 is P(roll greater than 4), which is the sum of the probabilities of rolling a 5, 6, 7, 8, 9, ..., 666. So,

P(roll greater than 4) = p(5) + p(6) + p(7) + ... + p(666)

P(roll greater than 4) = (1/666) + (1/666) + (1/666) + ... + (1/666)

(There are 661 terms)P(roll greater than 4) = 661(1/666)

P(roll greater than 4) = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

Alternatively, the probability of rolling greater than 4 is

   1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - (p(1) + p(2) + p(3) + p(4))P(roll greater than 4)

= 1 - (4/666)P(roll greater than 4)

= 1 - 0.0060P(roll greater than 4)

 = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

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Greek number prefixes are employed in the naming of molecular (covalent) substances.

Greek number prefixes are employed in the naming of molecular (covalent) substances. Prefixes are always combined in order of size (left-to-right in the table below). For instance, "heptadecatetracta" (7 + 10 + 400) would be the prefix for the number 417.

We utilise prefixes (mono-, di-, tri-, etc.) at the beginning of each element in molecular compounds to denote the element's subscript, but we only use the prefix mono- for the compound's second element.

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The probability that more than 8 hours are needed to grade all of the exams is about 52%

The probability of a standard normal distribution is the area under the curve of the normal distribution function within a specified interval.

Let X represent the random variable to grade an exam, and let Y represent the total time to grade all exams

The number of students = 50

Therefore;

Y = 50·X

The properties of the normal distribution indicates that we get;

E(Y) = E(50·X) = 50·E(X) = 50 × 9.7 = 485

Var(Y) = Var(50·X) = 50²·Var(X) = 50² × 1.92² = 9025

The standard deviation, SD(Y) = √(Var(Y)) = √(9025) = 95

The probability that more than 8 hours are needed can be found using the z-score of the normal distribution as follows;

8 hours = 480 minutes

Z = (480 - 485)/95 ≈ -0.0526

The probability obtained from a standard normal table, is therefore;

P(Z > -0.0526) = 1 - 0.48006 ≈ 0.52

The probability that more than 8 hours are needed to grade all students is therefore about 0.52 or 52%

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Answer:

The diver descends:

50 seconds x 5 feet/second = 250 feet

The diver ascends:

54 seconds x 4.4 feet/second = 237.6 feet

Therefore, the total change in elevation is:

250 feet (descent) - 237.6 feet (ascent) = 12.4 feet

So, the diver's final elevation is:

0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet

Therefore, the diver ends up 12.4 feet below sea level.

Answer:

it is 1

Step-by-step explanation:

its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg

Answer:

So 3 blue buckets and 4 white buckets were purchased

Step-by-step explanation:

We can solve this by algebra

Let B = number of blue buckets bought

Let W = number of white buckets bought

Total buckets bought:
B + W = 7    (1)

Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water

Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water

Totally they can hold
2B + 5W gallons

We are given that they both can hold  26 gallons of water

So our second equation is
2B + 5W = 26   (2)

By eliminating one of the variable terms we can solve for the other variable term

Let's eliminate the term for variable B

Multiply equation (1) by 2

(1) x 2 ==> 2(B + W) = 2(7)

2B + 2W = 14    (3)

Subtract (3) from (2); B terms are same so they cancel out

(2) - (3):
2B + 5W = 26    [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0    +  3W = 12
------------------------

3W = 12
W = 12/3

W = 4

Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7

B = 3

So 3 blue buckets and 4 white buckets were purchased

Answer:

Answer is in the picture

Step-by-step explanation:

Hope you understand :)

Answer:

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

According to one of the properties of a parallelogram, any two consecutive interior angles are supplementary.

We know supplementary angles add up to 180°.

Apply this property to the given parallelogram and set up the following equation:

The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.

To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:

Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2

For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:

Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)

We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:

MAD = |Actual demand – Forecasted demand|

To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:

MSE = (Actual demand – Forecasted demand)^2

After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.

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The z-score when x=108 is 3.1034. The z-score tells you that x=108 is 3.1034 standard deviations to the left of the mean.

Z-score is used in statistics to compare a score to a normal distribution. The z-score is a measure of how far away from the mean a value is in standard deviation units.

To find the z-score when x = 108, we use the formula:

z = (x - μ) / σ

where x = 108, μ = 153, and σ = 14.5.

Substituting these values, we get:

z = (108 - 153) / 14.5 = -3.1034

So the z-score when x = 108 is -3.1034.

The z-score tells us how many standard deviations away from the mean a particular value is. In this case, since the z-score is negative, we know that x = 108 is to the left of the mean.

The absolute value of the z-score tells us how many standard deviations away from the mean the value is. In this case, the absolute value of the z-score is approximately 3.1034, which means that x = 108 is approximately 3.1034 standard deviations to the left of the mean.

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1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.

The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.

Given,

Distance = D

D= 1.4t

Rate= ?

Substituting the given values in the formula t= d/r

where,

t= time in seconds

d= distance

r= rate

We get,

t= 1.4t/r

t/1.4t= 1/r

t gets cancelled

so we have,

1/1.4= 1/r

r= 1.4m/s

Therefore, 1.4m/s is the rate at which Roberto is walking.

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The complete question is as follows:

Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.

What is the rate that Roberto's walking in meters per second?

In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500

To find the number of bicycles they would need to sell to make the same amount of money,

We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:

250 + 50x = 400 + 20x

30x = 150

x = 5

So they would need to sell 5 bicycles to make the same amount of money.

To find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.

Let's use Jim's equation:

250 + 50(5) = 500

So they would make $500 for selling 5 bicycles.

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In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Rosmaria runs 1.5 hours.

In the first week, Rosmaria ran 3 hours.

Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3

                                                             = 54

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A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].

Lower triangular matrices resemble the following:

[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]

We can write it like this:

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]

This demonstrates the set's

[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]

covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

leads to

[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

which results in a = b = c = 0 right away. As there is no other way to

[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]

, these matrices are linearly independent if a = b = c = 0.

Since

[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]

they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.

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Considering the Markov chain with transition matrix, the chain does have stationary distribution which exhibits State 1 is transient and the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729).

(a) Yes, the chain has a stationary distribution. To find it, we need to solve the system of equations π = πP, where π   is the vector of probabilities for each state and P is the transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 10/97

π_{2} = 30/97

π_{3}= 40/97

π_{4} = 14/97

π_{5}= 3/97

So the stationary distribution is (10/97, 30/97, 40/97, 14/97, 3/97).

(b) State 1 is transient, and all other states are recurrent.

(c) Yes, the chain still has a stationary distribution. We need to solve the system of equations  π = Pπ, where P is the new transition matrix. This gives us:

π_{1} = π(1/2)

π_{2} = π(1/3) + π(2/2)

π_{3}= π(2/4) + π(3/2)

π_{4} = π(3/5) + π(4/2)

π_{5}= π4/5

We also have the normalization condition π1 + π2 + π3 + π4 + π5 = 1.

Solving this system of equations, we get:

π_{1} = 2/9

π_{2}  = 4/9

π_{3} = 8/27

π_{4} = 16/81

π_{5}  = 32/729

So the stationary distribution is (2/9, 4/9, 8/27, 16/81, 32/729)

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Answer:

[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]

[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the circumference of this circle.}[/tex]

[tex]\textsf{Let's review what the Circumference of a circle actually is.}[/tex]

[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]

[tex]\textsf{The Circumference is is the length 'on' the circle.}[/tex]

[tex]\textsf{Circumference is the Perimeter of the Circle; The sum of all the curved edges.}[/tex]

[tex]\large\underline{\textsf{How do we find the Circumference?}}[/tex]

[tex]\textsf{To find the Circumference, we should use a common, and simple formula.}[/tex]

[tex]\mathtt{Circumference=(Diameter) \pi}[/tex]

[tex]\textsf{Pi will be multiplied by the Diameter of the Circle.}[/tex]

[tex]\textsf{Because we are given the Diameter, we can start solving for x.}[/tex]

[tex]\large\underline{\textsf{Substitute;}}[/tex]

[tex]\mathtt{Circumference \ (C)=(100 \ in.) \pi}[/tex]

[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]

[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]

Two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.

Given that a soup recipe calls for two teaspoons of salt. We need to find out how many milligrams of sodium is that?

1 teaspoon = 5.69 grams      1 gram = 1000 milligrams

2 teaspoons of salt = 2 * 5.69 grams = 11.38 grams of salt

11.38 grams of salt = 11.38 * 1000 milligrams = 11380 milligrams of salt

Now, we have to find out how much sodium (Na) is there in 11380 milligrams of salt. Sodium chloride is the chemical name for table salt (NaCl). So, the atomic mass of NaCl can be calculated as follows:

Na = 1Cl = 35.45

Atomic mass of NaCl = Na + Cl= 1 + 35.45= 36.45

So, 1 mole of NaCl = 36.45 grams         11380 milligrams of NaCl = 11380/1000 grams= 11.38/36.45 moles

Therefore, Moles of Na = 11.38/36.45 = 0.3121

mol Atomic mass of Na is 22.99 g/mol.

So, 1 mole of Na weighs = 0.3121 * 22.99= 7.16 grams

Therefore, 11380 milligrams of NaCl = 7.16 grams of Na. Hence, two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.

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